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2.9 Frequency-Domain Analysis of Linear Circuits 165
In[49]:= Statistics[stacmoshfSBG]
Number of equations : 50
Number of variables : 50
Number of entries : 2500
Number of non−zero entries : 87
Complexity estimate : 48
Next, we solve for the capacitor voltage V$CL to obtain a simplified transfer function:
In[50]:= tfcmoshf = Together[V$CL
/. First[Solve[stacmoshfSBG, V$CL]]]
Out[50]=
Gds$M2 Gds$M3 gm$M1 V1 Gds$M3 gm$M1 gm$M2 V1
Gds$M2 gm$M1 gm$M3 V1 gm$M1 gm$M2 gm$M3 V1
Gds$M2 gm$M1 gm$M4 V1 gm$M1 gm$M2 gm$M4 V1
Gds$M1 Gds$M3 gm$M2 V2 Gds$M3 gm$M1 gm$M2 V2
Gds$M1 gm$M2 gm$M3 V2 gm$M1 gm$M2 gm$M3 V2
Gds$M1 gm$M2 gm$M4 V2 gm$M1 gm$M2 gm$M4 V2
Gds$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$M4 Cgd$M2 Gds$M1 Gds$M2 s
CL Gds$M1 Gds$M2 s Cgd$M2 Gds$M1 Gds$M3 s
Cgd$M4 Gds$M1 Gds$M3 s CL Gds$M1 Gds$M3 s
Cgd$M2 Gds$M2 Gds$M3 s Cgd$M4 Gds$M2 Gds$M3 s
CL Gds$M2 Gds$M3 s Cgd$M2 Gds$M3 gm$M1 s Cgd$M4 Gds$M3 gm$M1 s
CL Gds$M3 gm$M1 s Cgd$M2 Gds$M1 gm$M2 s CL Gds$M1 gm$M2 s
Cgd$M2 Gds$M3 gm$M2 s Cgd$M4 Gds$M3 gm$M2 s
CL Gds$M3 gm$M2 s Cgd$M2 Gds$M1 gm$M3 s Cgd$M4 Gds$M1 gm$M3 s
CL Gds$M1 gm$M3 s Cgd$M2 Gds$M2 gm$M3 s Cgd$M4 Gds$M2 gm$M3 s
CL Gds$M2 gm$M3 s Cgd$M2 gm$M1 gm$M3 s Cgd$M4 gm$M1 gm$M3 s
CL gm$M1 gm$M3 s Cgd$M2 gm$M2 gm$M3 s Cgd$M4 gm$M2 gm$M3 s
CL gm$M2 gm$M3 s Cgd$M4 Gds$M1 gm$M4 s Cgd$M4 Gds$M2 gm$M4 s
Cgd$M4 gm$M1 gm$M4 s Cgd$M4 gm$M2 gm$M4 s
Approximating the tableau equations has reduced the transfer function, which was initially of order
four, to the first-order formula we were looking for. In a last postprocessing step, we can remove all
remaining numerically irrelevant terms by solution-based approximation.
In[51]:= dpcmos2 = GetDesignPoint[stacmoshf];
In[52]:= tfcmoshfSAG = Simplify @
ApproximateTransferFunction[tfcmoshf, s, dpcmos2, 0.1]
Out[52]=
gm$M1 gm$M2 gm$M3 gm$M4 V1
Gds$M2 gm$M1 gm$M3 gm$M4 gm$M1 gm$M2 Gds$M4 gm$M3
Cgd$M2 gm$M3 CL gm$M3 Cgd$M4 gm$M3 gm$M4 s
From the above result we can now easily compute a formula for the pole of the transfer function by
solving the denominator of the expression for s:
In[53]:= Solve[Denominator[tfcmoshfSAG] == 0, s] // Simplify
Out[53]=
s Gds$M4 gm$M1 gm$M2 gm$M3
Gds$M2 gm$M1 gm$M3 gm$M4 gm$M1 gm$M2
Cgd$M2 gm$M3 CL gm$M3 Cgd$M4 gm$M3 gm$M4