13.2. Amplifier Gain of Differential Amplifier and Common-Source Stage in Cascade

In the example of Fig. 13.1, a differential stage and a common-source stage are connected in a cascade configuration; the input of the common-source stage is the output of the differential stage. The overall voltage gain is defined as a_v = v_o/v_i = v_d3/v_g1. But this is also

Equation 13.1

Therefore, the gain can be calculated by using the separate expressions considered previously for the differential amplifier stage [(8.15)] and the common-source stage [(5.5)]. This leads to

Equation 13.2

or using, from (4.5), g_m = 2I_D/V_eff,

Equation 13.3

Throughout this unit, the assumption is made that g_m1 = g_m2 and v_effn1 = V_effn2.

The gain expression neglects the transistor output resistance in the differential amplifier gain for simplicity without a great loss of accuracy, due to the relatively small value of R_D2. It also neglects the effect on the gain of the differential stage of R_bias. [R_bias and the output resistance are included in gain result (8.40), for comparison.] For a calculation of a numerical value of a representative gain, assume that V_effn1 = V_effp3 = 0.3 V, V_tno = V_tpo = 1.0 V (giving V_RD2 = 1.3 V), V_RD3 = 5 V (for V_ss = –5 V) and λp = 0.05 V^–1. The voltage-gain magnitude is |a_v| = 4.33 · 26.7 = 116. We compare this below with an amplifer that has better bias stability but which loses gain in a trade-off.