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2.8 Linear Symbolic Approximation 133
numerical reference values and then to discard all those terms which have negligible influence on
the result. In most cases, this leads to a dramatic reduction of expression complexity, thus allowing
for approximate symbolic analysis of reasonably large circuits.
1
R1
R3
V0 2 3
R2
R4
Figure 8.2: Double voltage divider
To understand how symbolic approximation works let’s look at a simple example – the transfer
function of the double voltage divider shown in Figure 8.2:
In[6]:= doubleVoltageDivider =
Netlist[
{V0, {1, 0}, V0},
{R1, {1, 2}, R1},
{R2, {2, 0}, R2},
{R3, {2, 3}, R3},
{R4, {3, 0}, R4}
]
Out[6]= NetlistRaw, 5
In[7]:= dvdmna = CircuitEquations[doubleVoltageDivider];
DisplayForm[dvdmna]
Out[8]//DisplayForm=
1
R1
1
R1
0 1
V$1 0
1 1
R1
R1
1
R2
1
R3
1
R3
0 V$2 0
. ⩵⩵
0
1
1
R3
R3
1
R4
0 V$3 0
1 0 0 0
I$V0 V0
In[9]:= tfdvd = (V$3 / V0) /. First[Solve[dvdmna, V$3]]
Out[9]=
R2 R4
R1 R2 R1 R3 R2 R3 R1 R4 R2 R4
Without any additional knowledge about the circuit this transfer function cannot be simplified much
further algebraically. Now, let’s assume that in this particular circuit the values of R1 and R2 are
approximately equal, as well as those of R3 and R4, but that R1 and R2 have much smaller values