3.2 SIMPLIS Monte Carlo Analysis

Exercise #1: Assign Uniform Distribution to the Input Source V1

1. Select the input voltage source V1.
   Result: The symbol changes from red to blue indicating the symbol is selected.
2. Use the keyboard shortcut F7 or double-click to open the Edit DC Source value editing dialog.
   Result: The Edit DC Source dialog opens:
   
3. Enter the uniform distribution: {Vin*Unif(0.0333)}
   Result: The configured dialog should appear as follows:
   
4. Click Ok.
   Result: The property value for the input voltage changes to the uniform distribution of 310V +/- 3.33%.
   
5. From the schematic menu, select Monte Carlo > Run Monte Carlo
   Result: The SIMPLIS Monte Carlo Analysis executes and the waveform viewer opens with the curves from the original 4 steps with a constant Input voltage, and the additional 4 steps from the second Monte Carlo Analysis with input voltage variation. The original curves are displayed as dotted lines.
   

Exercise #2: Verify L4 Values

1. Double click on L4.
   Result: The Define PWL Inductor: L4 dialog opens:
   
2. Note that each Flux Linkage value is multiplied by a constant value L4_Tol. Since the Flux Linkage values are the "y-axis" values, and the slope of each PWL segment represents the inductance of that segment, the inductance of every PWL segment changes by the same percentage.
3. Click Cancel on the Define PWL Inductor: L4 dialog.
4. Press F11 to open the command (F11) window. Scroll down to where the L4_Tol is defined:

   .rvar L4_Tol={Gauss(0.20)}
   { '*' }
   { '*' } L4's tolerance : {L4_Tol}
   { '*' }

   Note: See the .RVAR pre-processor statement section for more information.
   The first line assigns the return value of the Gauss(0.20) function to the variable L4_Tol, which is in turn, used to parametrize each y-axis point for L4. Note that the nominal return value of the Gauss() function is 1.0, so adding the tolerance does NOT shift the nominal value. The other three lines were purposely placed in the F11 window to allow us to easily see the value returned by the Gauss(0.20) function. Each line is a comment, with the middle line also displaying the value of L4_Tol.
5. As you did in section 3.0.2 What Actual Device is Simulated in SIMPLIS?, you look in the deck file to ascertain exactly what values are used for L4_Tol, and the PWL inductor L4. From the menu bar, select Simulator > Edit Netlist (after preprocess) .
   Result: the SIMPLIS Deck file opens in the netlist editor.
6. To search for the L4 tolerance comment line:
   1. Use the shortcut key Ctrl+F to open the search dialog.
   2. Type L4's
   3. Click on the Find Next button.
      Result: The deck file scrolls to line # 13 where the debug comment is located:
      
7. Finally, to search for the actual L4 device instantiation line:
   1. Use the shortcut key Ctrl+F to open the search dialog.
   2. Type !L$L4
   3. Click on the Find Next button three times.
      Result: The deck file scrolls to line # 49 where the L4 instantiation and its .MODEL line are located:
      

Piecewise Linear Inductors, such as L4 in this example, are implemented with a .MODEL statement, which in this case, starts on line #50. The PWL points are listed as X,Y pairs starting at X0 and Y0. Notice the X values have the same numerical values defined in the dialog. The Y-values are all multiplied by the constant value L4_Tol. The L4_Tol is constant because the value is evaluated once per Monte Carlo run, and from that point onwards, the same constant value is used in the expressions for L4_Tol. The value of L4_Tol will almost certainly be different for the next Monte Carlo simulation step.

The value of the L4_Tol variable is 1.0696640600968, which represents a 6.97% increase in inductance values. Calculating the change in inductance is left as an independent study exercise.

.RVAR pre-processor statement

Exercise #3: Enable Multi-Core

This exercise assumes your computer has more than one physical core and that you are using a SIMetrix/SIMPLIS Pro license.

1. Close the waveform viewer.
2. From the schematic menu, select Monte Carlo > Setup Monte Carlo...
   Result: The Define SIMPLIS Monte Carlo Analysis dialog opens with the Monte Carlo configuration information.
   
3. Change the Number of cores to 4, the maximum allowed by the Pro license.
   Note: Note: if your machine has either a single core or two cores, the dialog will limit your Number of cores entry. If you have a single core, you can skip this exercise.
4. Change the Number of steps to 32.
   Result: The configured dialog will appear as follows:
   
5. Click Run.
   Result: The Monte Carlo simulation runs 32 steps on the maximum number of physical cores.
   

Exercise #4: Plotting Histograms

Plotting histograms is different from plotting time domain curves because the histogram function is expecting a single measured value per Monte Carlo step. Compare this to plotting the converter output voltage after a transient simulation - there may be 10,000 points in the output voltage vector, each one representing the voltage at a particular simulation time. If you were to average the output voltage over the simulation time span, you would have just one measurement per Monte Carlo step. This is exactly what a histogram is - the frequency which a particular measured scalar value occurs over a statistical sample of Monte Carlo runs.

Therefore, every histogram will require a function to operate on the voltage or current, and this function must return a single scalar value for each Monte Carlo step. For the above mentioned example, the function used to return the average value of a voltage or current from a time-domain simulation is Mean1(). For this example you will plot the converter switching frequency using the Frequency() function.

1. From the schematic menu, select Probe > Create and Place Arbitrary Probe .
   Result: The Edit Probe dialog opens:
   
2. In the Multi-step mode box, select the Histogram radio button.
   Result: The Edit Probe dialog changes and should appear as follows:
   
3. Input the following information:
   1. The Probe expression field is where you enter your goal function. Use V(nnn) for voltages and I(sss) for currents, where nnn and sss may be any string starting with a letter. In the Probe expression field, type Frequency(V(POP)).
   2. The Curve label field is where you enter the name of the curve to appear on the waveform viewer. Enter POP Frequency Histogram.
4. The default number of histogram bins is defined by the equation:

   \[ N_{Bins} = \text{Floor} \left( \frac {\sqrt{\text{Number of Runs}}}{2} \right) \]

   which for a 32 run simulation will result in only 2 bins. For this exercise, you will change the number of histogram bins on the Define Performance Analysis dialog to 8. To change the number of histogram bins, follow these steps:
   1. In the Histogram options box, uncheck the default checkbox.
   2. Enter 8 in the Number of bins field.
      Result: The Edit Probe dialog should appear as follows:
      
   3. Click Ok.
      Result: Focus returns to the schematic viewer with a single input probe symbol attached to your mouse:
      
5. Place the probe near the POP Trigger
6. Wire the probe to the output of the POP Trigger
   Result: The probe will appear as follows:
   
7. Re-run the Monte Carlo simulation.
   Result: Along with the same waveforms from Exercise #3, you will now have the Histogram of the POP Frequency:
   

Some Histogram Tips and Tricks

• A list of functions which can be used to define the histogram expression is available by clicking on the Goal Functions... button.
• More information on using this dialog to generate plots is available by clicking on the Help button.

Exercise #5a: Find the Run Number Which Produced the Lowest Frequency

On the waveform viewer window:

1. Hover your mouse over the target curve until you see the square box:
2. Look at the far right side of the status bar:

In this exercise, you have found the run number which produced the lowest converter switching frequency. In the next exercise, you will find the seed value and the simulated parameter values from the Monte Carlo Log file.

Exercise #5b: Find the Parameter Values Used for a Particular Run Number

You now know that run number 22 produced the lowest switching frequency. To find the seed value which corresponds to this run number, you open the Monte Carlo Log file. To open the Monte Carlo Log file, follow these steps:

1. From the schematic menu select Monte Carlo > View Log File .
   Result: The Monte Carlo Log file opens.
2. Scroll to run #22:

Note the seed value 1988583953 which was used for this run. In this converter, the switching frequency is highly dependent on the inductance value. Not unexpectedly, the evaluated parameter value for the inductance is higher than the default value, which requires longer charging and discharging times, and hence a lower switching frequency results.

In the next exercise, you will run a single step simulation using the same parameter values which generated the lowest frequency simulation run. You do this by running a Monte Carlo simulation using the seed value found in this exercise.

Exercise #5c: Run a Single Step Using a Known Seed Number

1. From the schematic menu, select Monte Carlo > Setup Monte Carlo... .
   Result: The Define SIMPLIS Monte Carlo Analysis dialog opens with the Monte Carlo configuration information.
   
2. Make these three changes to the dialog values:
   1. In the Monte Carlo Seed field, paste the seed value: 1988583953
   2. Change the Number of steps to 1
   3. Change the Number of cores to 1
      Result: The configured dialog should appear as follows:
      
3. Click Run to run the known seed value of 1988583953.
   Result: A single Monte Carlo Step is run, reproducing the Monte Carlo run with the lowest frequency:
4. Press the Home key on the keyboard to zoom the waveform viewer to see the full waveforms:

Discussion: Exercise #6

There are a few items that should be pointed out about the schematic in it's current state.

DVM Control Symbol

The DVM control symbol stores specification information for the schematic. While the DVM control symbol has several forms, the one used in this example is the most basic version. The key specifications used in this example are the Monte Carlo parameters shown in the image below.