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1.2 Getting Started 17
In[10]:= reference = ACAnalysis[mnaAC741, V$26, {f, 0.1, 10^6}]
Out[10]=
V$26 InterpolatingFunction0.1, 1. 10 6 ,
Next, the frequency response calculated with Analog Insydes and the simulation data imported from
PSpice are compared graphically, using the capability of the command BodePlot to display several
transfer functions within one plot.
In[11]:= BodePlot[reference, {vout741PSpice[f], V$26[f]},
{f, 0.1, 10^6}, ShowLegend −> False]
Magnitude (dB)
100
80
60
40
20
0
1.0E-1 1.0E1 1.0E3 1.0E5
Frequency
0
Phase (deg)
-20
-40
-60
-80
1.0E-1 1.0E1 1.0E3 1.0E5
Frequency
Out[11]= Graphics
The curves match perfectly in the frequency range of interest. Hence, the simplified BJT model is
sufficient for being used in the next step of the symbolic analysis flow.
Calculating the Complexity of the Symbolic Transfer Function
Recall that the task is to calculate the symbolic transfer function in order to extract a formula for the
corner frequency. Thus, at this point it is useful to estimate the complexity of the symbolic transfer
function to find out whether the number of its terms is manageable. This can be done with the help
of the function ComplexityEstimate (Section 3.11.1).
In[12]:= ComplexityEstimate[mnaAC741] // N
Out[12]= 1.61868 10 21
ComplexityEstimate returns an integer value. We use Mathematica‘s N operator to transform this
integer into a real number. The result shows that the number of terms forming the fully expanded
symbolic transfer function is greater than ⨯ and thus too large to be handled. Therefore,
we will now apply a routine which removes all those terms whose influence on the behavior of the
transfer function is negligible. This drastically reduces the complexity.