Borel's lemma

Figure 1: Basic N-channel common-gate circuit (neglecting biasing details); current source I_D represents an active load; signal is applied at node V_in and output is taken from node V_out; output can be current or voltage

In electronics, a common-gate amplifier is one of three basic single-stage field-effect transistor (FET) amplifier topologies, typically used as a current buffer or voltage 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 ground, or "common," hence its name. The analogous bipolar junction transistor circuit is the common-base amplifier.

Applications

This configuration is used less often than the common source or source follower. 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 and potentially has lower noise. Gray and Meyer provide a general reference for this circuit.

Low-frequency characteristics

Figure 2: Small-signal low-frequency hybrid-pi model for amplifier driven by a Norton signal source

At low frequencies and under small-signal conditions, the circuit in Figure 1 can be represented by that in Figure 2, where the hybrid-pi model for the MOSFET has been employed.

Figure 3: Hybrid pi model with test source i_x at output to find output resistance

The amplifier characteristics are summarized below in Table 1. The approximate expressions use the assumptions (usually accurate) r_O >> R_L and g_mr_O >> 1.

Table 1	Definition	Expression	Approximate expression
Short-circuit current gain	${A_{i}}={i_{\mathrm {out} } \over i_{\mathrm {S} }}{\Big |}_{R_{L}=0}$	$\ 1$	$\ 1$
Open-circuit voltage gain	${A_{v}}={v_{\mathrm {out} } \over v_{\mathrm {S} }}{\Big |}_{R_{L}=\infty }$	${\begin{matrix}((g_{m}+g_{mb})r_{\mathrm {O} }+1){\frac {R_{L}}{r_{O}+R_{L}}}\end{matrix}}$	$\ g_{m}R_{L}$
Input resistance	$R_{\mathrm {in} }={\frac {v_{S}}{i_{S}}}$	${{R_{L}+r_{O}} \over {(g_{m}+g_{mb})r_{O}+1}}$	${\begin{matrix}{\frac {1}{g_{m}}}\end{matrix}}$
Output resistance	$R_{\mathrm {out} }={\frac {v_{x}}{i_{x}}}$	$\ (1+(g_{m}+g_{mb})r_{O})R_{S}+r_{O}$	$r_{O}$

Note: Parallel lines (||) indicate components in parallel.

In general the overall voltage/current gain may be substantially less than the open/short circuit gains listed above (depending on the source and load resistances) due to the loading effect.

Closed circuit voltage gain

Taking input and output loading into consideration, the closed circuit voltage gain (that is, the gain with load R_L and source with resistance R_S both attached) of the common gate can be written as:

${A_{\mathrm {v} }}\approx {\begin{matrix}{\frac {g_{m}R_{\mathrm {L} }}{1+g_{m}R_{S}}}\end{matrix}}$ ,

which has the simple limiting forms

$A_{\mathrm {v} }={\begin{matrix}{\frac {R_{L}}{R_{S}}}\end{matrix}}\ \ \mathrm {or} \ \ A_{\mathrm {v} }=g_{m}R_{L}$,

depending upon whether g_mR_S is much larger or much smaller than one.

In the first case the circuit acts as a current follower, as understood as follows: for R_S >> 1/g_m the voltage source can be replaced by its Norton equivalent with Norton current v_Thév / R_S and parallel Norton resistance R_S. Because the amplifier input resistance is small, the driver delivers by current division a current v_Thév / R_S to the amplifier. The current gain is unity, so the same current is delivered to the output load R_L, producing by Ohm's law an output voltage v_out = v_ThévR_L / R_S, that is, the first form of the voltage gain above.

In the second case R_S << 1/g_m 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 amplifier often is used instead. The cascode places a common-source amplifier between the voltage driver and the common-gate circuit to permit voltage amplification using a driver with R_S >> 1/g_m.

References

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See also

• Electronic amplifier variables
• Two-port networks
• Common drain
• Common source
• Common base
• Common emitter
• Common collector

External links

• A 24GHz CMOS Front-end