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400 3. Reference Manual
Plot the exact and
approximated functions
together.
In[19]:= BodePlot[acsweep, {V$5[f], sbgn2[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[19]= Graphics
Note that matrix approximation has reduced the polynomial order of the transfer function from four
to two. Therefore, we can now solve the transfer function for the low-frequency poles.
Solve for the
low-frequency poles.
In[20]:= Solve[Denominator[v52] == 0, s]
R1 R2
Out[20]= s
C1 R1 R2 , s 1
C2 RC RL
3.11.4 CompressMatrixEquation
CompressMatrixEquation[dae, var]
compresses the matrix equation dae with respect to the
variable of interest var
Command structure of CompressMatrixEquation.
Computing a transfer function from a linear system of circuit equations A x ⩵ b requires solving
the matrix equation for one single variable x k . The values of all other variables x j , j ≠ k, are of
no interest in this context. Systems of circuit equations usually contain a significant amount of
information which is only needed to determine the irrelevant variables, and the proportion of such
information increases during the approximation process as equations are algebraically decoupled by
removing negligible terms.
To reduce the computational effort needed for solving an approximated matrix, all unnecessary
information should be discarded from the equations prior to calling Solve (Section 3.5.4), using the
function CompressMatrixEquation. This function performs a recursive search on a matrix equation
to find and delete all rows and columns which are not needed to compute the variable of interest.
Note that compressing a matrix equation is a mathematically exact operation which does not change
the value of the output variable.