# Common gate > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Common_gate > Markdown URL: https://mediated.wiki/source/Common_gate.md > Source: https://en.wikipedia.org/wiki/Common_gate > Source revision: 1240759877 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) Electronic amplifier circuit type This article includes a list of general references, but it lacks sufficient corresponding inline citations. Please help to improve this article by introducing more precise citations. (April 2009) (Learn how and when to remove this message) Figure 1: Basic N-channel common-gate circuit (neglecting [biasing](/source/Biasing) details); current source *ID* represents an [active load](/source/Active_load); signal is applied at node *Vin* and output is taken from node *Vout*; output can be current or voltage In [electronics](/source/Electronics), a **common-gate** [amplifier](/source/Electronic_amplifier) is one of three basic single-stage [field-effect transistor](/source/Field-effect_transistor) (FET) amplifier topologies, typically used as a [current](/source/Electric_current) [buffer](/source/Buffer_amplifier) or [voltage](/source/Voltage) [amplifier](/source/Amplifier). In this circuit, the source terminal of the transistor serves as the input, the drain is the output, and the gate is connected to some DC biasing voltage (i.e. an AC ground), or "common," hence its name. The analogous [bipolar junction transistor](/source/Bipolar_junction_transistor) circuit is the [common-base amplifier](/source/Common_base). ## Applications This configuration is used less often than the [common source](/source/Common_source) or [source follower](/source/Source_follower). However, it can be combined with common source amplifiers to create [cascode](/source/Cascode) configurations. It is useful in, for example, CMOS RF receivers, especially when operating near the frequency limitations of the FETs; it is desirable because of the ease of [impedance matching](/source/Impedance_matching) and potentially has lower [noise](/source/Electronic_noise). Gray and Meyer[1] provide a general reference for this circuit. ## Low-frequency characteristics Figure 2: Small-signal low-frequency [hybrid-pi model](/source/Hybrid-pi_model) for amplifier driven by a [Norton signal source](/source/Norton's_theorem) At low frequencies and under [small-signal](/source/Small-signal) conditions, the circuit in Figure 1 can be represented by that in Figure 2, where the [hybrid-pi model](/source/Hybrid-pi_model) for the MOSFET has been employed. Figure 3: Hybrid pi model with test source *ix* at output to find [output resistance](/source/Output_resistance) The amplifier characteristics are summarized below in Table 1. The approximate expressions use the assumptions (usually accurate) *rO* >> *RL* and *gmrO* >> 1. Table 1 Definition Expression Approximate expression Short-circuit current gain A i = i o u t i S | R L = 0 {\displaystyle {A_{i}}={i_{\mathrm {out} } \over i_{\mathrm {S} }}{\Big |}_{R_{L}=0}} 1 {\displaystyle \ 1} 1 {\displaystyle \ 1} Open-circuit voltage gain A v = v o u t v S | R L = ∞ {\displaystyle {A_{v}}={v_{\mathrm {out} } \over v_{\mathrm {S} }}{\Big |}_{R_{L}=\infty }} ( ( g m + g m b ) r O + 1 ) R L r O + R L {\displaystyle {\begin{matrix}((g_{m}+g_{mb})r_{\mathrm {O} }+1){\frac {R_{L}}{r_{O}+R_{L}}}\end{matrix}}} g m R L {\displaystyle \ g_{m}R_{L}} Input resistance R i n = v S i S {\displaystyle R_{\mathrm {in} }={\frac {v_{S}}{i_{S}}}} R L + r O ( g m + g m b ) r O + 1 {\displaystyle {{R_{L}+r_{O}} \over {(g_{m}+g_{mb})r_{O}+1}}} 1 g m {\displaystyle {\begin{matrix}{\frac {1}{g_{m}}}\end{matrix}}} Output resistance R o u t = v x i x {\displaystyle R_{\mathrm {out} }={\frac {v_{x}}{i_{x}}}} ( 1 + ( g m + g m b ) r O ) R S + r O {\displaystyle \ (1+(g_{m}+g_{mb})r_{O})R_{S}+r_{O}} ( g m r O ) R S {\displaystyle (g_{m}r_{O})R_{S}} In general, the overall voltage/current [gain](/source/Gain_(electronics)) may be substantially less than the open/short circuit gains listed above (depending on the source and load resistances) due to the [loading effect](/source/Loading_effect). ### Closed circuit voltage gain Taking input and output loading into consideration, the closed circuit voltage gain (that is, the gain with load *RL* and source with resistance *RS* both attached) of the common gate can be written as: - A v ≈ g m R L 1 + g m R S {\displaystyle {A_{\mathrm {v} }}\approx {\begin{matrix}{\frac {g_{m}R_{\mathrm {L} }}{1+g_{m}R_{S}}}\end{matrix}}} , which has the simple limiting forms - A v = R L R S o r A v = g m R L {\displaystyle A_{\mathrm {v} }={\begin{matrix}{\frac {R_{L}}{R_{S}}}\end{matrix}}\ \ \mathrm {or} \ \ A_{\mathrm {v} }=g_{m}R_{L}} , depending upon whether *gmRS* is much larger or much smaller than one. In the first case the circuit acts as a current follower, as understood as follows: for *RS* >> 1/*gm* the voltage source can be replaced by its [Norton equivalent](/source/Norton's_theorem) with Norton current *vThév / RS* and parallel Norton resistance *RS*. Because the amplifier input resistance is small, the driver delivers by [current division](/source/Current_division) a current *vThév / RS* to the amplifier. The current gain is unity, so the same current is delivered to the output load *RL*, producing by Ohm's law an output voltage *vout = vThévRL / RS*, that is, the first form of the voltage gain above. In the second case *RS* << 1/*gm* and the Thévenin representation of the source is useful, producing the second form for the gain, typical of voltage amplifiers. Because the input impedance of the common-gate amplifier is very low, the [cascode](/source/Cascode) amplifier often is used instead. The cascode places a [common-source](/source/Common-source) amplifier between the voltage driver and the common-gate circuit to permit voltage amplification using a driver with *RS >> 1/gm*. ## See also - [Electronic amplifier variables](/source/Electronic_amplifier#Ideal) - [Two-port networks](/source/Two-port_network#Example:_common_base_amplifier) - [Common drain](/source/Common_drain) - [Common source](/source/Common_source) - [Common base](/source/Common_base) - [Common emitter](/source/Common_emitter) - [Common collector](/source/Common_collector) ## References 1. **[^](#cite_ref-Gray-Meyer_1-0)** Paul R. Gray; Paul J. Hurst; Stephen H. Lewis; Robert G. Meyer (2001). *Analysis and Design of Analog Integrated Circuits* (4th ed.). New York: Wiley. pp. 186–191. [ISBN](/source/ISBN_(identifier)) [0-471-32168-0](https://en.wikipedia.org/wiki/Special:BookSources/0-471-32168-0). ## External links - [A 24GHz CMOS Front-end](http://chic.caltech.edu/publication/a-24ghz-cmos-front-end/) v t e Transistor amplifiers Bipolar junction transistor: Common emitter Common collector Common base Field-effect transistor: Common source Common drain Common gate Multiple transistors: Darlington transistor Sziklai pair Cascode Long-tailed pair --- Adapted from the Wikipedia article [Common gate](https://en.wikipedia.org/wiki/Common_gate) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Common_gate?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.