Editing Common source

{{Short description|Electronic amplifier circuit type}}
{{More footnotes|date=January 2018}}

[[Image:N-channel JFET common source.svg|frame|Figure 1: Basic N-channel JFET common-source circuit (neglecting [[biasing]] details).]]
[[Image:N-channel JFET common source degeneration.svg|frame|Figure 2: Basic N-channel JFET common-source circuit with {{Clarify|date=May 2025|text=source degeneration}}.]]
In [[electronics]], a '''common-source''' [[electronic amplifier|amplifier]] is one of three basic single-stage [[field-effect transistor]] (FET) amplifier topologies, typically used as a [[Electronic amplifier#Ideal|voltage or transconductance]] [[amplifier]]. The easiest way to tell if a FET is common source, [[common drain]], or [[common gate]] 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 [[bipolar junction transistor]] circuit may be viewed as a transconductance amplifier or as a voltage amplifier. (See [[Electronic amplifier#Ideal|classification of amplifiers]]). 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 [[Ohm's law]].  However, the FET device's output resistance typically is not high enough for a reasonable transconductance amplifier ([[Electronic amplifier#Ideal|ideally infinite]]), nor low enough for a decent voltage amplifier ([[Electronic amplifier#Ideal|ideally zero]]). 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 ([[common-drain]] or CD stage), or a current follower ([[common-gate]] or CG stage), to obtain more favorable output and frequency characteristics. The CS–CG combination is called a [[cascode]] amplifier.


== Characteristics ==

At low frequencies and using a simplified [[hybrid-pi model]] (where the output resistance due to channel length modulation is not considered), the following closed-loop [[small-signal model|small-signal]] characteristics can be derived.

<div align="center">
{| class="wikitable" style="text-align:center"
!  !!style="width:2in"|Definition !!style="width:2in"|Expression 
|-
! '''[[Gain (electronics)|Current gain]]'''
|<math>A_\text{i} \triangleq \frac{i_\text{out}}{i_\text{in}}\,</math>
|<math>\infty\,</math>
|-
! '''[[Gain (electronics)|Voltage gain]]'''
|<math>A_\text{v} \triangleq \frac{v_\text{out}}{v_\text{in}}\,</math>
|<math>\begin{matrix}-\frac {g_\mathrm{m} R_\text{D}}{1+g_\mathrm{m}R_\text{S}}\end{matrix}\,</math> 
|-
! '''[[Input impedance]]'''
|<math>r_\text{in} \triangleq \frac{v_\text{in}}{i_\text{in}}\,</math>
|<math>\infty\,</math>
|-
! '''[[Output impedance]]'''
|<math>r_\text{out} \triangleq \frac{v_\text{out}}{i_\text{out}}</math>
|<math>R_\text{D}\,</math>
|}
</div>

===Bandwidth===

[[Image:Common source with active load.PNG|thumbnail|200px|Figure 3: Basic N-channel MOSFET common-source amplifier with [[active load]] ''I''<sub>D</sub>.]]
[[Image:Small-signal common source with C gd.PNG|thumbnail|250px|Figure 4: Small-signal circuit for N-channel MOSFET common-source amplifier.]]
[[Image:Small-signal common source with Miller cap.PNG|thumbnail|300px|Figure 5: Small-signal circuit for N-channel MOSFET common-source amplifier using Miller's theorem to introduce Miller capacitance ''C''<sub>M</sub>.]]
Bandwidth of common-source amplifier tends to be low, due to high capacitance resulting from the [[Miller effect]]. The gate-drain capacitance is effectively multiplied by the factor <math>1+|A_\text{v}|\,</math>, thus increasing the total input capacitance and lowering the overall bandwidth.

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

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

::<math>\  i_\mathrm{M} = j \omega C_\mathrm{M} v_\mathrm{GS} = j \omega C_\mathrm{M} v_\mathrm{G}</math> ,

to the current drawn from the input by capacitor ''C''<sub>gd</sub> in Figure 4, namely ''j&omega;C''<sub>gd</sub> ''v''<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:

::<math> 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)</math> .

Usually the frequency dependence of the gain ''v''<sub>D</sub> / ''v''<sub>G</sub> is unimportant for frequencies even somewhat above the corner frequency of the amplifier, which means a low-frequency [[hybrid-pi model]] is accurate for determining ''v''<sub>D</sub> / ''v''<sub>G</sub>. This evaluation is ''Miller's approximation''<ref name=Spencer>
{{cite book 
|author1=R.R. Spencer |author2=M.S. Ghausi |title=Introduction to electronic circuit design
|year=2003
|page=533 
|publisher=Prentice Hall/Pearson Education, Inc. 
|location=Upper Saddle River NJ 
|isbn=0-201-36183-3
|url=http://worldcat.org/isbn/0-201-36183-3}}
</ref> and provides the estimate (just set the capacitances to zero in Figure 5):

::<math> \frac {v_\mathrm{D}} {v_\mathrm{G}} \approx -g_\mathrm{m} (r_\mathrm{O} \parallel R_\mathrm{L})</math> ,

so the Miller capacitance is

::<math> C_\mathrm{M} = C_\mathrm{gd} \left( 1+g_\mathrm{m} (r_\mathrm{O} \parallel R_\mathrm{L})\right) </math> .

The gain ''g''<sub>m</sub> (''r''<sub>O</sub> || ''R''<sub>L</sub>) is large for large ''R''<sub>L</sub>, so even a small parasitic capacitance ''C''<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 [[common-gate]] (current-follower) stage to make a [[cascode]] 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 (''R''<sub>L</sub> ≈ 1 / ''g''<sub>m</sub> ≈ ''V''<sub>ov</sub> / (2''I''<sub>D</sub>) ; see [[common gate]]). Small ''R''<sub>L</sub> reduces ''C''<sub>M</sub>.<ref name=Lee>
{{cite book 
|author=Thomas H Lee
|title=The design of CMOS radio-frequency integrated circuits
|year= 2004
|edition=Second 
|publisher=Cambridge University Press 
|location=Cambridge UK 
|isbn=0-521-83539-9
|url=http://worldcat.org/isbn/0-521-83539-9
|pages=246&ndash;248}}
</ref> The article on the [[common emitter|common-emitter amplifier]] discusses other solutions to this problem.

Returning to Figure 5, the gate voltage is related to the input signal by [[voltage division]] as:

::<math> 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}} </math> .

The [[Bandwidth (signal processing)|bandwidth]] (also called the 3&nbsp;dB frequency) is the frequency where the signal drops to 1/ {{radic|2}} of its low-frequency value.  (In [[decibel]]s, dB({{radic|2}}) = 3.01&nbsp;dB).  A reduction to 1/ {{radic|2}}  occurs when ''ωC''<sub>M</sub> ''R''<sub>A</sub> = 1, making the input signal at this value of ''ω'' (call this value ''ω''<sub>3&nbsp;dB</sub>, say) ''v''<sub>G</sub> = ''V''<sub>A</sub> / (1+j). The [[Complex number#Operations|magnitude]] of (1+j) = {{radic|2}}. As a result, the 3&nbsp;dB frequency ''f''<sub>3&nbsp;dB</sub> = ''&omega;''<sub>3&nbsp;dB</sub> / (2π) is:

::<math> 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})]}</math> .

If the parasitic gate-to-source capacitance ''C''<sub>gs</sub> is included in the analysis, it simply is parallel with ''C''<sub>M</sub>, so 
::<math> 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}))]}</math> .

Notice that ''f''<sub>3&nbsp;dB</sub> becomes large if the source resistance ''R''<sub>A</sub> is small, so the Miller amplification of the capacitance has little effect upon the bandwidth for small ''R''<sub>A</sub>. This observation suggests another circuit trick to increase bandwidth: add a [[common-drain]] (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 ''R''<sub>A</sub> of the original driver.<ref name=Lee2>
{{cite book 
|author=Thomas H Lee
|title=pp.&nbsp;251&ndash;252
|year=2004
|isbn=0-521-83539-9
|url=http://worldcat.org/isbn/0-521-83539-9}}
</ref>

Examination of the output side of the circuit in Figure 2 enables the frequency dependence of the gain ''v''<sub>D</sub> / ''v''<sub>G</sub> to be found, providing a check that the low-frequency evaluation of the Miller capacitance is adequate for frequencies ''f'' even larger than ''f''<sub>3&nbsp;dB</sub>. (See article on [[pole splitting]] to see how the output side of the circuit is handled.)

== See also ==

*[[Miller effect]]
*[[Pole splitting]]
*[[Common gate]]
*[[Common drain]]
*[[Common base]]
*[[Common emitter]]
*[[Common collector]]

==References==
{{reflist}}

== External links ==
* [http://www.informit.com/content/images/chap5_0130470651/elementLinks/chap5_0130470651.pdf Common-Source Amplifier Stage]

{{Transistor amplifiers}}

{{DEFAULTSORT:Common Source}}
[[Category:Single-stage transistor amplifiers]]