Download - Wolfram Research

392 3. Reference Manual
Simplify the result.
In[11]:= Simplify[sag]
Out[11]=
C1 C2 R1 R2 RC RL s 2
Cbc$Q1 Cbe$Q1 Rbe$Q1 RE s 2 beta$Q1 1 Cbc$Q1 RE s
beta$Q1 R2 RE 1 C2 RL s R1 beta$Q1 RE 1 C2 RL s
R2 1 C2 RL s 1 C1 Cbc$Q1 Cbe$Q1 Rbe$Q1 RC RE s 3
beta$Q1 C1 RE s 1 Cbc$Q1 RC s
To validate the result, we compute the frequency response of the original system numerically and
compare it graphically with the approximated result.
Compute the frequency
response numerically.
In[12]:= acsweep = ACAnalysis[eqs, V$5, {f, 1, 1.0*^9}]
Out[12]=
V$5 InterpolatingFunction1., 1. 10 9 ,
Evaluate the approximated
expression numerically.
Plot the exact and
approximated functions
together.
In[13]:= sagn[s_] = sag /. dp
Out[13]=
9.7196 10 10 s 2 485.98 s 3 7.2897 10 8 s 4 3.41 10 14
1.6027 10 13 s 4.418 10 10 s 2 485.98 s 3 7.2897 10 8 s 4
In[14]:= BodePlot[acsweep, {V$5[f], sagn[2 Pi I f]},
{f, 1, 1.0*^9}, TraceNames −> {"Exact", "Approximated"}]
Magnitude (dB)
Phase (deg)
5
2.5
0
-2.5
-5
-7.5
-10
1.0E0 1.0E2 1.0E4 1.0E6 1.0E8
Frequency
-50 0
-100
-150
-200
-250
-300
-350
1.0E0 1.0E2 1.0E4 1.0E6 1.0E8
Frequency
Exact Approximated
Out[14]= Graphics
3.11.3 ApproximateMatrixEquation
ApproximateMatrixEquation[dae, var, errspec]
approximates a symbolic matrix equation dae with respect
to the output variable var and the error specification errspec
Command structure of ApproximateMatrixEquation.