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2.8 Linear Symbolic Approximation 143
too large to yield meaningful expressions for the poles. This shows that combining SBG with SAG
techniques can also be a powerful approach for computing other circuit characteristics than only
transfer functions.
In[37]:= voutsimp3n[s_] = voutsimp3s /. dpceamp
48.598 s
Out[37]=
2
1 0.047 s 147000. 470. s
Finally, we plot this simplified transfer function together with the original function to visualize the
effects of our low-and-mid-frequency approximation. The Bode plot shows that the approximation
is valid from zero frequency to the upper end of the passband at about MHz. High-frequency
effects are not described because we did not specify a design point in the frequency region beyond
the passband.
In[38]:= BodePlot[{voutexactn[2. Pi I f], voutsimp3n[2. Pi I f]},
{f, 1., 1.*10^9}, MagnitudeDisplay −> Linear,
PlotRange −> {{0, 2.5}, Automatic}]
Magnitude
2.5
2
1.5
1
0.5
1.0E0 1.0E2 1.0E4 1.0E6 1.0E8
Frequency
Phase (deg)
0
-50
-100
-150
-200
-250
-300
-350
1.0E0 1.0E2 1.0E4 1.0E6 1.0E8
Frequency
Out[38]= Graphics
2.8.5 Options for ApproximateMatrixEquation
ApproximateMatrixEquation can be called with a number of options, most of which are for
very advanced usage only and need not be changed unless there appear to be problems with the
default settings. Since all options from Options[ApproximateMatrixEquation] are documented in
Section 3.11.3, we will restrict ourselves to the discussion of the option SortingMethod. Note that
the option CompressEquations has already been introduced in Section 2.8.4.
SortingMethod
ApproximateMatrixEquation removes negligible contributions from a matrix equation term by term
following a ranking scheme which causes the term with the smallest influence on the solution to be
removed first. The term ranking is obtained by sorting the list of the individual numerical influences