Bias Circuit

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 av = vo/vi = vd3/vg1. 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), gm = 2ID/Veff,
Equation 13.3
Throughout this unit, the assumption is made that gm1 = gm2 and veffn1 = Veffn2.
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 RD2. It also
neglects the effect on the gain of the differential stage of Rbias. [Rbias 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 Veffn1 = Veffp3 = 0.3 V, Vtno = Vtpo = 1.0 V (giving VRD2 = 1.3
V), VRD3 = 5 V (for Vss = –5 V) and λp = 0.05 V –1 . The voltage-gain magnitude is |av| = 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.