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3.11 Linear Simplification Techniques 389
Compute the voltage
transfer function
symbolically and expand
the result.
In[6]:= solution = Solve[eqs, V$5];
v5 = Together[V$5 /. First[solution]]
Out[7]=
C2 R1 R2 RC RL s C1 RE s beta$Q1 C1 Ro$Q1 s C1 Cbc$Q1 Rbe$Q1 RE s 2
C1 Cbe$Q1 Rbe$Q1 RE s 2 C1 Cbc$Q1 Rbe$Q1 Ro$Q1 s 2
C1 Cbc$Q1 RE Ro$Q1 s 2 beta$Q1 C1 Cbc$Q1 RE Ro$Q1 s 2
C1 Cbc$Q1 Cbe$Q1 Rbe$Q1 RE Ro$Q1 s 3
R1 R2 RC R1 Rbe$Q1 RC R2 Rbe$Q1 RC R1 R2 RE R1 Rbe$Q1 RE
R2 Rbe$Q1 RE R1 RC RE R2 RC RE R1 R2 Ro$Q1 R1 Rbe$Q1 Ro$Q1
R2 Rbe$Q1 Ro$Q1 R1 RE Ro$Q1 beta$Q1 R1 RE Ro$Q1
R2 RE Ro$Q1 beta$Q1 R2 RE Ro$Q1 C1 R1 R2 Rbe$Q1 RC s
Cbc$Q1 R1 R2 Rbe$Q1 RC s Cbe$Q1 R1 R2 Rbe$Q1 RC s
C1 R1 R2 Rbe$Q1 RE s 94 C2 Cbe$Q1 R2 Rbe$Q1 RE RL Ro$Q1 s 2
C2 Cbc$Q1 R1 RC RE RL Ro$Q1 s 2 beta$Q1 C2 Cbc$Q1 R1 RC RE RL
Ro$Q1 s 2 C2 Cbc$Q1 R2 RC RE RL Ro$Q1 s 2 beta$Q1 C2 Cbc$Q1
R2 RC RE RL Ro$Q1 s 2 C1 C2 Cbc$Q1 R1 R2 Rbe$Q1 RC RE RL s 3
C1 C2 Cbe$Q1 R1 R2 Rbe$Q1 RC RE RL s 3 C1 C2 Cbe$Q1 R1 R2 Rbe$Q1
RC RE Ro$Q1 s 3 C1 Cbc$Q1 Cbe$Q1 R1 R2 Rbe$Q1 RC RE Ro$Q1 s 3
C2 Cbc$Q1 Cbe$Q1 R1 R2 Rbe$Q1 RC RE Ro$Q1 s 3
C1 C2 Cbc$Q1 R1 R2 Rbe$Q1 RC RL Ro$Q1 s 3 C2 Cbc$Q1 Cbe$Q1 R1 R2
Rbe$Q1 RC RL Ro$Q1 s 3 C1 C2 Cbe$Q1 R1 R2 Rbe$Q1 RE RL Ro$Q1 s 3
C2 Cbc$Q1 Cbe$Q1 R1 R2 Rbe$Q1 RE RL Ro$Q1 s 3
C1 C2 Cbc$Q1 R1 R2 RC RE RL Ro$Q1 s 3 beta$Q1 C1 C2 Cbc$Q1 R1 R2
RC RE RL Ro$Q1 s 3 C2 Cbc$Q1 Cbe$Q1 R1 Rbe$Q1 RC RE RL Ro$Q1 s 3
C2 Cbc$Q1 Cbe$Q1 R2 Rbe$Q1 RC RE RL Ro$Q1 s 3
C1 C2 Cbc$Q1 Cbe$Q1 R1 R2 Rbe$Q1 RC RE RL Ro$Q1 s 4
Here, the complexity estimate is identical to the true number of terms in the denominator of the
symbolic transfer function. In the general case, the estimate yields a lower bound for this number.
Determine number of
terms in the denominator
of the transfer function.
In[8]:= Length[Denominator[v5]]
Out[8]= 132
3.11.2 ApproximateTransferFunction
ApproximateTransferFunction[expr, fvar, dp, error]
approximates the transfer function expr by discarding
insignificant terms where fvar, dp, and error denote the
complex frequency variable, the design point, and the
bound for the coefficient error
Command structure of ApproximateTransferFunction.
ApproximateTransferFunction approximates a symbolic transfer function by discarding insignificant
terms from its coefficients (simplification after generation, SAG). The significance or insignificance of
a term is evaluated on the basis of numerical reference values for the symbols (the design point). For
each coefficient, the algorithm removes the numerically least significant terms until the maximum
coefficient error is reached.