ECEstream: Networks

AC Fundamentals

<div dir="ltr" style="text-align: left;" trbidi="on">
<div dir="ltr" style="text-align: left;" trbidi="on">
<div dir="ltr" style="text-align: left;" trbidi="on">
<div style="text-align: justify;">
The ac fundamentals are necessary for analyzing the electrical networks.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b><i><u>Alternating waveform:</u></i></b></div>
<div style="text-align: justify;">
</div>
<ul>
<li>The alternating quantity such as voltage, current, power etc can take any shape such as triangular, square, sine etc.</li>
<li>But the most popular shape is sine wave as shown in figure below:</li>
</ul>
<br />
<div class="separator" style="clear: both; text-align: center;">
<img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9YZwEXnaL5Kd8S4v6Uj6T_xs1BW3Jb8-balB3q3i0h3PNq8kVxv7Oo32CittQbjyxqVbjdLDDPFbnIU6qDD1A3hqNr_wvkuNapFtxhNTEmHPjO77TDBkDNSvrvNHtyuZCVa3dXU7fdvcc/s1600/sinewave.png" /></div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<hr />
<div class="separator" style="clear: both; text-align: justify;">
<b><i><u>Some Definitions Related to Alternating Quantities:</u></i></b></div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
<b>Instantaneous Value:</b></div>
<div class="separator" style="clear: both; text-align: justify;">
</div>
<ul>
<li>The instantaneous value of an AC quantity is defined as the value of that quantity at a particular instant of time.</li>
<li>For example in Figure A, V(t1) is the instantaneous value of the ac voltage at t1 or V(t2) is its instantaneous value at t2.</li>
</ul>
<br />
<div class="separator" style="clear: both; text-align: center;">
<img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqRrPqhJsuku3SXz0ryoO24cuDNNMkomxNsIfLy8_rv6xgDO0ukBFB4dPzo5ow4POknp0574EFfGeHYDrYWyP207NR89Lv7HTxOxaBzgmSvZPQ6TbPRcgVCNlMNUKVYteNA87IETEpvS1_/s1600/sinewave+-+Copy.png" /></div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
<b>Cycle:</b></div>
<div class="separator" style="clear: both; text-align: justify;">
</div>
<ul>
<li>In an ac waveform, a particular portion consisting of one positive and negative part repeats many times. Each repetition consisting of one positive and one identical negative part is called as one cycle of the waveform. Refer Figure A.</li>
<li>If the waveform is plotted by plotting angle on the X-axis in place of time, then cycle is that portion of the waveform corresponding to an angle span of 2<span style="font-family: Verdana, sans-serif; font-size: 12pt; line-height: 115%; text-align: left;">ϖ</span> radians.</li>
</ul>
<br />
<div class="separator" style="clear: both; text-align: center;">
<i><b>1 Cycle = 2<span style="font-family: Verdana, sans-serif; font-size: 12pt; line-height: 115%; text-align: left;">ϖ</span> radians</b></i></div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: justify;">
<b>Time Period or Periodic Time (T):</b></div>
<div class="separator" style="clear: both; text-align: justify;">
</div>
<ul>
<li>Time period (T) is defined as the time taken in seconds by the waveform of an ac quantity to complete one cycle. After every T seconds, the cycle repeats itself.</li>
<li><i><b>Time period T = Time corresponding to one cycle</b></i></li>
</ul>
<div>
<b>Frequency:</b></div>
<div>
<ul>
<li>Frequency is defined as the number of cycles completed by an alternating quantity in one second. It is denoted by "f" and its units are cycles/second or Hertz (Hz).</li>
<li>As the time period (T) is the time in seconds per cycle denoted in seconds/cycle, hence relation between frequency and time period is as follows:</li>
<li>Frequency (f) = cycles/second = 1/(second/cycle) = 1/T</li>
<li>Therefore, <i><b>f = 1/T Hz</b></i></li>
</ul>
</div>
<div>
<b>Amplitude:</b></div>
<div>
<ul>
<li>The maximum value or peak value of an ac quantity is called as its amplitude.</li>
<li>The amplitude is denoted by <span style="font-size: 12pt; line-height: 115%;"><span style="font-family: inherit;">V<sub>m</sub></span></span> for voltage, I<sub style="line-height: 18.3999996185303px;">m</sub> for current waveform etc.</li>
</ul>
</div>
<div>
<b>Angular Velocity (<span style="font-family: Verdana, sans-serif; font-size: 12pt; line-height: 115%;">ω</span>):</b></div>
<div>
<ul>
<li>The angular velocity (<span style="font-family: Verdana, sans-serif; font-size: 12pt; line-height: 115%;">ω</span>) is the rate of change of angle <span style="font-family: Verdana, sans-serif; font-size: 12pt; line-height: 115%;">ω</span>t with respect to time.</li>
<li>Therefore, <span style="font-family: Verdana, sans-serif; font-size: 12pt; line-height: 115%;">ω</span> = d<span style="font-size: 12pt; line-height: 115%;"><span style="font-family: inherit;">θ</span></span>/dt, where d<span style="font-size: 12pt; line-height: 115%;"><span style="font-family: inherit;">θ</span></span> is the change in angle in time dt.</li>
<li>If dt = T i.e. time period, (one cycle) then the corresponding change in <span style="font-size: 12pt; line-height: 115%;"><span style="font-family: inherit;">θ</span></span> is 2<span style="font-family: Verdana, sans-serif; font-size: 16px; line-height: 18.3999996185303px; text-align: left;">ϖ</span> radians.</li>
<li>Therefore, d<span style="font-size: 16px; line-height: 18.3999996185303px;">θ</span> = 2<span style="font-family: Verdana, sans-serif; font-size: 16px; line-height: 18.3999996185303px; text-align: left;">ϖ</span></li>
<li>Therefore, <span style="font-family: Verdana, sans-serif; font-size: 16px; line-height: 18.3999996185303px;">ω</span> = 2<span style="font-family: Verdana, sans-serif; font-size: 16px; line-height: 18.3999996185303px; text-align: left;">ϖ</span>/T</li>
<li>But I/T = f.</li>
<li>Therefore, <i><b><span style="font-family: Verdana, sans-serif; font-size: 16px; line-height: 18.3999996185303px;">ω</span> = 2<span style="font-family: Verdana, sans-serif; font-size: 16px; line-height: 18.3999996185303px; text-align: left;">ϖ</span>f</b></i></li>
</ul>
</div>
</div>
<hr />
<b><i><u>Mathematical Expression  for an Alternating Quantity:</u></i></b><br />
<div>
<br /></div>
<div>
The alternating voltage is mathematically expressed as follows:</div>
<div>
<b><i>v(t) = <span style="font-size: 16px; line-height: 18.3999996185303px;">V</span><sub style="line-height: 18.3999996185303px;">m</sub>sin(2<span style="font-family: Verdana, sans-serif; font-size: 16px; line-height: 18.3999996185303px;">ϖ</span><span style="font-family: inherit;">f<span style="font-size: 13px; line-height: 18.3999996185303px;">o</span></span><span style="font-family: inherit; font-size: 16px; line-height: 18.3999996185303px;">t</span><span style="font-family: Verdana, sans-serif; font-size: 16px; line-height: 18.3999996185303px;">)</span></i></b></div>
<div>
<ul style="text-align: left;">
<li><span style="font-family: inherit; line-height: 18.3999996185303px;">v(t) = instantaneous voltage</span></li>
<li><span style="font-family: inherit;"><span style="font-size: 16px; line-height: 18.3999996185303px;">V</span><sub style="line-height: 18.3999996185303px;">m</sub></span><span style="line-height: 18.3999996185303px;"><span style="font-family: inherit;">  = Peak Value (or maximum value)</span></span></li>
<li>f<span style="font-size: 13px; line-height: 18.3999996185303px;">o</span><span style="line-height: 18.3999996185303px;"><span style="font-family: inherit;"> = frequency in Hz</span></span></li>
<li><span style="font-family: inherit; line-height: 18.3999996185303px;">and "sin" represents the shape of the waveform</span></li>
</ul>
</div>
<div>
<span style="line-height: 18.3999996185303px;"><span style="font-family: inherit;">It can also be represented as </span></span></div>
<div>
<b><i>v(t) = <span style="font-size: 16px; line-height: 18.3999996185303px;">V</span><sub style="line-height: 18.3999996185303px;">m</sub>sin(</i></b><i><b><span style="font-family: Verdana, sans-serif; font-size: 16px; line-height: 18.3999996185303px;">ω</span></b></i><i><span style="font-family: inherit; font-weight: bold;"><span style="font-size: 13px; line-height: 18.3999996185303px;">o</span></span><span style="font-family: inherit; font-size: 16px; font-weight: bold; line-height: 18.3999996185303px;">t</span><span style="font-family: Verdana, sans-serif; font-size: 16px; line-height: 18.3999996185303px;"><b>)  </b>or<b>  </b></span></i><b><i>v(t) = <span style="font-size: 16px; line-height: 18.3999996185303px;">V</span><sub style="line-height: 18.3999996185303px;">m</sub>sin(</i></b><span style="font-size: 16px; line-height: 18.3999996185303px;"><b>θ</b></span><b><i><span style="font-family: Verdana, sans-serif; font-size: 16px; line-height: 18.3999996185303px;">)</span></i></b></div>
<div>
<ul style="text-align: left;">
<li><span style="line-height: 18.3999996185303px;"><span style="font-family: inherit;">where </span></span><span style="font-size: 16px; line-height: 18.3999996185303px;">θ</span><span style="font-family: inherit; line-height: 18.3999996185303px;"> = </span><span style="font-family: Verdana, sans-serif; font-size: 16px; line-height: 18.3999996185303px;">ω</span><span style="font-family: inherit;"><span style="font-size: 13px; line-height: 18.3999996185303px;">o</span></span><span style="font-family: inherit; line-height: 18.3999996185303px;">t = </span>2<span style="font-family: Verdana, sans-serif; font-size: 16px; line-height: 18.3999996185303px;">ϖ</span>f<span style="font-size: 13px; line-height: 18.3999996185303px;">o</span><span style="font-family: inherit; line-height: 18.3999996185303px;">t</span></li>
</ul>
</div>
<div>
<span style="font-family: inherit; line-height: 18.3999996185303px;">Similarly an alternating current is mathematically represented as,</span></div>
<div>
<b><i><span style="font-family: inherit; line-height: 18.3999996185303px;">i(t) = </span>I<sub style="line-height: 18.3999996185303px;">m</sub><span style="font-family: inherit; line-height: 18.3999996185303px;">sin(2</span><span style="font-family: Verdana, sans-serif; font-size: 16px; line-height: 18.3999996185303px;">ϖ</span><span style="font-family: inherit;">f<span style="font-size: 13px; line-height: 18.3999996185303px;">o</span></span><span style="font-family: inherit; line-height: 18.3999996185303px;">t)</span></i></b></div>
<div>
<ul style="text-align: left;">
<li><span style="font-family: inherit; line-height: 18.3999996185303px;">i(t) = instantaneous voltage</span></li>
<li>I<sub style="line-height: 18.3999996185303px;">m</sub><span style="font-family: inherit; line-height: 18.3999996185303px;"> = Peak value</span></li>
<li>f<span style="font-size: 13px; line-height: 18.3999996185303px;">o</span><span style="font-family: inherit; line-height: 18.3999996185303px;"> = frequency in Hz</span></li>
</ul>
</div>
</div>
<hr />
<b><u><i>Effective or RMS Value:</i></u></b><div>
<br /></div>
<div>
<b>Definition:</b> The effective or RMS value of an AC current is equal to the steady state or DC current that is required to produce the same amount of heat as produced by the AC current provided that the resistance and time for which these currents flow are identical.</div>
<div>
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9cQNvTNZYl-0Ud0RQ0xAlgF4uctnAxBPaJeSZKPVL3WNa0I2CePvK59U1PvydUC7LfJcElBwPLDVJ_q_KB4ysvV2msHqlizQQ2W7osXTnvIezuJbXCaMWU60d-M5OxYlzE24FHk7ADgoZ/s1600/sinewave+-+Copy+(2).png" /></div>
<div style="text-align: justify;">
<div>
<br /></div>
<div>
RMS value of a sinusoidal waveform (sine or cosine) is equal to 0.707 times its peak value.</div>
<div>
<b><span style="text-align: left;">I</span><sub style="line-height: 18.3999996185303px; text-align: left;">rms</sub> = 0.707 <span style="text-align: left;">I</span><sub style="line-height: 18.3999996185303px; text-align: left;">m</sub></b>  and  <b><span style="text-align: left;">V</span><sub style="line-height: 18.3999996185303px; text-align: left;">rms</sub> = 0.707 <span style="text-align: left;">V</span><sub style="line-height: 18.3999996185303px; text-align: left;">m</sub></b></div>
</div>
<div style="text-align: justify;">
<ul>
<li>All the ac currents or voltages are expressed as RMS values unless clearly specified other.</li>
<li>RMS value of ac current is denoted by <span style="text-align: left;">I</span><sub style="line-height: 18.3999996185303px; text-align: left;">rms</sub> and RMS voltage is denoted by <span style="text-align: left;">V</span><sub style="line-height: 18.3999996185303px; text-align: left;">rms</sub>.</li>
<li>RMS value is called as the heat producing component of ac current.</li>
</ul>
<div>
<b><i><u>Average Value:</u></i></b></div>
<div>
<br /></div>
<div>
<b>Definition:</b> The average value of an alternating quantity is equal to the average of all, the instantaneous values over a period of half cycle.</div>
<div>
<br /></div>
<div>
The average value of ac current denoted by <b><span style="text-align: left;">I</span><sub style="line-height: 18.3999996185303px; text-align: left;">av</sub></b> or <b><span style="text-align: left;">I</span><sub style="line-height: 18.3999996185303px; text-align: left;">dc</sub></b>. The average value of a sinusoidal waveform is equal to 0.637 times its peak value. And is expressed as:</div>
<div>
<b><span style="text-align: left;">I</span><sub style="line-height: 18.3999996185303px; text-align: left;">av</sub> = 0.637 <span style="text-align: left;">I</span><sub style="line-height: 18.3999996185303px; text-align: left;">m</sub></b>  and  <b><span style="text-align: left;">V</span><sub style="line-height: 18.3999996185303px; text-align: left;">av</sub> = 0.637 <span style="text-align: left;">V</span><sub style="line-height: 18.3999996185303px; text-align: left;">m</sub></b></div>
<div>
<ul>
<li>The dc ammeters or voltmeters indicate the average value.</li>
<li>Average value of a full cycle of a symmetrical ac waveform is zero.</li>
</ul>
<div>
<b><i><u>Form Factor:</u></i></b></div>
</div>
<div>
<br /></div>
<div>
The form factor of an alternating quantity is defined as the ratio of its RMS value to its average.</div>
<div>
Therfore, Form factor, <b><span style="text-align: left;">K</span><sub style="line-height: 18.3999996185303px; text-align: left;">f</sub> = RMS value / Average value</b></div>
<div>
<ul>
<li>Form factor is dimensionless quantity and its value is always higher than one.</li>
<li>Form factor of a sinusoidal alternating current is given by:</li>
<li><span style="text-align: left;">K</span><sub style="line-height: 18.3999996185303px; text-align: left;">f</sub> = <span style="text-align: left;">I</span><sub style="line-height: 18.3999996185303px; text-align: left;">rms </sub>/ <span style="text-align: left;">I</span><sub style="line-height: 18.3999996185303px; text-align: left;">av</sub> = 0.707<span style="text-align: left;">I</span><sub style="line-height: 18.3999996185303px; text-align: left;">m </sub>/ 0.637<span style="text-align: left;">I</span><sub style="line-height: 18.3999996185303px; text-align: left;">m</sub></li>
<li>Therefore, <b>K = 1.11</b></li>
</ul>
</div>
</div>
</div>

AC Fundamentals

The ac fundamentals are necessary for analyzing the electrical networks. Alternating waveform: The alternating quantity such as ...

Voltage and Current Sources

<div dir="ltr" style="text-align: left;" trbidi="on">
<div style="text-align: justify;">
For the operation of all the electrical/electronic circuits a source of power/energy is essential. These sources are classified into two categories as:</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
(i) Voltage Sources  (ii) Current Sources</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
The voltage and current sources can be further classified as dependent sources and independent sources.<br />
<br /></div>
<div style="text-align: justify;">
<div class="separator" style="clear: both; text-align: center;">
<img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYqA5oTn3cyNxry-nCXAz7fphDrLgLV0dpsEuhBhrwk_y-hAQ7HIHU-EPJ6Cm1xH9rXFXig0G6cpse92DPnRrxvaqs0HTcJamrYAokNtn0mjsaxFB4pEB_nf4ASQxupma_oSV1U5IsKXAP/s1600/Voltage+&+current+sources.png" /></div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<b><i><u>Independent Voltage Sources:</u></i></b><br />
<br />
In the independent voltage source, the terminal voltage of the source is not dependent on any other voltage source or current source. The independent voltage sources can be further classified as:<br />
(i) Ideal voltage sources   (ii) Practical voltage sources<br />
<br />
<b>Time invariant sources:</b> The time invariant voltage source is the source whose terminal voltage does not change with time. That means it is a D.C. voltage source.<br />
<br />
<b>Time variant sources:</b> The terminal voltage of these sources changes with time. So they are basically the ac voltage.<br />
<br />
<b><i><u>Independent Current Sources:</u></i></b><br />
<br />
For an independent current source, the current supplied by the source does not depend on any other voltage source or current source. The independent current sources are further classified as:<br />
(i) Ideal current sources  (ii) Practical current sources<br />
<br />
<b>Time invariant current source:</b> The output current of this source does not change with time. So basically this is a dc current source.<br />
<br />
<b>Time variant current source:</b> The output current of this source changes with time. So basically it is an ac source.<br />
<br />
<b><i><u>Dependent Sources:</u></i></b><br />
<br />
The dependent voltage sources or dependent current sources will produce terminal voltage or current that is dependent on some other voltage or current in the same circuit.<br />
<br />
<b>Voltage Dependent Voltage Source (VDVS):</b> This is a voltage source which produces a terminal voltage V which is dependent on some other voltage V' produced in the same circuit. Hence, V = kV'.<br />
<br />
<b>Current Dependent Voltage Source (CDVS):</b> This is a voltage source which produces a terminal voltage V which is dependent on current I' produced in the same circuit. Hence, V = kI'.<br />
<br />
<b>Voltage Dependent Current Source (VDCS):</b> This is a current source which produces a current which is dependent on voltage V' produced in the same circuit. Hence, I = kV'.<br />
<br />
<b>Current Dependent Current Source (CDCS):</b> This is a current source which produces an output current I which is dependent on some other current I' produced in the same circuit. Hence, I = kI'.</div>
</div>

Voltage and Current Sources

For the operation of all the electrical/electronic circuits a source of power/energy is essential. These sources are classified into two c...

Basic Terminology : Associated with Networks

<div dir="ltr" style="text-align: left;" trbidi="on">
<div style="text-align: justify;">
<b>Circuit element</b></div>
<div style="text-align: justify;">
A circuit element is any individual circuit component which gets connected to the other components in a network.</div>
<div style="text-align: justify;">
Resistors, capacitors, voltage sources etc. are the examples of circuit elements.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b>Open circuit</b></div>
<div style="text-align: justify;">
Two points in a circuit are said to be open circuited if there is no circuit element or direct connection between them.</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/AVvXsEjOLS0qV8LdHurvXBRJuh1HlQUlaVOg-OdEC2JwxbE3u1gwinXz9OEa1LeGbc693TpXM538MD0cdLdyjlfdgqKgbnZhKvqIZYSvii29a5nDQw5taiEeNDcgvZqqI-JdYLQNLvbY6SLujIEj/s1600/DC+network.png" /></div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
An open circuit exists between points A and B in above Figure.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b>Short circuit</b></div>
<div style="text-align: justify;">
Two points in a circuit are said to be short circuited when they are connected to each other by a good conducting wire.</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/AVvXsEhV6Uswr2VNxXXjeDCOKRzrtvyHRxuFuB4kemG9DQ1MWqZSwhVHEz-j7u_7xwjyZbn7Ry2gDyy97BXGkxPhMpUd3Woe1j8E_GS6w-uBeOqTb3N9kZX5UvRlZlns1ZDtuXP44Xz_Tr7zkgr4/s1600/DC+network.png" /></div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div style="text-align: justify;">
Points A and B are short circuited in above Figure.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b>Branch</b></div>
<div style="text-align: justify;">
A branch of a network is defined as the group of elements connected in series or parallel and which has two terminals from connections. In figure below the branches are : AB, BC, CD, BE, EF, AF.</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/AVvXsEisoe9TsItjIaAC0csEN9C_Kl7Ew_oks92vnz5GijQwgpO0CSUyudzeQXpBl6Bu2LH5PbGJgp8VTwM5B_PB4yYAUXv1dEQxteRGD5u2cAQVPBAbEvovuscBACZ38lpHNpA-9oQ7_iDPfsDA/s1600/Branch,loop,node.png" /></div>
<div class="separator" style="clear: both; text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b>Mesh or Loop</b></div>
<div style="text-align: justify;">
A mesh or loop is a set of branches, forming a closed path in a network. For example in figure above the closed path A-B-E-F-A forms Loop-I or the closed path B-C-D-E-B forms Loop-II.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b>Node or junction</b></div>
<div style="text-align: justify;">
It is common point in a network at which two or more branches meet. In figure above, the points A, B, C, E, F are nodes.</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<b><i>Analysis of a circuit:</i></b></div>
<div style="text-align: justify;">
</div>
<ul>
<li>The DC circuits contain batteries and resistors.</li>
<li>Obtaining the voltage, current, and power associated with each circuit element is called as the circuit analysis.</li>
<li>The analysis of circuits first requires simplification of the given circuit.</li>
</ul>
</div>

Basic Terminology : Associated with Networks

Circuit element A circuit element is any individual circuit component which gets connected to the other components in a network. Resis...

What is a Network? And its Types.

<div dir="ltr" style="text-align: left;" trbidi="on">
<div style="text-align: justify;">
<b><i>Network</i></b> is an electrical configuration in which various components such as <a href="http://www.ecestream.com/2014/11/resistor.html" target="_blank">resistors</a>, <a href="http://www.ecestream.com/2014/11/capacitor.html" target="_blank">capacitors</a>, <a href="http://www.ecestream.com/2014/11/inductor.html" target="_blank">inductors</a>, and <a href="http://www.ecestream.com/2014/11/voltage-and-current-sources.html" target="_blank">voltage sources</a> or <a href="http://www.ecestream.com/2014/11/voltage-and-current-sources.html" target="_blank">current sources</a> are electrically connected to each other. A network can also be called as circuit.<br />
<br />
(i) <i>DC Circuit</i><br />
<div class="separator" style="clear: both; text-align: left;">
<img border="0" height="151" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWq_fw5H7AldjKNXt3qKCuT8PY7XcImyZBRsUkrARwv_lQvXsEiyb86tpMHuPtwsKfQQK6Ob7eVOqq4gK7axEnmEO_6FKOtBpgKwePt0-OS-hBHAJ4lzCTWU-pU0zNXl3Is6OfFZozAFRN/s1600/DC+network.png" width="320" /></div>
<i><br /></i>
(ii) <i>AC Circuit</i><br />
<div class="separator" style="clear: both; text-align: left;">
<img border="0" height="179" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOcnG786f5_a2sRL81KsDP_ykfvrlRKQB46QkS6BO7abXLuYzcG1salSreRe-aExI3eU6XTPt1GuR_a6jm9o3Si2npPBrOnTOk0IRVU6Z8DPsN1VFc-zMwuF2cG8mxuA10dDjQ08MYcVXX/s1600/AC+Network.png" width="320" /></div>
<i><br /></i>
The networks can be DC or AC depending on the type of source involved. For the DC circuits, the voltage and current sources are DC whereas AC sources are connected in the AC circuits. Example of a DC source is a battery and that of an AC source is the AC mains supply.<br />
<br />
<b>Classification of Electric Networks:</b><br />
<br />
<i><b>Classification based on presence or absence of sources</b></i><br />
<br />
<b>Active Network:</b> If a network consists of an energy source, then it is called as an active network. The type of energy source can be a voltage source or a current source.<br />
<br />
<b>Passive Network:</b> If a network does not contain any energy source then it is called as the passive network.<br />
<br />
<b><i>Classification based on the direction of current</i></b><br />
<br />
<b>Bilateral network:</b> It is the network whose characteristics or response does not depend on the direction of current through the various elements in it. Resistive networks are bilateral type.<br />
<br />
<b>Unilateral network:</b> If the characteristics, response or behaviour of a network is dependent on the direction of current through its elements in it, then the network is called as a unilateral network. The networks containing elements such as diodes, transistors, etc. are called unilateral network.<br />
<br />
<b><i>Classification based on separability of components</i></b><br />
<br />
<b>Distributed network:</b> If the network element such as resistances, capacitances, inductances are not physically separable, then it is called as a distributed network. Example of a distributed network is the transmission line.<br />
<br />
<b>Lumped network:</b> If the network elements can be separated physically from each other, then they are called as lumped network. All the simple electric networks are lumped network.<br />
<br />
<b><i>Classification based on linearity</i></b><br />
<br />
<b>Linear network:</b> It the characteristics, parameters such as resistances, capacitances, inductances etc. remain constant  irrespective of changes in temperature, time, voltage etc., then the network is called as linear network.<br />
<ul>
<li>We can apply the ohm's law only to linear networks.</li>
<li>The superposition theorem also is applicable only to the linear networks.</li>
</ul>
<b>Nonlinear networks:</b> If the parameters of a network change their values with the change in voltage, temperature, time etc., then the network is called as a nonlinear network.<br />
<ul>
<li>The ohm's law is is not applicable to the nonlinear networks.</li>
<li>The superposition theorem also is not applicable to the nonlinear networks.</li>
</ul>
</div>
</div>

What is a Network? And its Types.

Network is an electrical configuration in which various components such as resistors , capacitors , inductors , and voltage sources or c...

Network Theorems

<div dir="ltr" style="text-align: left;" trbidi="on">
<div style="text-align: justify;">
Solving for currents and voltages in multi-loop electric circuits can be quite complicated, particularly for AC circuits. The voltage law and current law always apply, but using them may lead to long systems of equations. Certain theorems help with network analysis:</div>
<div style="text-align: justify;">
<br /></div>
<div style="text-align: justify;">
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVd0c7driZJn7a2Sr61AS-tOl40EcRP3vGqDBa0wmjC498iWqWwhBKcQ2awWcdze2cPCzMikLdaAkGho8jQ5ZoLsqob65a7RmA9B-upTG5w3gEYmL1OIquCt_cEKOebT7bAylV4pe8_rv8/s1600/Network+Theorems.png" style="margin-left: auto; margin-right: auto;" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><b><i>Fig.  Basic Network</i></b></td></tr>
</tbody></table>
<b><u>Superposition Theorem</u></b></div>
<div style="text-align: justify;">
The superposition theorem is applicable to linear and bilateral networks.<br />
<b>Statement:</b> It states that in an active linear network containing several sources, the voltage across or current through any element of that network is equal to the sum of individual voltages or currents, produced separately across or in that element by each source acting independently with all the remaining sources replaced by their respective internal impedances.</div>
<div style="text-align: justify;">
<br /></div>
<b><u>Thevenin's Theorem</u></b><br />
<div style="text-align: justify;">
The Thevenin's theorem is used for simplification of complicated networks.<br />
<b>Statement: </b>Any network containing active and passive elements and one or more dependent and independent voltage/current sources can be replaced by an equivalent network containing a voltage source ( <span style="line-height: 18.3999996185303px;">V</span><sub style="font-family: 'Times New Roman', serif; line-height: 115%; text-align: left;">th</sub> or <span style="line-height: 18.3999996185303px;">V</span><span style="font-family: 'Times New Roman', serif; line-height: 15.3333320617676px; text-align: left;"><span style="font-size: x-small;">oc</span></span>) and a series impedance (<span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%; text-align: left;">Z</span><sub style="font-family: 'Times New Roman', serif; line-height: 115%; text-align: left;">th</sub>). Vth is the Thevenin's equivalent voltage. It is the open circuit voltage measured at two terminals of interest with load impedance <span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%; text-align: left;">Z</span><sub style="font-family: 'Times New Roman', serif; line-height: 115%; text-align: left;">L</sub> removed. <span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%; text-align: left;">Z</span><sub style="font-family: 'Times New Roman', serif; line-height: 115%; text-align: left;">th</sub> is the Thevenin's equivalent impedance. It is the impedance with load impedance <span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 18.3999996185303px; text-align: left;">Z</span><sub style="font-family: 'Times New Roman', serif; line-height: 15.3333320617676px; text-align: left;">L</sub> removed when all the independent voltage/current sources are replaced by their internal impedances.</div>
<div style="text-align: justify;">
<br /></div>
<b><u>Norton's Theorem</u></b><br />
<div style="text-align: justify;">
This theorem is called as the dual of the Thevenin's theorem. This is because the Thevenin's equivalent voltage source is converted to an equivalent current source. The obtained equivalent is called Norton's equivalent.<br />
<b>Statement:</b> Any linear network containing of active sources and bilateral elements can be replaced by an equivalent circuit containing a current source called Norton's equivalent current (<span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%; text-align: left;">I</span><sub style="font-family: 'Times New Roman', serif; line-height: 115%; text-align: left;">N</sub> or <span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%; text-align: left;">I</span><sub style="font-family: 'Times New Roman', serif; line-height: 115%; text-align: left;">SC</sub>) and an equivalent impedance in parallel (<span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 18.3999996185303px; text-align: left;">Z</span><sub style="font-family: 'Times New Roman', serif; line-height: 15.3333320617676px; text-align: left;">th</sub> or <span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 18.3999996185303px; text-align: left;">Z</span><span style="font-family: 'Times New Roman', serif; line-height: 15.3333320617676px; text-align: left;"><span style="font-size: x-small;">eq</span></span>) across the two terminals of load. <span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 18.3999996185303px; text-align: left;">I</span><sub style="font-family: 'Times New Roman', serif; line-height: 15.3333320617676px; text-align: left;">N</sub> is the short circuit current flowing through the short circuited path that is replaced of load impedance <span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 18.3999996185303px; text-align: left;">Z</span><sub style="font-family: 'Times New Roman', serif; line-height: 15.3333320617676px; text-align: left;">L</sub>. Hence it is also called short circuit current <span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 18.3999996185303px; text-align: left;">I</span><sub style="font-family: 'Times New Roman', serif; line-height: 15.3333320617676px; text-align: left;">SC</sub> or Norton's current <span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 18.3999996185303px; text-align: left;">I</span><sub style="font-family: 'Times New Roman', serif; line-height: 15.3333320617676px; text-align: left;">N</sub>. The equivalent impedance <span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 18.3999996185303px; text-align: left;">Z</span><sub style="font-family: 'Times New Roman', serif; line-height: 15.3333320617676px; text-align: left;">th</sub> is obtained when looking through load impedance, with load impedance <span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 18.3999996185303px; text-align: left;">Z</span><sub style="font-family: 'Times New Roman', serif; line-height: 15.3333320617676px; text-align: left;">L </sub>removed and all the independent voltage/current sources are replaced by their internal impedances.</div>
<div style="text-align: justify;">
<br /></div>
<b><u>Maximum Power Transfer Theorem</u></b><br />
<div style="text-align: justify;">
The maximum power transfer theorem is used in communication circuits for transferring maximum power from source to load.<br />
<b>Statement:</b> In an active network, maximum power will be transferred from source to load if the load impedance is the complex conjugate of the internal impedance of the circuit as seen from terminals of the load.</div>
</div>

Network Theorems

Solving for currents and voltages in multi-loop electric circuits can be quite complicated, particularly for AC circuits. The voltage law ...

ECEstream

AC Fundamentals

Voltage and Current Sources

Basic Terminology : Associated with Networks

What is a Network? And its Types.

Network Theorems

Popular Articles

Categories

Pages

Contact Form