Download - Wolfram Research

2.8 Linear Symbolic Approximation 135
In[13]:= dvdmna = CircuitEquations[doubleVoltageDivider,
ElementValues −> Symbolic]
Out[13]= DAEAC, 4 4
In[14]:= designpoint = GetDesignPoint[dvdmna]
Out[14]=
V0 1., R1 10., R2 10., R3 1000., R4 1000.
With these reference values we can evaluate the symbolic expression numerically. Below, we apply
the function HoldForm to the Plus operation which prevents the denominator from being evaluated
to a single number.
In[15]:= tfdvd /. Plus −> HoldForm[Plus] /. designpoint
Out[15]=
10000.
Plus100., 10000., 10000., 10000., 10000.
By comparing the individual numerical values we, as well as a computer, can now clearly see that
the first argument of the Plus expression, corresponding to the term R1R2, contributes only to
the total value of the denominator. The term can thus be safely removed from the transfer function
if we allow for an error of, say, or less in the design point.
2.8.2 Solution-Based Symbolic Approximation
Groups of Symbolic Approximation Techniques
Symbolic approximation techniques can be divided into three different groups of methods which
perform Simplifications Before, During, or After the Generation of symbolic formulas (SBG, SDG,
and SAG methods). The approach discussed above is thus an SAG, or solution-based, method
because we computed the complete transfer function first and then simplified it. While the principle
behind this SAG technique was demonstrated on the transfer function of a non-dynamic system it
can be applied to general transfer functions containing powers of the frequency variable s as well.
In this case, all symbolic coefficients of the different powers of s are simplified separately up to a
given maximum error.
Approximating Transfer Functions
Analog Insydes provides the function ApproximateTransferFunction (Section 3.11.2) for solutionbased
symbolic approximation. The argument sequence is
ApproximateTransferFunction[tfunc, fvar, dp, maxerr]
where tfunc is a rational transfer function in the frequency variable fvar, dp is a design-point
specification, and maxerr is the maximum relative error of the simplified coefficients of fvar in the
design point. The design point must be specified as a list of rules which associate numerical values
with the symbols in tfunc, and maxerr is a real number between and .