User`s guide

Worst-Case Analysis 13
-29
conditions under which worst-case analysis works well and
those that can produce misleading results when output is not
monotonic with a variable parameter (see Figure 13-15 and
Figure 13-16).
For demonstration, the parametric analysis is run first,
generating the curve shown in Figure 13-15 and Figure 13-16.
This curve, derived using the YatX goal function shown in
Figure 13-13, illustrates the non-monotonic dependence of gain
on Rb2. To do this yourself, place the goal function definition in
a
probe.gf file in the circuit directory. Then run Probe, load all
of the AC sweeps, set up the X axis for performance analysis,
and add the following trace:
YatX(Vm([OUT]),100k)
Next, the parametric analysis is commented out and the worst-
case analysis is enabled. Two runs are made using the two
versions of the Rbmod .MODEL statement shown in the circuit
file. The model parameter, R, is a multiplier which is used to
scale the nominal value of any resistor referencing the Rbmod
model (Rb2 in this case).
The first .MODEL statement leaves the nominal value of Rb2 at
720 ohms. The sensitivity analysis increments R by a small
amount and checks its effect on Vm([OUT]). This slight
increase in R causes an increase in the base bias voltage of the
BJT, and increases the amplifier’s gain, Vm([OUT]). The worst-
case analysis correctly sets R to its minimum value for the
lowest possible Vm([OUT]) (see Figure 13-15).
The second .MODEL statement scales the nominal value of Rb2
by 1.1 to approximately 800 ohms. The gain still increases with
a small increase in R, but a larger increase in R increases the
base voltage so much that it drives the BJT into saturation and
nearly eliminates the gain. The worst-case analysis is fooled by
the sensitivity analysis into assuming that Rb2 must be
minimized to degrade the gain, but maximizing Rb2 is much
worse (see Figure 13-16). Note that even an optimizer, which
checks the local gradients to determine how the parameters
should be varied, is fooled by this circuit.
Consider a slightly different scenario: Rb2 is set to 720 ohms so
that maximizing it is not enough to saturate the BJT, but Rb1 is
variable also. The true worst case occurs when Rb2 is
YatX(1, X_value)=y1
{
1|sfxv(X_value)!1;
}
Fi
g
ure 13-13
YatX Goal
Note The YatX
g
oal function
is used on the simulation
results for the parametric
sweep (.STEP) defined in
Fi
g
ure 13-14. The resultin
g
curves are shown in
Fi
g
ure 13-15 and
Fi
g
ure 13-16.