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2.3 Circuits and Subcircuits 57
In[7]:= eqAmpSimple = CircuitEquations[flatAmpSimple];
DisplayForm[eqAmpSimple]
Out[8]//DisplayForm=
1
R1
1
R2
1
R1
0 0 0 1 0 1
1 1
R1
R1
1
RC
1
RC
0 0 0 1 0
0 1 1
RC
RC
0 0 0 0 beta
1
0 0 0
RB
1
RE
1
RB
0 0 beta .
0 0 0
1 1
RB
RB
0 0 1
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
1 0 0 0 1 0 0 0
V$1 0
V$2
0
V$3
0
V$4
0
⩵⩵
V$X$Q1 0
I$V1 1
I$VCC 0
IC$CC$Q1 0
To compute the small-signal voltage transfer function we must solve the MNA equations for the
node voltage V$3 at the output node 3.
In[9]:= v3 = Solve[eqAmpSimple, V$3]
beta RC
Out[9]= V$3
RB RE beta RE
The following command extracts the symbolic transfer function expression from the return value of
Solve.
In[10]:= vtf = V$3 /. First[v3]
beta RC
Out[10]=
RB RE beta RE
Now, let’s see what happens when we make the (usually realistic) assumption that the transistor
current gain is very large:
In[11]:= Limit[vtf, beta −> Infinity]
Out[11]= RC
RE
The above result is indeed identical to the well-known approximate formula for the voltage gain of
a common-emitter amplifier. Doing the same calculations for the other transistor model shall be left
to the reader as an exercise.