Worst Case Analysis is a statistical technique that uses a “what if” approach to provide a practical result and its primary purpose is to identify the most critical components of a circuit. This analysis helps you answer the question: What will be the worst possible effects of variations in component parameters?
In Worst Case Analysis, components are varied one at a time. This allows you to calculate the sensitivity of an output variable for each component in the circuit. Finally, after each component has been varied, a final run is done with all the components parameters. This gives the worst case output.
Multisim performs Worst Case Analysis using the following process:
Assumptions: Applied to an analog circuit, DC and small-signal. Models are linearized.
Consider the Wien-bridge oscillator circuit shown in Figure 1. The feedback to the non-inverting pin is designed to stabilize the amplitude of the oscillator, thus R1-R4 must be chosen carefully to ensure this circuit will oscillate. The following two conditions must be met:
Figure 1. Wien-bridge oscillator circuit.
In this example you will use Worst Case Analysis to determine if the circuit will continue to oscillate under the worst conditions.
Complete the following steps to configure and run a Worst Case Analysis:
Figure 2. Adding tolerance parameters.
Figure 3. Model tolerance list.
Figure 4. Worst Case Analysis parameters.
Table 1. Parameters used in Worst Case Analysis.
Specifies the operation to be performed on the values of the output variable to reduce these to a single number that will be used in the sensitivity calculations (this option is enabled when you select an AC Analysis). There are five functions available:
Describes what kind of output will be generated and limits the range over which the Collating Function operates. Multisim supports the option:
Note: In SPICE, the command that performs a Worst Case Analysis has the following form:
.WCASE <ANALYSIS> <OUTPUT_VARIABLE> <FUNCTION> [OPTION]
Note that these are the same parameters that were defined in Table 1, however, in Multisim you do not have to worry about the SPICE syntax.
The Worst Case Analysis section shows the DC Operating Point at V(OUT) for both nominal and worst case. The Run Log Descriptions section displays the resistance values required to achieve the greatest difference from the nominal value.
Figure 5. Worst Case Analysis results.
Inserting the output results in the two conditions for oscillation:
As you can see, only one condition is met, therefore, the circuit may fail if the components tolerances are not carefully chosen. Try entering the worst case values in the Wien-bridge circuit. Does it oscillate?
For AC circuits, the Worst Case Analysis generates separate plots for the nominal and worst case runs. A list of the components and their worst case values appears in tabular form. You can find an additional example file (speech_filter.ms11) in the Downloads section. In this case, resistors and capacitors of the Speech Filter circuit are varied to see the effects in the AC response.
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