8.6. Common-Mode Voltage Gain

The common-mode gain is defined for the same voltage applied simultaneously to both inputs. The output must be the same at either output terminal (again assuming that g_m1 = g_m2 and R_D1 = R_D2). For example, for the output V_d2, the gain can be determined by a superposition of gains, inverting (input, V_g2) and noninverting (input, V_g1), with R_D2 in both equations.

Using (8.19) (noninverting) and (8.20) (inverting), the gain for finite R_bias is, accordingly,

Equation 8.25

which is

Equation 8.26

The result is that of a common-source stage with source resistance 2R_bias. This is intuitively correct as taken from the half-circuit viewpoint, where the circuit is completely symmetrical. The input from either side looks at a common-source stage except that the opposite side is contributing an equal amount of source current, thus giving an effective source resistance equal to twice the actual value. A valid approximate form for well-designed circuits (in terms of common-mode gain) is

Equation 8.27

The same result applies to the case of the output taken at the opposite drain, with the substitution of R_D1 for R_D2. Using the circuit values following (8.23) plus R_bias = 85 kΩ, a_vcm ≈ –0.3. Note that this result in combination with the gain from (8.23) would indicate that this is not a particularly good design. The goal is for a_vd >> a_vcm.