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 Ad or A, and the feedback circuit is composed of two resistors R1 and Rf. as shown in Figure 1.
Figure 1
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.
The closed loop voltage gain is given by
The product A and B is called loop gain. The gain loop gain is very large such that AB >> 1
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.
Physically, what is happening in the circuit? 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 Vd voltage to decrease. This almost completely offset the attempted increases in output voltage.
Similarly, if A decreases, The output voltage decreases. It reduces the feedback voltage Vf and hence, Vd voltage increases. Thus the output voltage increases almost to same level.
Different Input voltage is ideally zero
Again considering the voltage equation,
Vo = Ad Vd
or Vd = Vo / Ad
Since Ad is very large (ideally infinite).
Therefore; Vd ≈ 0.
and V1 = V2 (ideal).
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 Ad 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.
Input Resistance with Feedback
Figure 2, shows a voltage series feedback with the OP-AMP equivalent circuit.
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Figure 2
In this circuit Ri is the input resistance (open loop) of the OP-AMP and Rif is the input resistance of the feedback amplifier. The input resistance with feedback is defined as
Since AB is much larger than 1, which means that Rif is much larger that Ri. Thus Rif approaches infinity and therefore, this amplifier approximates an ideal voltage amplifier.
Output Resistance with Feedback
Output resistance is the resistance determined looking back into the feedback amplifier from the output terminal. To find output resistance with feedback Rf, input Vin is reduced to zero, an external voltage Vo is applied as shown in Figure 3.
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Figure 3
The output resistance (Rof) is defined as
This shows that the output resistance of the voltage series feedback amplifier is ( 1 / 1+AB ) times the output resistance Ro of the op-amp. It is very small because (1 + AB) is very large. It approaches to zero for an ideal voltage amplifier.
Reduced Non-linear Distortion
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 r'e 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.
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 .
Consider, under large signal conditions, the open loop OP-AMP circuit produces a distortion voltage, designated Vdist. It can be represented by connecting a source Vdist in series with Avd. Without negative feedback all the distortion voltage Vdist appears at the output. But with negative feedback, a fraction of Vdist 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.
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.
Bandwidth with Feedback
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 105 the bandwidth is approximately 5 Hz. On the other hand, the bandwidth is approximately 1 MHz when the gain is unity.
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Figure 4
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.
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.
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).
Bandwidth with feedback = (1+ A B) x (B.W. without feedback)
ff = fo (1+ AB)
Output Offset Voltage
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.
- Input offset voltage.
- Input bias voltage.
- Input offset current.
Figure 5, shows a feedback amplifier with an output offset voltage source in series with the open loop output Avd. 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.
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Figure 5
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.
Voltage Follower
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.
To obtain voltage follower, R1 is open circuited and Rf is shorted in a negative feedback amplifier of Figure 5. The resultant circuit is shown in Figure 6.
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Figure 6
Vout = AVd = A (V1 – V2)
V1 = Vin
V2 = Vout
V1 = V2 if A >> 1
Vout = Vin
The gain of the feedback circuit (B) is 1. Therefore
Af = 1 / B = 1
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