Bias Circuit

8.7 Voltage Gains Including Transistor Output
Resistance
In Project 9 we measure the gain of a "balanced" stage with drain resistors for both
transistors. The amplifier is the PMOS version of the NMOS amplifier of Fig. 8.2. We obtain an
exact Level 1 SPICE solution for the gains for both outputs. The example is used to explore the
use of a simulator for obtaining precision results to compare with simple hand calculations.
For larger λn values (NMOS), the output resistance can influence the gain and complicate the
gain expressions considerably. Here we consider the effect due to gds1 and gds2 while retaining
the effect of Rbias. In the following, the gain of the inverting input, av1, is obtained again as a
common-source stage with source resistance. The effect of gds2 on the effective source
resistance is included (input at the source of M2). The effects due to gds1 are also taken into
consideration.
The gain of the noninverting case, av2, is obtained by considering the cascade of the source
follower stage (M1) and the common-gate stage (M2), as, in effect, was done in the
development of (8.19). The source-follower gain takes into account effects from gds1 and gds2,
and the gain of the common-gate stage depends on gds2.
8.7.1 Gain of the Common-Source Stage with Transistor Output
Conductance and Source Resistor
The circuit transconductance for a common-source stage with source resistor, with the
inclusion of gds, was developed in Unit 4 [(4.18)]. This will be reviewed and reinforced here in
the form of a slightly different approach to the result. The signal circuit for this case is again
given in Fig. 8.4. Using the variables of Fig. 8.4, the circuit transconductance is Gm1 = Id1/Vi.
The object is thus to obtain a relation between these two variables.
Figure 8.4. Circuit for obtaining the gain for the inverting output with
the transistor output resistance included. Rs includes all resistance
contributions at the source.
The fraction of the current produced by the intrinsic transistor, gm1Vgs1, which flows into Rs is
Equation 8.28