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130 2. Tutorial
2.8 Linear Symbolic Approximation
2.8.1 Introduction to Symbolic Approximation
The Complexity Problem
If you have previous experiences with symbolic circuit analysis programs or if you have done some
experiments with Analog Insydes before reading this chapter you may have already become aware
of a major obstacle which is inherent to symbolic computations. While the carefully selected example
circuits analyzed in the preceding chapters all yield transfer functions of no more than a few lines
in length minor modifications such as adding an element or two to the circuit or choosing a slightly
more complex transistor model may already lead to expressions of incredible size. In fact, expression
complexity increases exponentially with the number of symbols in your circuit descriptions, allowing
for full symbolic analysis of very small circuits only.
6
V1
R1
100k
RC
2.2k
C2
3 5
C1
1u
1 2
VCC
Q1
100n 4 RL Vout
47k
R2 RE
47k
1k
Figure 8.1: Common-emitter amplifier with coupling capacitors and resistive load
Let us demonstrate this effect by computing the symbolic voltage transfer function of the commonemitter
amplifier displayed in Figure 8.1. This circuit is essentially the same as the common-emitter
amplifier from Section 2.3.1 (see Figure 3.1) except that coupling capacitors and a resistive load have
been added.