The document discusses various analysis tools in MultiSIM including parameter sweep analysis and Monte Carlo analysis. Parameter sweep analysis allows the user to vary a component parameter over a range to see its effect on circuit output. Monte Carlo analysis randomly varies component parameters according to a probability distribution to simulate real-world tolerance effects across many trials. An example uses Monte Carlo analysis on a common-emitter amplifier to show that even with a 20% tolerance on transistor beta, the circuit output remains stable.

1. ECD302
Tests and Troubleshooting Tools

2. Parameter Sweep
One of the best tools to help you better
understand your circuit is the
“parameter sweep” analysis.
With this analysis, you can choose to
vary one of your component parameters
(for example, the resistance of a
resistor) over a certain range to find out
how changing this particular resistor
value would affect your circuit output.

3. Low-Pass Filter
Take for example, a very simple low-
pass filter:
Filename:
L5_cct01.msm

4. AC Analysis
Doing AC analysis will tell you that this
particular filter cuts-off at a frequency of
roughly 165 Hz:
Find the cut-off
frequency at 3 dB
below the
acceptance gain
(in this case, it is
0 dB)

5. The Capacitor and the Cut-off
Frequency…
Now, if I wished to find out the
relationship between the capacitor
value and the cut-off frequency, I could
either directly change the capacitor
value, and then re-do the AC analysis,
or, better still, I could use the parameter
sweep analysis!

6. Invoking the Parameter
Sweep analysis…
It is under the
“Simulate” menu,
under “Analyses”.

7. Choose
“Device
Parameter”
We want to
investigate
the effects of
the capacitor,
so, what else
can you
choose?
“List” means you
would like to list
all the values one
by one…
List here all the
capacitor
values you
want to
simulate with.
Select “AC analysis”, as that is the
analysis we wish to run.
Before you click “Simulate”, you should
do some further settings for your AC
analysis.

8. As usual, we should set the vertical scale of our AC
analysis as “decibel”. Unless you really want the results as
linear values…
After accepting your AC analysis settings, do not forget to click on the “output
variable” tab to specify your output node:

9. Then click “Simulate” to get the following results:
Click here for the legend.
From the output, we can see that, with smaller capacitance,
the cut-off frequency is higher.
So, we may conclude that there is an proportionally
inverse relationship between the capacitor value and the
cut-off frequency of the low-pass filter.

10. Monte Carlo
No, this is not a hidden gambling
module in MultiSIM.
The “Monte Carlo” analysis is an
analysis very similar to “parameter
sweep”, whereby you can see the
effects of varying a certain component
parameter.

11. Monte Carlo
The difference between “Monte Carlo”
and “parameter sweep” is that, in
“parameter sweep”, the user can
specify the actual variation in
component parameters. In “Monte
Carlo”, however, the variations in
component parameters is determined
randomly by the software. Since the
variations are determined “by chance”,
it is thus named “Monte Carlo”.

12. Why Monte Carlo?
Why do we need Monte Carlo if we
already have parameter sweep?
What Monte Carlo can tell us is, for a
certain circuit design that we have, if we
put the design through mass
production, what are the chances a
finished product would have an output
that deviates from our ideal output.

13. Common-Emitter Amplifier
Let us take for example, a simple
common-emitter amplifier:
Filename:
L5_cct02.msm

14. Ideal output
Ideally, the output should be as shown
below:
Black : input
Red : output

15. Effect of Tolerance in
Transistor Current Gain
Let us say, we are interested to find out,
if the transistor 2N2222A in real life has
a forward current gain, βf, that is
subjected to a tolerance of 20%, how
that would affect the output if we mass
produce the circuit using a batch of
2N2222A transistors whose βf might
have a 20% deviation.

16. Invoking Monte Carlo Analysis
Look under
“Simulate”, then
under “Analyses”:

17. Click on “Add a new tolerance”…

18. Choose bf for “ideal
forward beta”, that is,
the forward current
gain
The bf value is
presently 220
Choose “Gaussian” to
assume that the
transistor tolerance has
a normal distribution.
There will be further
discussion of this later.
We want the tolerance in
percentage, and we want it set
at 20%

19. Do the following further settings under the “Analysis Parameters” tab:
Choose “Transient
analysis” for output
equivalent to that of
oscilloscope (that is, the
output variable versus
time).
Running 25 times means we
would like to simulate the
production of 25 sets of the
common-emitter amplifier.
Each would be randomly
assigned a bf value
according to our earlier
settings.
Choose “node 8” to simulate the
voltage transient at node 8.
Then press this for
further settings for the
transient analysis…

20. With our input frequency of 100 kHz,
simulating for 0.1 ms should be
enough to show us the output
transient for at least 10 cycles.

21. Upon clicking “Simulate”, you need a bit of patience to wait till all the 25 runs are
finished. Then you would get the output and a report as shown below:

22. Result Assessment
From the results of overlapping output
transient, you can see that, for all the 25
sets of supposed finished product of CE
amplifier, their results are very closely
similar.
In fact, the worst case that happened
was a 3.35% deviation of bf value, and
even for that run, the result looks OK.

23. What does this mean?
This means the design should do just
fine when put through mass production,
even if the transistor beta has a
tolerance of 20%.

24. Gaussian distribution of
tolerance
But wait: didn’t we set the tolerance at 20%? How
come the highest deviation is only 3.35%?
Well, a normal distribution of tolerance means that
possibility of a 20% deviation happening is very low
compared to 2%, due to the bell shape of the
possibility distribution:
That is why in the 25 runs, only a couple of runs had
deviation higher than 1%.
Possibility
2% 20%
Deviation