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<title>Common source</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Common source</span></span>

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<p>In <a href="Electronics" title="Electronics">electronics</a>, a <b>common-source</b> <a href="Electronic_amplifier" class="mw-redirect" title="Electronic amplifier">amplifier</a> is one of three basic single-stage <a href="Field-effect_transistor" title="Field-effect transistor">field-effect transistor</a> (FET) amplifier topologies, typically used as a <a href="Electronic_amplifier" class="mw-redirect" title="Electronic amplifier">voltage or transconductance</a> <a href="Amplifier" title="Amplifier">amplifier</a>. The easiest way to tell if a FET is common source, <a href="Common_drain" title="Common drain">common drain</a>, or <a href="Common_gate" title="Common gate">common gate</a> is to examine where the signal enters and leaves. The remaining terminal is what is known as "common". In this example, the signal enters the gate, and exits the drain. The only terminal remaining is the source. This is a common-source FET circuit. The analogous <a href="Bipolar_junction_transistor" title="Bipolar junction transistor">bipolar junction transistor</a> circuit may be viewed as a transconductance amplifier or as a voltage amplifier. (See <a href="Electronic_amplifier" class="mw-redirect" title="Electronic amplifier">classification of amplifiers</a>). As a transconductance amplifier, the input voltage is seen as modulating the current going to the load. As a voltage amplifier, input voltage modulates the current flowing through the FET, changing the voltage across the output resistance according to <a href="Ohm's_law" title="Ohm's law">Ohm's law</a>. However, the FET device's output resistance typically is not high enough for a reasonable transconductance amplifier (<a href="Electronic_amplifier" class="mw-redirect" title="Electronic amplifier">ideally infinite</a>), nor low enough for a decent voltage amplifier (<a href="Electronic_amplifier" class="mw-redirect" title="Electronic amplifier">ideally zero</a>). As seen below in the formula, the voltage gain depends on the load resistance, so it cannot be applied to drive low-resistance devices, such as a speaker (having a resistance of 8 ohms). Another major drawback is the amplifier's limited high-frequency response. Therefore, in practice the output often is routed through either a voltage follower (<a href="Common-drain" class="mw-redirect" title="Common-drain">common-drain</a> or CD stage), or a current follower (<a href="Common-gate" class="mw-redirect" title="Common-gate">common-gate</a> or CG stage), to obtain more favorable output and frequency characteristics. The CS–CG combination is called a <a href="Cascode" title="Cascode">cascode</a> amplifier.

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<div class="mw-heading mw-heading2"><h2 id="Characteristics">Characteristics</h2></div>

<p>At low frequencies and using a simplified <a href="Hybrid-pi_model" title="Hybrid-pi model">hybrid-pi model</a> (where the output resistance due to channel length modulation is not considered), the following closed-loop <a href="Small-signal_model" title="Small-signal model">small-signal</a> characteristics can be derived.

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<th style="width:2in">Definition</th>

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<th><b><a href="Gain_(electronics)" title="Gain (electronics)">Current gain</a></b>

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<annotation encoding="application/x-tex">{\displaystyle A_{\text{i}}\triangleq {\frac {i_{\text{out}}}{i_{\text{in}}}}\,}</annotation>

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</math></span><img src="./147f5dde84b584303659c8c985f8471704669cfa.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:10.165ex; height:5.509ex;" alt="{\displaystyle A_{\text{i}}\triangleq {\frac {i_{\text{out}}}{i_{\text{in}}}}\,}" loading="lazy"></span>

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<annotation encoding="application/x-tex">{\displaystyle \infty \,}</annotation>

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<th><b><a href="Gain_(electronics)" title="Gain (electronics)">Voltage gain</a></b>

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<annotation encoding="application/x-tex">{\displaystyle A_{\text{v}}\triangleq {\frac {v_{\text{out}}}{v_{\text{in}}}}\,}</annotation>

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<annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}-{\frac {g_{\mathrm {m} }R_{\text{D}}}{1+g_{\mathrm {m} }R_{\text{S}}}}\end{matrix}}\,}</annotation>

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</math></span><img src="./8569a36aa1d989aafa0e8b38ce06cf28602c6f01.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:10.097ex; height:4.509ex;" alt="{\displaystyle {\begin{matrix}-{\frac {g_{\mathrm {m} }R_{\text{D}}}{1+g_{\mathrm {m} }R_{\text{S}}}}\end{matrix}}\,}" loading="lazy"></span>

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<th><b><a href="Input_impedance" title="Input impedance">Input impedance</a></b>

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<annotation encoding="application/x-tex">{\displaystyle r_{\text{in}}\triangleq {\frac {v_{\text{in}}}{i_{\text{in}}}}\,}</annotation>

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<annotation encoding="application/x-tex">{\displaystyle R_{\text{D}}\,}</annotation>

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<div class="mw-heading mw-heading3"><h3 id="Bandwidth">Bandwidth</h3></div>

<p>Bandwidth of common-source amplifier tends to be low, due to high capacitance resulting from the <a href="Miller_effect" title="Miller effect">Miller effect</a>. The gate-drain capacitance is effectively multiplied by the factor <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1+|A_{\text{v}}|\,}">

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</p><p>Figure 3 shows a MOSFET common-source amplifier with an <a href="Active_load" title="Active load">active load</a>. Figure 4 shows the corresponding small-signal circuit when a load resistor <i>R</i><sub>L</sub> is added at the output node and a <a href="Th%C3%A9venin's_theorem" title="Thévenin's theorem">Thévenin driver</a> of applied voltage <i>V</i><sub>A</sub> and series resistance <i>R</i><sub>A</sub> is added at the input node. The limitation on bandwidth in this circuit stems from the coupling of <a href="Parasitic_capacitance" title="Parasitic capacitance">parasitic transistor capacitance</a> <i>C</i><sub>gd</sub> between gate and drain and the series resistance of the source <i>R</i><sub>A</sub>. (There are other parasitic capacitances, but they are neglected here as they have only a secondary effect on bandwidth.)

</p><p>Using <a href="Miller_effect" title="Miller effect">Miller's theorem</a>, the circuit of Figure 4 is transformed to that of Figure 5, which shows the <i>Miller capacitance</i> <i>C</i><sub>M</sub> on the input side of the circuit. The size of <i>C</i><sub>M</sub> is decided by equating the current in the input circuit of Figure 5 through the Miller capacitance, say <i>i</i><sub>M</sub>, which is:

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<annotation encoding="application/x-tex">{\displaystyle \ i_{\mathrm {M} }=j\omega C_{\mathrm {M} }v_{\mathrm {GS} }=j\omega C_{\mathrm {M} }v_{\mathrm {G} }}</annotation>

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</math></span><img src="./4c4b27e23a3aa5f24400f54a1fa29e0ae53fdaab.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:27.142ex; height:2.509ex;" alt="{\displaystyle \ i_{\mathrm {M} }=j\omega C_{\mathrm {M} }v_{\mathrm {GS} }=j\omega C_{\mathrm {M} }v_{\mathrm {G} }}" loading="lazy"></span> ,</dd></dl></dd></dl>

<p>to the current drawn from the input by capacitor <i>C</i><sub>gd</sub> in Figure 4, namely <i>jωC</i><sub>gd</sub> <i>v</i><sub>GD</sub>. These two currents are the same, making the two circuits have the same input behavior, provided the Miller capacitance is given by:

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<annotation encoding="application/x-tex">{\displaystyle C_{\mathrm {M} }=C_{\mathrm {gd} }{\frac {v_{\mathrm {GD} }}{v_{\mathrm {GS} }}}=C_{\mathrm {gd} }\left(1-{\frac {v_{\mathrm {D} }}{v_{\mathrm {G} }}}\right)}</annotation>

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</math></span><img src="./860772e131b78f3805d63fddcc2873d55a6dfc84.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:32.897ex; height:6.176ex;" alt="{\displaystyle C_{\mathrm {M} }=C_{\mathrm {gd} }{\frac {v_{\mathrm {GD} }}{v_{\mathrm {GS} }}}=C_{\mathrm {gd} }\left(1-{\frac {v_{\mathrm {D} }}{v_{\mathrm {G} }}}\right)}" loading="lazy"></span> .</dd></dl></dd></dl>

<p>Usually the frequency dependence of the gain <i>v</i><sub>D</sub> / <i>v</i><sub>G</sub> is unimportant for frequencies even somewhat above the corner frequency of the amplifier, which means a low-frequency <a href="Hybrid-pi_model" title="Hybrid-pi model">hybrid-pi model</a> is accurate for determining <i>v</i><sub>D</sub> / <i>v</i><sub>G</sub>. This evaluation is <i>Miller's approximation</i><sup id="cite_ref-Spencer_1-0" class="reference"><a href="#cite_note-Spencer-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> and provides the estimate (just set the capacitances to zero in Figure 5):

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<annotation encoding="application/x-tex">{\displaystyle {\frac {v_{\mathrm {D} }}{v_{\mathrm {G} }}}\approx -g_{\mathrm {m} }(r_{\mathrm {O} }\parallel R_{\mathrm {L} })}</annotation>

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</math></span><img src="./5754a11d3655f93d0e1e834f680f5b03fde408c8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:20.948ex; height:5.009ex;" alt="{\displaystyle {\frac {v_{\mathrm {D} }}{v_{\mathrm {G} }}}\approx -g_{\mathrm {m} }(r_{\mathrm {O} }\parallel R_{\mathrm {L} })}" loading="lazy"></span> ,</dd></dl></dd></dl>

<p>so the Miller capacitance is

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<annotation encoding="application/x-tex">{\displaystyle C_{\mathrm {M} }=C_{\mathrm {gd} }\left(1+g_{\mathrm {m} }(r_{\mathrm {O} }\parallel R_{\mathrm {L} })\right)}</annotation>

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</math></span><img src="./707323c7d678abc913e6b63edfa108a4ec048c71.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:28.884ex; height:3.009ex;" alt="{\displaystyle C_{\mathrm {M} }=C_{\mathrm {gd} }\left(1+g_{\mathrm {m} }(r_{\mathrm {O} }\parallel R_{\mathrm {L} })\right)}" loading="lazy"></span> .</dd></dl></dd></dl>

<p>The gain <i>g</i><sub>m</sub> (<i>r</i><sub>O</sub> || <i>R</i><sub>L</sub>) is large for large <i>R</i><sub>L</sub>, so even a small parasitic capacitance <i>C</i><sub>gd</sub> can become a large influence in the frequency response of the amplifier, and many circuit tricks are used to counteract this effect. One trick is to add a <a href="Common-gate" class="mw-redirect" title="Common-gate">common-gate</a> (current-follower) stage to make a <a href="Cascode" title="Cascode">cascode</a> circuit. The current-follower stage presents a load to the common-source stage that is very small, namely the input resistance of the current follower (<i>R</i><sub>L</sub> ≈ 1 / <i>g</i><sub>m</sub> ≈ <i>V</i><sub>ov</sub> / (2<i>I</i><sub>D</sub>) ; see <a href="Common_gate" title="Common gate">common gate</a>). Small <i>R</i><sub>L</sub> reduces <i>C</i><sub>M</sub>.<sup id="cite_ref-Lee_2-0" class="reference"><a href="#cite_note-Lee-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The article on the <a href="Common_emitter" title="Common emitter">common-emitter amplifier</a> discusses other solutions to this problem.

</p><p>Returning to Figure 5, the gate voltage is related to the input signal by <a href="Voltage_division" class="mw-redirect" title="Voltage division">voltage division</a> as:

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<annotation encoding="application/x-tex">{\displaystyle v_{\mathrm {G} }=V_{\mathrm {A} }{\frac {1/(j\omega C_{\mathrm {M} })}{1/(j\omega C_{\mathrm {M} })+R_{\mathrm {A} }}}=V_{\mathrm {A} }{\frac {1}{1+j\omega C_{\mathrm {M} }R_{\mathrm {A} }}}}</annotation>

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</math></span><img src="./f44f37227045bbf3eff4ff141c8e5c8d60e6cbe6.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:45.204ex; height:6.509ex;" alt="{\displaystyle v_{\mathrm {G} }=V_{\mathrm {A} }{\frac {1/(j\omega C_{\mathrm {M} })}{1/(j\omega C_{\mathrm {M} })+R_{\mathrm {A} }}}=V_{\mathrm {A} }{\frac {1}{1+j\omega C_{\mathrm {M} }R_{\mathrm {A} }}}}" loading="lazy"></span> .</dd></dl></dd></dl>

<p>The <a href="Bandwidth_(signal_processing)" title="Bandwidth (signal processing)">bandwidth</a> (also called the 3 dB frequency) is the frequency where the signal drops to 1/ <span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">2</span></span> of its low-frequency value. (In <a href="Decibel" title="Decibel">decibels</a>, dB(<span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">2</span></span>) = 3.01 dB). A reduction to 1/ <span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">2</span></span> occurs when <i>ωC</i><sub>M</sub> <i>R</i><sub>A</sub> = 1, making the input signal at this value of <i>ω</i> (call this value <i>ω</i><sub>3 dB</sub>, say) <i>v</i><sub>G</sub> = <i>V</i><sub>A</sub> / (1+j). The <a href="Complex_number#Operations" title="Complex number">magnitude</a> of (1+j) = <span class="nowrap">√<span style="border-top:1px solid; padding:0 0.1em;">2</span></span>. As a result, the 3 dB frequency <i>f</i><sub>3 dB</sub> = <i>ω</i><sub>3 dB</sub> / (2π) is:

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<annotation encoding="application/x-tex">{\displaystyle f_{\mathrm {3dB} }={\frac {1}{2\pi R_{\mathrm {A} }C_{\mathrm {M} }}}={\frac {1}{2\pi R_{\mathrm {A} }[C_{\mathrm {gd} }(1+g_{\mathrm {m} }(r_{\mathrm {O} }\parallel R_{\mathrm {L} })]}}}</annotation>

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</math></span><img src="./80495f020da5aece3e61f21738d61ab16c636e5b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:49.374ex; height:6.009ex;" alt="{\displaystyle f_{\mathrm {3dB} }={\frac {1}{2\pi R_{\mathrm {A} }C_{\mathrm {M} }}}={\frac {1}{2\pi R_{\mathrm {A} }[C_{\mathrm {gd} }(1+g_{\mathrm {m} }(r_{\mathrm {O} }\parallel R_{\mathrm {L} })]}}}" loading="lazy"></span> .</dd></dl></dd></dl>

<p>If the parasitic gate-to-source capacitance <i>C</i><sub>gs</sub> is included in the analysis, it simply is parallel with <i>C</i><sub>M</sub>, so

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<annotation encoding="application/x-tex">{\displaystyle f_{\mathrm {3dB} }={\frac {1}{2\pi R_{\mathrm {A} }(C_{\mathrm {M} }+C_{\mathrm {gs} })}}={\frac {1}{2\pi R_{\mathrm {A} }[C_{\mathrm {gs} }+C_{\mathrm {gd} }(1+g_{\mathrm {m} }(r_{\mathrm {O} }\parallel R_{\mathrm {L} }))]}}}</annotation>

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</math></span><img src="./6b45722804f6daf3ba64cfb06d8af586da60770b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:64.497ex; height:6.009ex;" alt="{\displaystyle f_{\mathrm {3dB} }={\frac {1}{2\pi R_{\mathrm {A} }(C_{\mathrm {M} }+C_{\mathrm {gs} })}}={\frac {1}{2\pi R_{\mathrm {A} }[C_{\mathrm {gs} }+C_{\mathrm {gd} }(1+g_{\mathrm {m} }(r_{\mathrm {O} }\parallel R_{\mathrm {L} }))]}}}" loading="lazy"></span> .</dd></dl></dd></dl>

<p>Notice that <i>f</i><sub>3 dB</sub> becomes large if the source resistance <i>R</i><sub>A</sub> is small, so the Miller amplification of the capacitance has little effect upon the bandwidth for small <i>R</i><sub>A</sub>. This observation suggests another circuit trick to increase bandwidth: add a <a href="Common-drain" class="mw-redirect" title="Common-drain">common-drain</a> (voltage-follower) stage between the driver and the common-source stage so the Thévenin resistance of the combined driver plus voltage follower is less than the <i>R</i><sub>A</sub> of the original driver.<sup id="cite_ref-Lee2_3-0" class="reference"><a href="#cite_note-Lee2-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

</p><p>Examination of the output side of the circuit in Figure 2 enables the frequency dependence of the gain <i>v</i><sub>D</sub> / <i>v</i><sub>G</sub> to be found, providing a check that the low-frequency evaluation of the Miller capacitance is adequate for frequencies <i>f</i> even larger than <i>f</i><sub>3 dB</sub>. (See article on <a href="Pole_splitting" title="Pole splitting">pole splitting</a> to see how the output side of the circuit is handled.)

</p>

<ul><li><a href="Miller_effect" title="Miller effect">Miller effect</a></li>

<li><a href="Pole_splitting" title="Pole splitting">Pole splitting</a></li>

<li><a href="Common_gate" title="Common gate">Common gate</a></li>

<li><a href="Common_drain" title="Common drain">Common drain</a></li>

<li><a href="Common_base" title="Common base">Common base</a></li>

<li><a href="Common_emitter" title="Common emitter">Common emitter</a></li>

<li><a href="Common_collector" title="Common collector">Common collector</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFR.R._SpencerM.S._Ghausi2003" class="citation book cs1">R.R. Spencer; M.S. Ghausi (2003). <a rel="nofollow" class="external text" href="http://worldcat.org/isbn/0-201-36183-3"><i>Introduction to electronic circuit design</i></a>. Upper Saddle River NJ: Prentice Hall/Pearson Education, Inc. p. 533. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-201-36183-3</bdi>.</cite></span>

</li>

<cite id="CITEREFThomas_H_Lee2004" class="citation book cs1">Thomas H Lee (2004). <a rel="nofollow" class="external text" href="http://worldcat.org/isbn/0-521-83539-9"><i>The design of CMOS radio-frequency integrated circuits</i></a> (Second ed.). Cambridge UK: Cambridge University Press. pp. <span class="nowrap">246–</span>248. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-521-83539-9</bdi>.</cite></span>

</li>

<cite id="CITEREFThomas_H_Lee2004" class="citation book cs1">Thomas H Lee (2004). <a rel="nofollow" class="external text" href="http://worldcat.org/isbn/0-521-83539-9"><i>pp. 251–252</i></a>. Cambridge University Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-521-83539-9</bdi>.</cite></span>

</li>

</ol></div></div>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="http://www.informit.com/content/images/chap5_0130470651/elementLinks/chap5_0130470651.pdf">Common-Source Amplifier Stage</a></li></ul>

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</style><div id="Transistor_amplifiers110" style="font-size:114%;margin:0 4em"><a href="Transistor" title="Transistor">Transistor</a> <a href="Amplifier" title="Amplifier">amplifiers</a></div></th></tr><tr><td class="noviewer navbox-image" rowspan="3" style="width:1px;padding:0 2px 0 0"><div><span typeof="mw:File"></span></div></td><th scope="row" class="navbox-group" style="width:1%"><a href="Bipolar_junction_transistor" title="Bipolar junction transistor">Bipolar junction transistor</a>:</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Common_emitter" title="Common emitter">Common emitter</a></li>

<li><a href="Common_collector" title="Common collector">Common collector</a></li>

<li><a href="Common_base" title="Common base">Common base</a></li></ul>

</div></td><td class="noviewer navbox-image" rowspan="3" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Field-effect_transistor" title="Field-effect transistor">Field-effect transistor</a>:</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul>

<li><a href="Common_drain" title="Common drain">Common drain</a></li>

<li><a href="Common_gate" title="Common gate">Common gate</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Multiple transistors:</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Darlington_transistor" title="Darlington transistor">Darlington transistor</a></li>

<li><a href="Sziklai_pair" title="Sziklai pair">Sziklai pair</a></li>

<li><a href="Cascode" title="Cascode">Cascode</a></li>

<li><a href="Differential_amplifier#Long-tailed_pair" title="Differential amplifier">Long-tailed pair</a></li></ul>

</div></td></tr></tbody></table></div></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-06-01" href="https://en.wikipedia.org/wiki/?title=Common_source&oldid=1293479144">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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