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104 2. Tutorial
In[14]:= mnaeqsfa = CircuitEquations[
bjtbias /. BJTModel −> EbersMollForwardActive,
AnalysisMode −> DC, ElementValues −> Symbolic];
DisplayForm[mnaeqsfa]
Out[15]//DisplayForm=
V$1 V$3
I$RB I$VCC
⩵⩵ 0, I$BC$Q1 I$BE$Q1 I$RB ⩵⩵ 0,
RC
V$1 V$3
I$BC$Q1
⩵⩵ 0, V$1 ⩵⩵ VCC,
RC
I$RB RB V$1 V$2 ⩵⩵ 0, I$BC$Q1 ⩵⩵ 2.4 10 15 38.6676 V$2 ,
I$BE$Q1 ⩵⩵ 2.424 10 15 38.6676 V$2 ,
V$1, V$2, V$3, I$VCC, I$RB, I$BC$Q1, I$BE$Q1,
DesignPoint VCC 12., RB 500000., RC 4000.
This system of equations can be solved by Analog Insydes’ numerical root finding function NDAESolve
(Section 3.7.5), which starts from an initial guess for the values of the variables. By default, initial
values of for all unknowns are chosen which is very often close enough to ensure convergence.
In[16]:= NDAESolve[mnaeqsfa, {t, 0}]
Out[16]=
V$1 12., V$2 0.712996, V$3 2.9704, I$VCC 0.00227997,
I$RB 0.000022574, I$BC$Q1 0.0022574, I$BE$Q1 0.00227997
From the result we can immediately read off the operating point. We have
VBE ⩵ V$2 ⩵ V
VCE ⩵ V$3 ⩵ V
IB ⩵ I$RB ⩵ mA
IC ⩵ I$BC$Q1 ⩵ mA
Next, we repeat the same calculation for RB ⩵ k using the command UpdateDesignPoint
(Section 3.6.14) to alter the numeric element value for RB.
In[17]:= mnaeqsfa = UpdateDesignPoint[mnaeqsfa, RB −> 1.*10^5];
NDAESolve[mnaeqsfa, {t, 0}]
Out[18]=
V$1 12., V$2 0.75452, V$3 32.9819, I$VCC 0.0113579,
I$RB 0.000112455, I$BC$Q1 0.0112455, I$BE$Q1 0.0113579
This time, we obtain a physically nonsensical value of V for VCE which indicates that our
initial assumption about the operating condition of Q1 has been violated. Indeed, for RB ⩵ k,
Q1 operates in deep saturation. We must therefore select the full Ebers-Moll model to take these
effects into account.