1. [50] In the differential amplifier shown below, two resistors are used at the output for
common-mode feedback. The amplifier does not need any bias circuit to function properly.
You may assume perfect differential matching between the two halves of the circuit, and
the gm’s and ro’s of M1-M8 are known. Consider only the devices shown in the diagram,
answer the following questions.
1) Derive an expression for the differential mode voltage gain Adm, assuming that M5-M8
are biased in saturation.
2) Repeat 1) by assuming M5-M8 are operating in triode region. To make this amplifier
function properly, i.e., to obtain a large Adm, should M5-M8 be biased in saturation or
triode region?
3) Derive an expression for the common-mode gain Acm with the CMFB loop closed.
Compare this to Adm of 1) or 2). What’s your CMRR (= Adm/Acm)?
4) Consider a capacitor Cx on the node Voc. Re-derive your CMRR expression at very low
frequencies and at very high frequencies. Cx is the only capacitor in the circuit.
5) Does the bias current of the amplifier depend on the input CM level? Why or why not?
VDD
M7
M8
M3
Vi+
R
R
M4
Vo+
VoM1
M5
M2
Voc
2
M6
Vi-
2. [50] A source-degenerated CS gain stage is shown below. Consider only the devices
shown in the circuit. You may ignore the ro of M1 and assume gm1RS 1.
1) Derive an expression for the short-circuit output current noise PSD due to the thermal
noises of M1, RS and RL.
2) Derive an expression for the output voltage noise PSD.
3) Compare the noise contributions of M1 and RS by sketching them on the same graph.
Mark all important frequency points. Does the relative contribution seem to vary over
frequency? How?
RL
Vo
Vi
M1
RS
CL
CS
4