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2.3 Circuits and Subcircuits 69
{VC, {"B", "E", "C", "E"}, beta / RB}
So why should we use translation rules at all The answer is that parameter value translations can
also be specified by means of delayed rules, i.e. the RuleDelayed lhs :> rhs instead of the Rule
lhs −> rhs. Since delayed rules are left unevaluated until the very moment they are needed, their
right-hand sides also contain calls to external functions which perform calculations depending on
the model parameter values. For instance, let’s define a function which, given values for beta and
RB, calculates the transconductance of a transistor by solving the formula gm RB ⩵ beta numerically
for gm, using gm ⩵ as initial guess.
In[30]:= Transconductance[b_Real, r_Real] :=
Module[ {g},
Print["Computing gm for beta = ", b, " and RB = ", r];
g /. FindRoot[g * r == b, {g, 1.0}]
]
By means of a delayed translation rule for gm we can instruct Mathematica not to execute the function
call at the time the transistor model is defined but to wait until the rule is used to compute gm for a
particular subcircuit instance.
In[31]:= Circuit[
Model[
Name −> NPNTransistor,
Selector −> ACgm,
Scope −> Global,
Ports −> {"B", "C", "E"},
Parameters −> {RB, beta},
Translation −> {gm :> Transconductance[beta, RB]},
Definition −>
Netlist[
{RB, {"B", "E"}, RB},
{VC, {"B", "E", "C", "E"}, gm}
]
]
] // ExpandSubcircuits;
If we had used an immediate rule above, gm −> Transconductance[beta, RB], Mathematica would
have already called Transconductance with the symbolic arguments beta and RB at the time
of model definition. On the other hand, the delayed rule permits Analog Insydes to replace the
arguments with instance-specific values before making the function call. This is done once per
subcircuit instance as can be seen from the following output:
In[32]:= ExpandSubcircuits[darlNumParams] // DisplayForm
Computing gm for beta = 150. and RB = 400.
Computing gm for beta = 50. and RB = 100.
Out[32]//DisplayForm=
Netlist Flat, 6 Entries:
I1, 0, 1, 1
RB$Q1, 1, 3, 400.
VC$Q1, 1, 3, 2, 3, 0.375
RB$Q2, 3, 0, 100.
VC$Q2, 3, 0, 2, 0, 0.5
Load, 0, 2, Type Resistor, Value RL, Pattern Impedance