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2.7 Time-Domain Analysis of Nonlinear Dynamic Circuits 107
Is (saturation current) and Vt (thermal voltage) are set to Is ⩵ pA and Vt ⩵ mV. The values of
the circuit elements are assumed to be R1 ⩵ and C1 ⩵ nF.
In[1]:= 100.},
{C1, {2, 0}, Symbolic −> C1, Value −> 1.*10^−7},
{D1, {1 −> A, 2 −> C},
Model −> "Diode", Selector −> "Spice",
IS −> 1.*10^−12}
]
]
Out[2]= Circuit
Next, we use the function CircuitEquations (Section 3.5.1) to set up a system of nonlinear
differential MNA equations in the time domain. In oder to express all voltages and currents as
functions of time f t and to include time derivatives f ′ t introduced by dynamic components the
option AnalysisMode −> Transient must be specified in the function call.
AnalysisMode −> Transient implies MatrixEquation −> False, therefore the equations are written
as list of equations regardless of the current setting of MatrixEquation. CircuitEquations returns
a Transient DAEObject which can be displayed via the command DisplayForm.
In[3]:= rectifierMNA = CircuitEquations[rectifier,
AnalysisMode −> Transient];
DisplayForm[rectifierMNA]
Out[4]//DisplayForm=
I$AC$D1t I$V0t ⩵⩵ 0,
I$AC$D1t 0.01 V$2t 1. 10 7 V$2 ′ t ⩵⩵ 0,
V$1t ⩵⩵ Vin, I$AC$D1t ⩵⩵
1. 10 12 1 38.6635 V$1tV$2t 1. 10 12 V$1t V$2t,
V$1t, V$2t, I$V0t, I$AC$D1t, DesignPoint
This set of modified nodal equations is a typical DAE system. It comprises implicit differential
equations as well as both linear and nonlinear algebraic constraints.
The NDAESolve Command
Analog Insydes provides the function NDAESolve (Section 3.7.5) for solving DAE systems numerically.
NDAESolve[dae, {tvar, t , t } , params , opts]
where dae is a DC or Transient DAEObject containing the circuit equations and variables. The
argument tvar denotes the time variable for which the solutions are computed in the time interval
tvar ∈ t t , or at the time instant tvar ⩵ t . Additionally, params allows for carrying out a parametric
analysis. For possible parameter specifications please refer to Section 3.7.2. Finally, opts is a sequence
of zero or more solver options of the form option −> value (see Section 2.7.4).