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2.9 Frequency-Domain Analysis of Linear Circuits 151
In[9]:= tfcmos = Together[
solcmos /. {V1 −> 1, V2 −> 0, IBIAS −> 0, VDD −> 0}]
Out[9]=
Gds$M2 Gds$M3 gm$M1 Gds$M3 gm$M1 gm$M2 Gds$M2 gm$M1 gm$M3
gm$M1 gm$M2 gm$M3 Gds$M2 gm$M1 gm$M4 gm$M1 gm$M2 gm$M4
Gds$M1 Gds$M2 Gds$M3 Gds$M1 Gds$M2 Gds$M4 Gds$M1 Gds$M3
Gds$M4 Gds$M2 Gds$M3 Gds$M4 Gds$M2 Gds$M3 gm$M1
Gds$M3 Gds$M4 gm$M1 Gds$M1 Gds$M4 gm$M2 Gds$M3 Gds$M4 gm$M2
Gds$M1 Gds$M2 gm$M3 Gds$M1 Gds$M4 gm$M3 Gds$M2 Gds$M4 gm$M3
Gds$M2 gm$M1 gm$M3 Gds$M4 gm$M1 gm$M3 Gds$M4 gm$M2 gm$M3
Gds$M1 Gds$M2 gm$M4 Gds$M2 gm$M1 gm$M4 CL Gds$M1 Gds$M2 s
CL Gds$M1 Gds$M3 s CL Gds$M2 Gds$M3 s CL Gds$M3 gm$M1 s
CL Gds$M1 gm$M2 s CL Gds$M3 gm$M2 s CL Gds$M1 gm$M3 s
CL Gds$M2 gm$M3 s CL gm$M1 gm$M3 s CL gm$M2 gm$M3 s
Note that alternatively one could use the functions UpdateDesignPoint (Section 3.6.14) and
ApplyDesignPoint (Section 3.6.13) to modify or insert design-point values.
Computing Differential Gains
Similarly, we can compute the differential gain of the amplifier by splitting up the input signal into
two equal parts with opposite phase, i.e. V1 ⩵ and V2 ⩵ .
In[10]:= diffgain = Together[
solcmos /. {V1 −> 1/2, V2 −> −1/2, IBIAS −> 0, VDD −> 0}]
Out[10]=
Gds$M2 Gds$M3 gm$M1 Gds$M1 Gds$M3 gm$M2 2 Gds$M3 gm$M1 gm$M2
Gds$M2 gm$M1 gm$M3 Gds$M1 gm$M2 gm$M3 2 gm$M1 gm$M2 gm$M3
Gds$M2 gm$M1 gm$M4 Gds$M1 gm$M2 gm$M4 2 gm$M1 gm$M2 gm$M4
2 Gds$M1 Gds$M2 Gds$M3 Gds$M1 Gds$M2 Gds$M4
Gds$M1 Gds$M3 Gds$M4 Gds$M2 Gds$M3 Gds$M4
Gds$M2 Gds$M3 gm$M1 Gds$M3 Gds$M4 gm$M1
Gds$M1 Gds$M4 gm$M2 Gds$M3 Gds$M4 gm$M2 Gds$M1 Gds$M2
gm$M3 Gds$M1 Gds$M4 gm$M3 Gds$M2 Gds$M4 gm$M3
Gds$M2 gm$M1 gm$M3 Gds$M4 gm$M1 gm$M3 Gds$M4 gm$M2 gm$M3
Gds$M1 Gds$M2 gm$M4 Gds$M2 gm$M1 gm$M4 CL Gds$M1 Gds$M2 s
CL Gds$M1 Gds$M3 s CL Gds$M2 Gds$M3 s CL Gds$M3 gm$M1 s
CL Gds$M1 gm$M2 s CL Gds$M3 gm$M2 s CL Gds$M1 gm$M3 s
CL Gds$M2 gm$M3 s CL gm$M1 gm$M3 s CL gm$M2 gm$M3 s
From this formula, the DC gain can be obtained by setting the complex Laplace frequency s ⩵ :
In[11]:= diffgainDC = diffgain /. s −> 0
Out[11]=
Gds$M2 Gds$M3 gm$M1 Gds$M1 Gds$M3 gm$M2 2 Gds$M3 gm$M1 gm$M2
Gds$M2 gm$M1 gm$M3 Gds$M1 gm$M2 gm$M3 2 gm$M1 gm$M2 gm$M3
Gds$M2 gm$M1 gm$M4 Gds$M1 gm$M2 gm$M4 2 gm$M1 gm$M2 gm$M4
2 Gds$M1 Gds$M2 Gds$M3 Gds$M1 Gds$M2 Gds$M4 Gds$M1 Gds$M3
Gds$M4 Gds$M2 Gds$M3 Gds$M4 Gds$M2 Gds$M3 gm$M1
Gds$M3 Gds$M4 gm$M1 Gds$M1 Gds$M4 gm$M2 Gds$M3 Gds$M4
gm$M2 Gds$M1 Gds$M2 gm$M3 Gds$M1 Gds$M4 gm$M3
Gds$M2 Gds$M4 gm$M3 Gds$M2 gm$M1 gm$M3 Gds$M4 gm$M1 gm$M3
Gds$M4 gm$M2 gm$M3 Gds$M1 Gds$M2 gm$M4 Gds$M2 gm$M1 gm$M4