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2.7 Time-Domain Analysis of Nonlinear Dynamic Circuits 109
in terms of these variables. The symbol tvar denotes the time variable for which the waveforms are
plotted from tvar ⩵ t to tvar ⩵ t . Zero or more options opts can be specified as sequence of rules of
the form option −> value (see Section 2.7.6).
To visualize the transient waveforms of the node voltages V$1 and V$2 in the simulated time interval
we can use TransientPlot as shown below. By default, all waveforms are superimposed in one
single graph.
In[8]:= TransientPlot[solutions, {V$1[t], V$2[t]},
{t, 0., 2.*10^−5}]
1
0.5
V$1[t]
-6
5. 10
0.00001 0.000015 0.00002 t
V$2[t]
-0.5
-1
Out[8]= Graphics
Quasi-DC Analysis
To demonstrate the influence of the capacitor C1 on the output voltage we rerun the simulation,
but this time we neglect the dynamic components of the circuit equations. This can be achieved
by setting the NDAESolve option AnalysisMode from its default value Transient to DC. The DC
analysis method replaces all time derivatives in the circuit equations by zero. Thus, inductors are
replaced by short circuits because all inductor voltages are set to zero, and capacitors are replaced
by open circuits because all capacitor currents are set to zero.
Inductor:
Capacitor:
V L t ⩵ L I Lt
t
I C t ⩵ C U Ct
t
DC
⩵ V L t ⩵ ∼ ⩵ Short Circuit
DC
⩵ I C t ⩵ ∼ ⩵ Open Circuit
Let’s apply quasi-DC analysis to our rectifier circuit by specifying the above-mentioned option in the
call to NDAESolve.
In[9]:= solDC = NDAESolve[rectifierMNA /. Vin −> Sin[10^6 t],
{t, 0., 10^−5}, AnalysisMode −> DC]
Out[9]=
V$1 InterpolatingFunction0., 0.00001, ,
V$2 InterpolatingFunction0., 0.00001, ,
I$V0 InterpolatingFunction0., 0.00001, ,
I$AC$D1 InterpolatingFunction0., 0.00001,