Voltage to Current Converter using OP-AMP

<div dir="ltr" style="text-align: left;" trbidi="on"> <div style="text-align: justify;"> <b><span style="color: red;"><u>Voltage to Current Converter with Floating Load</u></span></b></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> Figure 1, shows a voltage to current converter in which load resistor <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">L</span></sub> is floating (not connected to ground).</div> <div class="separator" style="clear: both; text-align: center;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgw92Yc-Q4ysboRjW67PXA5qlVN_reNbz-nBuO0jHZnK8RIt7ZxmFF4of-ZT9YWKDF0UhU98-4Crp_H0aVHVSkE_AaeSobE1egV3aSun6T1ODh42Gq0PopvhknDEL6uQnW7uueRlSMrDX5W/s1600/vtc.png" /></div> <div class="separator" style="clear: both; text-align: center;"> <b><i>Figure 1</i></b></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> The input voltage is applied to the non-inverting input terminal and the feedback voltage across R drives the inverting input terminal. This circuit is also called a current series negative feedback, amplifier because the feedback voltage across R depends on the output current <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">L</span></sub> and is in series with the input difference voltage <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">d</span></sub>.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> Writing the voltage equation for the input loop.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">d</span></sub> + <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> But vd » since A is very large,therefore,</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub></div> <div style="text-align: justify;"> <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub> = R <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub></div> <div style="text-align: justify;"> <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub> / R</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> and since input current is zero.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> <b><i><span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">L</span></sub> = <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub> = <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub> / R</i></b></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> The value of load resistance does not appear in this equation. Therefore, the output current is independent of the value of load resistance. Thus the input voltage is converted into current, the source must be capable of supplying this load current.<br /> <br /> <b><u><span style="color: red;">Voltage to Current Converter with Grounded Load</span></u></b><br /> <br /> If the load has to be grounded, then the above circuit cannot be used. The modified circuit is shown in Figure 2.<br /> <br /> <div class="separator" style="clear: both; text-align: center;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEit3q2sEv1KRtEbC7kOYB6e_cudwC1rdvLGaXcxb6pq0D-pDcGiZRSuxIS6MCLdKTX2Agi3kSWFgzKJthr3IZ-4PNBd9JzU7JuzUOgdas_Zbjn8jtRW5r6agHD0ohRpx-JuFZSgHtvM6Tnm/s1600/vtc1.png" /></div> <div class="separator" style="clear: both; text-align: center;"> <b><i>Figure 2</i></b></div> <br /> Since the collector and emitter currents are equal to a close approximation and the input impedance of OP-AMP is very high, the load current also flows through the feedback resistor R. On account of this, there is still current feedback, which means that the load current is stabilized.<br /> <br /> Since <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">d</span></sub> = 0<br /> Therefore; <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">2</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub><br /> Therefore <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">out</span></sub> = (<span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">CC</span></sub> – <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub>) / R<br /> <br /> Thus the load current becomes nearly equal to <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">out</span></sub>. There is a limit to the output current that the circuit can supply. The base current in the transistor equals <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">out</span></sub> / <span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">β</span>dc. Since the op-amp has to supply this base current <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">out</span></sub> / <span style="font-family: Calibri, sans-serif; font-size: 15px; line-height: 16.8666667938232px;">β</span>dc must be less than <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">I</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">out</span></sub> (max) of the op-amp, typically 10 to 15 mA.<br /> <br /> There is also a limit on the output voltage, as the load resistance increases, the load voltage increases and then the transistor goes into saturation. Since the emitter is at <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub> w.r.t. ground, the maximum load voltage is slightly less than <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub>.<br /> <br /> In this circuit, because of negative feedback <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">BE</span></sub> is automatically adjusted. For instance, if the load resistance decreases the load current tries to increase. This means that more voltage is feedback to the inverting input, which decreases <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">BE</span></sub> just enough to al­most completely nullify the attempted increase in load current. From the output current expression it is clear that as <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub> increases the load current decreases.<br /> <br /> Another circuit in which load current increases as <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub> increases is shown in Figure 3.<br /> <br /> <div class="separator" style="clear: both; text-align: center;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1BtZduxv1ZCSpE-zsacV5Q9EimgJ97GwTtF9S2jzInpUyRbSuMLYW3kuPepBzGyqcHEqenCDPMOG_La8tZf7bCTu-3BeXjMeyRcHqjwQuoUSCdang3vBSeNn__RQImNhZjebTxkAy6yog/s1600/figure3.jpg" /></div> <div class="separator" style="clear: both; text-align: center;"> <b><i>Figure 3</i></b></div> <br /> The current through the first transistor is<br /> <br /> i = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub> / R<br /> <br /> This current produces a collector voltage of <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">C</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">CC </span></sub>– i R = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">CC</span></sub> – <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub><br /> <br /> Since this voltage drives the non-inverting input of the second op-amp. The inverting voltage is <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">CC </span></sub>- <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub> to a close approximation. This implies that the voltage across the final R is<br /> <br /> <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">CC</span></sub> - (<span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">CC</span></sub> - <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub>) = vin<br /> <br /> and the output current .<br /> <br /> <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">out</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub> / R<br /> <br /> As before, this output current must satisfy the condition, that <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">out </span></sub>/ βdc must be less than the <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">out</span></sub>(max) of the OP-AMP. Furthermore, the load voltage cannot exceed <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">CC </span></sub>- <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub> because of transistor saturation, therefore <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">out</span></sub> R must be less than <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">CC</span></sub> - <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub>. This current source produces unidirectional load current. Figure 4, shows a Howland current source, that can produce a bi-directional load current.<br /> <br /> <div class="separator" style="clear: both; text-align: center;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj74BwiUq8wv2rRZdEKJRm6J6pEnKAjHGfs_B95H87YWhVwdxteByph1UsBoIpXyMLM44gIhRSxcgP6F3p5h5NvLtp7-6ickwtKz2T1HfO4-U9mBsgutXdSOYUYw5RGo-XiWGXF79W0hoCE/s1600/figure4.jpg" /></div> <div class="separator" style="clear: both; text-align: center;"> <b><i>Figure 4</i></b></div> <br /> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMj3B2yh9jnJrLlv6hkUbUu1erl25G1PGeconPaFuwIYOtka9tvLc0w86K7MUoIukrtBhrkQixbiwEdUjFdBV_FqauutwSE5vE3Ctq7djgai_-XRnxBpORvsFxFBq63drZ5emInKEKKUKk/s1600/equation1.png" /></div> <br /> The maximum load current is <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">CC</span></sub> / R. In this circuit <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub> in may be positive or negative.</div> </div>

Voltage to Current Converter using OP-AMP

Voltage to Current Converter with Floating Load Figure 1, shows a voltage to current converter in which load resistor  R L  is floatin...

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Differentiator using OP-AMP

<div dir="ltr" style="text-align: left;" trbidi="on"> <div style="text-align: justify;"> The differentiation or differentiator circuit performs the mathematical operation of differentiation; that is, the output waveform is the derivative of the input waveform. A circuit in which the output voltage waveform is the differentiation of input voltage is called differentiator as shown in Figure 1.</div> <div style="text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: center;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5fweh5Xua7CauXME13RDBxYACw4brVwwgGRY5OitgB9p7FW_hJacNYZzoFzPrzjk32Ic9UQF1L_zweB6SDRuxNqaUPSQ5wA5HWTBEz2xBEYiBNXl3en-xrBR6weuV5-UlK7HQZV6-62fN/s1600/diffrentiator.png" /></div> <div class="separator" style="clear: both; text-align: center;"> <b><i>Figure 1</i></b></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> The expression for the output voltage can be obtained from the Kirchoff's current equation written at node <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">2</span></sub>.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> Thus the output <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o</span></sub> is equal to the RC times the negative instantaneous rate of change of the input voltage <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub> with time. A cosine wave input produces sine output. Figure 1 also shows the output waveform for different input voltages.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> The input signal will be differentiated properly if the time period T of the input signal is larger than or equal to <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub><span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">C</span>.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> T <span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 115%; text-align: left;">≥</span> <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub><span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">C</span></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> As the frequency changes, the gain changes. Also at higher frequencies the circuit is highly susceptible at high frequency noise and noise gets amplified. Both the high frequency noise and problem can be corrected by adding few components. as shown in figure 2.</div> <div style="text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: center;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTMrUxrU73larvsBkPdjX3AnfvamoPI2jDxK0HvrNv10rYNODeOcoZ1CaNadtsxLuH_a36BNZdOiRcsGsqPNfwt9saoZ2mvE1ZkVc1FgpuEIl9eFj7afYAl437nNNoSgPRObXgMrePOOO3/s1600/diffrentiator2.png" /></div> <div class="separator" style="clear: both; text-align: center;"> <b><i>Figure 2</i></b></div> </div>

Differentiator using OP-AMP

The differentiation or differentiator circuit performs the mathematical operation of differentiation; that is, the output waveform is the ...

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Integrator using OP-AMP

<div dir="ltr" style="text-align: left;" trbidi="on"> <div style="text-align: justify;"> A circuit in which the output voltage waveform is the integral of the input voltage waveform is called integrator. Figure 1, shows an integrator circuit using OP-AMP.</div> <div style="text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: center;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWW4Gugv7NlbDUG_hjpkCKoohdow8zJ-o8IG4YoK8YQppwNMMkhb2ubr1ke-ZdH1r94F7vu8StXfwKDC8E5lNXcs2LYEzh48D03EnKRLcsjPvNdPKIpx5xn4YNWy1FMiE0t1epgJKRBIaX/s1600/op-amp9.png" /></div> <div class="separator" style="clear: both; text-align: center;"> <b><i>Figure 1</i></b></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> Here, the feedback element is a capacitor. The current drawn by OP-AMP is zero and also the <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">2</span></sub> is virtually grounded.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> Therefore, <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub> and <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">2</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub> = 0</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8szYP12BWNki1n3Z0yuZeIkNHyYbr5BkHBgCqLp_w4c0evt635R-Elui4AJLWmTjCP7hyy4cq3qwjuWaDcagE22NyfI68wZ-n5wYO70NzgQk74qMCcbf_X1UCIU7JZXz4vG9Nap99uwj2/s1600/op-amp10.png" /></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> Integrating both sides with respect to time from 0 to t, we get</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8dCuRuPu-UUhTvn0JgjkkQGMPDmDPXoj1uUjHr947SuSgrYQuX7mIotimYPVBEWgt5jv_NtTm5yoINkt96yVCbBXiAKkojvnEcqNY9rLnE5MWjHfelOE7KNtXL4fuWJsVPVM00-mvbDfI/s1600/op-amp11.png" /></div> <div class="separator" style="clear: both; text-align: left;"> <br /></div> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhX4TtrrP0Tufj8xEOI_R4oGC9uV17fBzJGd1MZ17E7iJ0NerEMznVwtlcDkRHYgWgHg96KafZeVB-7_e7QKIfgN0M5kdhAVJHtDcFF9u7X4I00hXxu-wUmt80_XKqHzbWb56vpnD905cPU/s1600/op-amp12.png" /></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> The output voltage is directly proportional to the negative integral of the input voltage and inversely proportional to the time constant RC.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> If the input is a sine wave the output will be cosine wave. If the input is a square wave, the output will be a triangu­lar wave. For accurate integration, the time period of the input signal T must be longer than or equal to RC.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> Figure 2, shows the output of integrator for square and sinusoidal inputs.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: center;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEis6KkF0qq24f9fJB-AGEb8M1h3Q8An66koxy6xd6mM1J9nYunW8-WgtpGBMgcLn4BV2dJRdlicC8wnu1z2adYcxM_vIG83iniFZ-foQwjhtEUjKrVnbmB3WfdlkOfIIsS3WXWM4oaez1BN/s1600/op-amp13.png" /></div> <div class="separator" style="clear: both; text-align: center;"> <b><i>Figure 2</i></b></div> </div>

Integrator using OP-AMP

A circuit in which the output voltage waveform is the integral of the input voltage waveform is called integrator. Figure 1, shows an inte...

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Summing, Scaling and Averaging Amplifiers

<div dir="ltr" style="text-align: left;" trbidi="on"> <div style="text-align: justify;"> This article shows how the inverting, noninverting, and differential configurations are useful in such applications as summing, scaling,  and averaging amplifiers.<br /> <br /> <b><u><span style="color: red;">Analog Inverter and Scale Changer</span></u></b></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> The circuit of analog inverter is shown in Figure 1. It is same as inverting voltage amplifier.</div> <div style="text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: center;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixE_4mGeiFEdjhmm4poBnCLT7R8M4iGqHttc7bMQ-sn6kbMfdHcg5xXsz-t1PWL67njxNssLW8u3sMnOul_H0JqGnSHuSZyThKdXb15OBDppThcMpuPbjDAFoux1zUWdbPxHsvfbbswIIY/s1600/op-amp.png" /></div> <div class="separator" style="clear: both; text-align: center;"> <b><i>Figure 1</i></b></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> Assuming OP-AMP to be an ideal one, the differential input voltage is zero.</div> <div style="text-align: justify;"> i.e. <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">d</span></sub> = 0 </div> <div style="text-align: justify;"> Therefore, <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">2</span></sub> = 0</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> Since input impedance is very high, therefore, input current is zero. OP-AMP do not sink any current.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> Therefore; <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in </span></sub>= <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub></div> <div style="text-align: justify;"> <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub> / R = - <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o</span></sub> / <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub></div> <div style="text-align: justify;"> <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o</span></sub> = - (<span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub> / R) <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> If R = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub> then <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o</span></sub> = - <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub>, the circuit behaves like an inverter.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> If <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub> / R = K (a constant) then the circuit is called inverting amplifier or scale changer voltages.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> <b><span style="color: red;"><u>Inverting Summer</u></span></b></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> The configuration is shown in Figure 2. With three input voltages <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">a</span></sub>, <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">b</span></sub> & <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">c</span></sub>. Depending upon the value of <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub> and the input resistors <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">a</span></sub>, <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">b</span></sub>, <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">c</span></sub> the circuit can be used as a summing amplifier, scaling amplifier, or averaging amplifier.</div> <div style="text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: center;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVLPzxRly5gQPWkMRh6D1eeIGGJvlbLW3fAB3hQihBoxSZqzRIX_7X0luy1dXoszSVdErYCG3x4g4aqcHU15Bdmxxqbmmd_2l_J90-MubklZe5fTK4pOdls-OnDwxDCbQly3hnyPDqDccQ/s1600/op-amp3.png" /></div> <div class="separator" style="clear: both; text-align: center;"> <b><i>Figure 2</i></b></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> Again, for an ideal OP-AMP, <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">2</span></sub>. The current drawn by OP-AMP is zero. Thus, applying KCL at <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">2</span></sub> node</div> <div style="text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoD2UQxLxZM0ELmtnDdXeZU5zaQhHW_mpCCvR-_hPYlfthbzLOvcbPTt1eOjjHxa75diIZ2EKlY4ymlTNLQnddI3UIYBAhMmFo4kUnnIH05omNnaNHtas8nt52KAA-V9XoMjXQi_9FEM0e/s1600/op-amp1.png" /></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> This means that the output voltage is equal to the negative sum of all the inputs times the gain of the circuit <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f </span></sub>/ R; hence the circuit is called a summing amplifier. When <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub> = R then the output voltage is equal to the negative sum of all inputs.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o</span></sub> = -(<span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">a </span></sub>+ <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">b </span></sub>+ <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">c</span></sub>)</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> If each input voltage is amplified by a different factor in other words weighted differently at the output, the circuit is called then scaling amplifier.</div> <div style="text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnw8MwNULWIDcwLWogDuc_sPeCOf9aPcuvSPtOQbAv7j73tAw1S59miYpvABiV8BNyro3IBB9uW-LHj5r22t_cuUzfVAsqsPoCmrFOACOeMS7JP_yOE8gULodNAj3lh9SbKRg_Julh3aNS/s1600/op-amp2.png" /></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> The circuit can be used as an averaging circuit, in which the output voltage is equal to the average of all the input voltages.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> In this case, <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">a</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">b</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">c</span></sub> = R and <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub> / R = 1 / n, where n is the number of inputs. Here; <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub> / R = 1 / 3.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o</span></sub> = -(<span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">a </span></sub>+ <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">b</span></sub> + <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">c</span></sub>) / 3</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> In all these applications input could be either ac or dc.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> <b><u><span style="color: red;">Non-Inverting Configuration</span></u></b></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> If the input voltages are connected to non-inverting input through resistors, then the circuit can be used as a summing or averaging amplifier through proper selection of <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub>, <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">2</span></sub>, <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">3</span></sub> and <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub> as shown in Figure 3.</div> <div style="text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: center;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_-36SX2jsDZPLK6FwDcSHwTYJpkoK5w2AF8dlvgQ_gjhBBZJUImkC6OP6EBh9rneBrkzKyz-ayzgWFRWuTsxCAxaCUBd2bX-pYZh-W2lHK4Nltad0k2ee4hDe3YStQ17b448JtLcRqjxq/s1600/op-amp6.png" /></div> <div class="separator" style="clear: both; text-align: center;"> <b><i>Figure 3</i></b></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> To find the output voltage expression, <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub> is required. Applying superposition theorem, the voltage <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub> at the non-inverting terminal is given by</div> <div style="text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4v1o8G_GgenyAge4hvsxspHmyW4f_9GL8kG3-IB-DKpsnFO2aqiMQGQvJxhF_sftmpiAtMWeD0xYKnJitHKb7-FIbOttgdJIC9yQprUdjYphz6NIGDfiLacSHff14v7SHpRpPmC2aZV2e/s1600/op-amp4.png" /></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> Hence the output voltage is</div> <div style="text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxNtEtEhcE4DWCRlJNepPXsgoM80JaiDN8tvL6X6DyfyPioOYgPe5EdZarqMYt2hybDJdhMYyVomLULKsgcXphrwGrArq3j7Jlh8qPaEGhxV4u-PzjhD3SjTlaFlrJz-XiYRTGW5-YVddZ/s1600/op-amp5.png" /></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> This shows that the output is equal to the average of all input voltages times the gain of the circuit (1 + <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub> / <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub>), hence the name averaging amplifier.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> If (1 + <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f </span></sub>/ <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub>) is made equal to 3 then the output voltage becomes sum of all three input voltages.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">a</span></sub> + <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">b </span></sub>+ <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">c</span></sub></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> Hence, the circuit is called summing amplifier.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> <b><span style="color: red;"><u>Differential Amplifier</u></span></b><br /> <br /> The basic differential amplifier is shown in Figure 4.<br /> <br /> <div class="separator" style="clear: both; text-align: center;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFBl48Kp_GfqGZX3nS60nWaZzlgh8UA0QRzghyphenhyphenM1NftJiZVLAEt4RtOxocXYBvhNFEU9LzAJB7VIPNyU8hYiMS0jsbVJL4Gp7C9ictGUTtn_mJPHPquwAX3co2_hPSfLsy0A-3MKC-b4uY/s1600/op-amp7.png" /></div> <div class="separator" style="clear: both; text-align: center;"> <b><i>Figure 4</i></b></div> <br /> Since there are two inputs superposition theorem can be used to find the output voltage. When <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">b </span></sub>= 0, then the circuit becomes inverting amplifier, hence the output due to <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">a</span></sub> only is<br /> <br /> <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o</span></sub>(a) = -(<span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub> / <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub>) <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">a</span></sub><br /> <br /> Similarly when, Va = 0, the configuration is a inverting amplifier having a voltage divided network at the non-inverting input<br /> <br /> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhH1OAWO_-53eP1Wx9CEnYPKkH7icgPv_z1565CtP2gC0_XhOCodPA-PICP0dFO3j1LMPGUGGvoL9Ed4kr4rlRzTnmOl4maITVIrHgxIOMInjgshXxBVtINpwkggNbWRBIO_GcEsVybYPBh/s1600/op-amp8.png" /></div> </div> </div>

Summing, Scaling and Averaging Amplifiers

This article shows how the inverting, noninverting, and differential configurations are useful in such applications as summing, scaling,  ...

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Voltage Shunt Feedback Amplifier

<div dir="ltr" style="text-align: left;" trbidi="on"> <div style="text-align: justify;"> Figure 1, shows the voltage shunt feedback amplifier using OP-AMP.</div> <div style="text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: center;"> </div> <div class="separator" style="clear: both; text-align: center;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi06YFFnsjc92Uxow6VVTjGtTNsF8vpnlHcu8Z4EPdbZO4MekCpGf5gX3CY0-Jlg-b4kUL1FJNqxa-7lNstc1X5rUnAg_AOTfv8J6FqOFxv2U2P2tvKfXKqEAMu99AxR34D-hJmuXU5-nKL/s1600/dia1.jpg" /></div> <div class="separator" style="clear: both; text-align: center;"> <b><i>Figure 1</i></b></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> The input voltage drives the inverting terminal, and the amplified as well as inverted output signal is also applied to the inverting input via the feedback resistor <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub>. This arrangement forms a negative feedback because any increase in the output signal results in a feedback signal into the inverting input signal causing a decrease in the output signal. The non-inverting terminal is grounded. Resistor <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub> is connected in series with the source.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> The closed loop voltage gain can be obtained by, writing Kirchoff's current equation at the input node <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">2</span></sub>.</div> <div style="text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjx2QKmGAZ_Y7JM2cPSVAyukZJu9Az5iGOBVG4w1AoTuX59ZDjp-Qm_FlYNDvguxGvSHvLXrVSZJZAuihgcNTS3aZ5xQkrK7Vm6_tbUYpxXEN9Twd9PtVuyNFdV9LOVZ2oDN9eA2jDMYXId/s1600/dia2.png" /></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> The negative sign in equation indicates that the input and output signals are out of phase by 180. Therefore it is called inverting amplifier. The gain can be selected by selecting <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub> and <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub> (even < 1).</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> <b><span style="color: red;">Inverting Input at Virtual Ground</span></b></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> In the Figure 1, shown earlier, the non-inverting terminal is grounded and the- input signal is applied to the inverting terminal via resistor <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub>. The difference input voltage <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">d</span></sub> is ideally zero, (<span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">d</span></sub> = <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o</span></sub>/ A) is the voltage at the inverting terminals (<span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">2</span></sub>) is approximately equal to that of the non-inverting terminal (<span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub>). In other words, the inverting terminal voltage (<span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub>) is approximately at ground potential. Therefore, it is said to be at virtual ground.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSMb5P3CADe8s8Mi2IqkDNHP0AlYc6-UL-AJY-n92GEep-t-58xGQJzASeEZeudnxod10InqV2kNfCOxo485JYtzGWRVoRPP2Y86um4zO0RfcsAi8FflFqXKuQMyVHf6h66WX_W82HX9W3/s1600/dia3.png" /></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> <b><span style="color: red;">Input Resistance with Feedback</span></b></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> To find the input resistance Miller equivalent of the feedback resistor <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub>, is obtained, i.e. <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub> is splitted into its two Miller components as shown in Figure 2.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: center;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghOwR_ej24Hd1OzFrEmsitb5n1IeVR6qQbmiwF63eHRpSTLb6mYxGhIjZ2P-MRgpLFO5LO9todo7WAfwJg91hiqGlZ9Xh-yojhag7hsVrtomvKlD_1TA09OuUREXopVLjMOV1mKkEiXdMf/s1600/dia4.jpg" /></div> <div class="separator" style="clear: both; text-align: center;"> <b><i>Figure 2</i></b></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> Therefore, input resistance with feedback <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">if</span></sub> is then</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiO2-Z9pDUmEcN5hjwTIHjmcaho7QALv652XqqsRQCF-kRueiLfL1rwedtC_VnD-SaFTMY59eDLux40Gr-11oT0T3w8NHZueqZra8T2awt7Q0j5i0I4RiLjJXWfdPXcr6DMyvmA7_UONgpb/s1600/dia5.jpg" /></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> <b><span style="color: red;">Output Resistance with Feedback</span></b></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> The output resistance with feedback <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">of</span></sub> is the resistance measured at the output terminal of the feedback amplifier. The output resistance can be obtained using Thevenin's equivalent circuit,shown in Figure 3.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: center;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2iUFaP3bMd0X6zRkbHVNc6_wJmLQZF5-KXtWrYh8phjPS7-JGwF6D5mGK2IUEkOZMFj1nzXLj6LZvMfaeiiFQ4tlSygekGL8syVb1thl1qEMLcu82eezGiEiiFtpI7r1b8X6UQLfaaG1g/s1600/dia6.jpg" /></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> <b><i><span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">a</span></sub> + <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">b</span></sub></i></b></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> Since <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o</span></sub> is very small as compared to <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub> + (<span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub> || <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">2</span></sub>)</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> Therefore, i.e. <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o </span></sub>= <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">a</span></sub></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o</span></sub> <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">i</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o</span></sub> + A<span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">d</span></sub></div> <div class="separator" style="clear: both; text-align: justify;"> <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">d </span></sub>= <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub> – <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">2</span></sub> = 0 - B<span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o</span></sub></div> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZRLM4jaXG8GTsm5oCpqTL-KCCt_UD64MF0TDrV1_ptMJpHx7Q3bSOpjhCAyoyaNCI5ZrS049_HyAiiX2DxCYgSFCn2sCSCNSm6J8khA6TynSeZauFc3stIQLOPM_WrU_zPo8paLPcsv5b/s1600/dia7.jpg" /></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> Similarly, the bandwidth increases by (1+AB) and total output offset voltage reduces by (1+AB).</div> </div>

Voltage Shunt Feedback Amplifier

Figure 1, shows the voltage shunt feedback amplifier using OP-AMP. Figure 1 The input voltage drives the inverting terminal, a...

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Voltage Series Feedback Amplifier

<div dir="ltr" style="text-align: left;" trbidi="on"> <div style="text-align: justify;"> It is also called non-inverting voltage feedback circuit. With this type of feedback, the input signal drives the non-inverting input of an amplifier; a fraction of the output voltage is then fed back to the inverting input. The op-amp is represented by its symbol including its large signal voltage gain <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">A</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">d</span></sub> or A, and the feedback circuit is composed of two resistors <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub> and <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub>. as shown in Figure 1.</div> <div style="text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: center;"> <img border="0" height="234" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgS52yDHOFc8RnmrXx5QO-UJ1yn22GCrjyDCy2YLd-K-FuAVkUvVRkO-V8Ya4513y5NeWfdNfALCwQNZn9WvbaDVsPfkjoOigoqjTP7ra_IX1SIS98Hwm-007tzqJ4uUwMqtnWcVZJSV5bD/s1600/fig5.jpg" width="640" /></div> <div class="separator" style="clear: both; text-align: center;"> <b><i>Figure 1</i></b></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmeLgyRY7sTQxSSJBWoghyphenhyphenOdf6q1oIbmOsKtQx4_c3qWaYniBanGQuVg7fB9IpiytGojwMabst8Rk8t0k9h4_3ErwrSrpTqOrRFXfumAKeZXx6aiBWj1R4Zh2J8t1yiDwiRtEYUZh82yKb/s1600/equ10.png" /></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> The feedback voltage always opposes the input voltage, (or is out of phase by 180° with respect to input voltage), hence the feedback is said to be negative.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> The closed loop voltage gain is given by</div> <div style="text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjioqrTopQdm46eF41gZefMuTjzaPZq0FL2yHPcfdrlG7XM6xzHP7A5D8bv7zYGQ3gD59yQWohQ2Vvmkw185N8NwDoVJ3B0gpfdwwFAm_VaWfocu4XU3gc9-50jyboO_mLjxV2zLI0ABl-/s1600/equ20.png" /></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> The product A and B is called loop gain. The gain loop gain is very large such that AB >> 1</div> <div style="text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPRHqI-ZTkpvMtCOlHOkmV0v2wmCIu0gFXuBMFg5yfAsZR6sMjeZ951oAK9A2EB-kqQk3CboqqIPGPV1SAMld9uYVKFhiIb8WHXgVyT_66tqrZAuuyZ3xYNLNPAgbYD7W-r5H2oEJAz0p2/s1600/equ40.png" /></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> This shows that overall voltage gain of the circuit equals the reciprocal of B, the feedback gain. It means that closed loop gain is no longer dependent on the gain of the op-amp, but depends on the feedback of the voltage divider. The feedback gain B can be precisely controlled and it is independent of the amplifier.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> <u>Physically, what is happening in the circuit</u>? The gain is approximately constant, even though differential voltage gain may change. Suppose A increases for some reasons (temperature change). Then the output voltage will try to increase. This means that more voltage is fedback to the inverting input, causing <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">d</span></sub> voltage to decrease. This almost completely offset the attempted increases in output voltage.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> Similarly, if A decreases, The output voltage decreases. It reduces the feedback voltage <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub> and hence, <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">d</span></sub> voltage increases. Thus the output voltage increases almost to same level.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> <b><u><span style="color: red;">Different Input voltage is ideally zero</span></u></b></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> Again considering the voltage equation,</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;">            <b><i><span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">A</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">d</span></sub> <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">d</span></sub></i></b></div> <div style="text-align: justify;">  or       <b><i><span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">d</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o</span></sub> / <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">A</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">d</span></sub></i></b></div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> Since <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">A</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">d</span></sub> is very large (ideally infinite).</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> Therefore; <b><i><span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">d</span></sub> <span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">≈</span> 0</i></b>.</div> <div style="text-align: justify;"> and    <b><i><span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">2</span></sub> (ideal)</i></b>.</div> <div style="text-align: justify;"> <br /></div> <div style="text-align: justify;"> This says, that the voltage at non-inverting input terminal of an op-amp is approximately equal to that at the inverting input terminal provided that <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">A</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">d</span></sub> is very large. This concept is useful in the analysis of closed loop OP-AMP circuits. For example, ideal closed loop voltage again can be obtained using the results.</div> <div style="text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyTZezuvdRKtBonN6hhiL_Zo6aPih5iBEeB6BX_icfk8KiuG1T0rXMG8QK8DCnjHz5kVh1OJvbOBLOfFnrP-cH06fd9EeU4troV9VL93FExGe6qgzRdPGyb3KMKv1maMAyFE3o1Ses9yHi/s1600/equ30.png" /></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> <b><u><span style="color: red;">Input Resistance with Feedback</span></u></b></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> Figure 2, shows a voltage series feedback with the OP-AMP equivalent circuit.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: center;"> <img border="0" height="235" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnUMlcYiu94cJNci3orw-DxHQy6RUl4_6cqgA1QK6IcB8h5r1wHiEwJJHwtqKMtBmbu0_RgePu4_XOBRV6RnJ4dyWeHcLkT-wr9gHrwVf3uPVHKeKF0uZvJ5W3qBsQct6iQLL2SqX7nqIh/s1600/fig1+(1).jpg" width="320" /></div> <div class="separator" style="clear: both; text-align: center;"> <b><i>Figure 2</i></b></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> In this circuit <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">i</span></sub> is the input resistance (open loop) of the OP-AMP and <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">if</span></sub> is the input resistance of the feedback amplifier. The input resistance with feedback is defined as</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmwS4sFOOANBJdpwuXwSyJ5ZWAPtkxzbuYD3krF5-iPOP-rqnOb6CT1Z8J5OwwkSs6vD7095M7L8_GPclJ0P_u9ytsct-lJrTrh7dFkqzKBv0dLpNsHBBk5C0o-gOqG60BVhXRHlkcAxqO/s1600/equ100.png" /></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> Since AB is much larger than 1, which means that <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">if</span></sub> is much larger that <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">i</span></sub>. Thus <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">if</span></sub> approaches infinity and therefore, this amplifier approximates an ideal voltage amplifier.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> <b><u><span style="color: red;">Output Resistance with Feedback</span></u></b></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> Output resistance is the resistance determined looking back into the feedback amplifier from the output terminal. To find output resistance with feedback <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub>, input <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub> is reduced to zero, an external voltage <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o</span></sub> is applied as shown in Figure 3.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: center;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVBQsQra83FRR4H4FQSxAJ77WrAn7N6IEPqlMhBgb7S7o-1u9ca_gjRFZzJdaaUYEfQoFSt3sSvzMtXnvjhk8GZMdWdx3m19lbxEX3uw0747QNHuVmBt7iHTJjOp_mtl4YmygqWHinIJc3/s1600/fig2+(1).jpg" /></div> <div class="separator" style="clear: both; text-align: center;"> <b><i>Figure 3</i></b></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> The output resistance (<span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">of</span></sub>) is defined as</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9lk5lKNCNsdjpwlEAANmsWmQeMUAhEnO0e57PBzrFngjNR1o3vXxK11osrkjiDXAJLQyLNl9OJI0Kgbl6T5c-R1Vl4Dy89zLO09JHfvCcDTE-KiWnz44rfiay1TIPnvV8QNEEGRvFTAsI/s1600/equ200.png" /></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> This shows that the output resistance of the voltage series feedback amplifier is ( 1 / 1+AB ) times the output resistance <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o</span></sub> of the op-amp. It is very small because (1 + AB) is very large. It approaches to zero for an ideal voltage amplifier.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> <b><u><span style="color: red;">Reduced Non-linear Distortion</span></u></b></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> The final stage of an OP-AMP has non-linear distortion when the signal swings over most of the ac load line. Large swings in current cause the <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">r'</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">e</span></sub> of a transistor to change during the cycle. In other words, the open loop gain varies throughout the cycle of when a large signal is being applied. It is this changing voltage gain that is a source of the non-linear distortion.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> Non-inverting voltage feedback reduces non-linear distortion because the feedback stabilizes the closed loop voltage gain, making it almost independent of the changes in open loop voltage gain. As long as loop gain, is much greater than 1, the output voltage equals 1/B times the input voltage. This implies that output will be a more faithful reproduction of the input .</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> Consider, under large signal conditions, the open loop OP-AMP circuit produces a distortion voltage, designated <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">dist</span></sub>. It can be represented by connecting a source <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">dist</span></sub> in series with Avd. Without negative feedback all the distortion voltage <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">dist</span></sub> appears at the output. But with negative feedback, a fraction of <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">dist</span></sub> is feedback to inverting input. This is amplified and arrives at the output with inverted phase almost completely canceling the original distortion produced by the output stage.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhk_e1_b05HJcjy6zZGpNUCJ-00uBlsB4SaSIABq5a8J6H9DWhEbrcaQZ49tl3M3jFWAhtVMmC6N4T9gDDq_ThnS1C-He-ykAjtuDzGrgYY8dzJ2JVAtSK1loY-bQa-Mokt2LTuSQ9l20-8/s1600/equ300.png" /></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> The first term is the amplified output voltage. The second term in the distortion that appears at the final output. The distortion voltage is very much, reduced because AB>>1.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> <b><u><span style="color: red;">Bandwidth with Feedback</span></u></b></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> The bandwidth of an amplifier is defined as the band of frequencies for which the gain remains constant. Figure 4, shows the open loop gain vs frequency curve of 741C OP-AMP. From this curve for a gain of 2 x <span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">10⁵</span> the bandwidth is approximately 5 Hz. On the other hand, the bandwidth is approximately 1 MHz when the gain is unity.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: center;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGST9W3-yjMWoeBG4u45Au4TNPf-qSKBZGRr7AwNGBaGlGmrS_vl4jyiaSFmeFiknIVEtK7DPH_HSgcJh7_XVd0emo1L3spN6VFFNLgi9UCQn4S4PVjNFo4sIE5VphdsZZmIigZFo2F8ds/s1600/fig3+(1).jpg" /></div> <div class="separator" style="clear: both; text-align: center;"> <b><i>Figure 4</i></b></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> The frequency at which gain equals 1 is known as the unity gain bandwidth. It is the maximum frequency the OP-AMP can be used for.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> Furthermore, the gain bandwidth product obtained from the open loop gain vs frequency curve is equal to the unity gain bandwidth of the OP-AMP.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> Since the gain bandwidth product is constant obviously the higher the gain the smaller the bandwidth and vice versa. If negative feedback is used gain decrease from A to A / (1+AB). Therefore the closed loop bandwidth increases by (1+AB).</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> Bandwidth with feedback = (1+ A B) x (B.W. without feedback)</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">f</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub> = <span style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">f</span><sub style="background-color: white; color: #333333; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">o</span></sub> (1+ AB)</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> <b><u><span style="color: red;">Output Offset Voltage</span></u></b></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> In an OP-AMP even if the input voltage is zero an output voltage can exist. There are three cause of this unwanted offset voltage.</div> <div class="separator" style="clear: both; text-align: justify;"> </div> <ol> <li>Input offset voltage.</li> <li>Input bias voltage.</li> <li>Input offset current.</li> </ol> <br /> <div class="separator" style="clear: both; text-align: justify;"> Figure 5, shows a feedback amplifier with an output offset voltage source in series with the open loop output <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">A</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">vd</span></sub>. The actual output offset voltage with negative feedback is smaller. The reasoning is similar to that given for distortion. Some of the output offset voltage is fed back to the inverting input. After amplification an out of phase voltage arrives at the output canceling most of the original output offset voltage.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: center;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxxGxaDg_b0eCjezN3zakrcb4p5vNaIJpdQ2znR1m_OfVnw95utd8ORLLc9I24mpRF3V6KcwfZySzw9Z6XzbcLRgu8NtEVtKT11FKave8S6tVRs8TDOw3UFBMlPuc2XwDusD0IpgVviB19/s1600/fig4+(1).jpg" /></div> <div class="separator" style="clear: both; text-align: center;"> <b><i>Figure 5</i></b></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: left;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWhlcDn2pY5KnxR2eOR0kzUxZ-6mNSr8nzpv8j0-fYW2PghvA0z7Wpk25QUIKf5d5xNpC_Odgofcw_GbcBCmX-UdU06RLIYdGBHKG4B20cxLcKekFMsUbveESavEVDjJnjhS9jiJLt8n9m/s1600/equation4.png" /></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> When loop gain AB is much greater than 1, the closed loop output offset voltage is much smaller than the open loop output offset voltage.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> <b><u><span style="color: red;">Voltage Follower</span></u></b></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> The lowest gain that can be obtained from a non-inverting amplifier with feedback is 1. When the non-inverting amplifier gives unity gain, it is called voltage follower because the output voltage is equal to the input voltage and in phase with the input voltage. In other words the output voltage follows the input voltage.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> To obtain voltage follower, <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub> is open circuited and <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">R</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub> is shorted in a negative feedback amplifier of Figure 5. The resultant circuit is shown in Figure 6.</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: center;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAhWGU-Iwgio9sDQEwVcfVS_2XxgSxRjpqs4YhXQ52MYOrY__yBoKTAPK9ufyILkQ0lJ23bUXNO1apYhLqu4nolDpNJdkX9wLXSrLc-CJjg95auSCE2UsodPim6ztQT7iDE5y7jp7kb8JI/s1600/fig5+(1).jpg" /></div> <div class="separator" style="clear: both; text-align: center;"> <b><i>Figure 6</i></b></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> <b><i><span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">out</span></sub> = A<span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">d </span></sub>= A (<span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub> – <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">2</span></sub>)</i></b></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub></div> <div class="separator" style="clear: both; text-align: justify;"> <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">2</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">out</span></sub></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> <b><i><span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">1</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">2</span></sub> if A >> 1</i></b></div> <div class="separator" style="clear: both; text-align: justify;"> <b><i><span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">out</span></sub> = <span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">V</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">in</span></sub></i></b></div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> The gain of the feedback circuit (B) is 1. Therefore</div> <div class="separator" style="clear: both; text-align: justify;"> <br /></div> <div class="separator" style="clear: both; text-align: justify;"> <b><i><span style="background-color: white; font-family: Verdana, Geneva, sans-serif; font-size: 14px; line-height: 22.3999996185303px;">A</span><sub style="background-color: white; font-family: Verdana, Geneva, sans-serif; line-height: 22.3999996185303px;"><span style="font-family: 'Times New Roman', serif; font-size: 10pt; line-height: 15.3333320617676px;">f</span></sub> = 1 / B = 1</i></b></div> </div>

Voltage Series Feedback Amplifier

It is also called non-inverting voltage feedback circuit. With this type of feedback, the input signal drives the non-inverting input of a...

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