What is SIMPLIS?

The SIMPLIS Periodic Operating Point (POP) analysis excels at finding the steadystate ONOFF limit cycle of a stable periodic switching system.
Because of its uniqueness to SIMPLIS, POP analysis is one of the more challenging, but also more rewarding aspects of SIMPLIS to master. Understanding how the SIMPLIS POP analysis and the POP algorithm work is critical to receiving the maximum benefit from the SIMPLIS simulation capability. These primary benefits are:
To reach steady state, POP simulates the system in the time domain by performing these tasks:
In practice, once POP has found the steady state of a switching system, the largest difference between two successive snapshot values for capacitor voltage or inductor current is in the range of 1.0e10% to 1.0e13%. These are miniscule errors compared to a typical RELTOL in SPICE of 1.0e3.
In a system with a reasonable set of initial conditions, the SIMPLIS POP algorithm iteratively seeks the following conditions to arrive at a steady state.
This SIMPLIS POP algorithm works best in finding the steadystate operating point of switching timesampled systems such as the following:
Many of these systems use a feedback loop for control. If the system with its feedback loop is unstable and has no steadystate operating point, then the POP analysis will not be successful. As long as this feedback system is stable, the POP analysis can be successful.
In real life, when you characterize a switching system such as a switching power supply, more than 95% of the measurements begin with the system in steady state operation. The SIMPLIS POP analysis quickly drives a switching circuit into a steady state. Once the system reaches steady state, the system can be disturbed and the resulting system response can be measured.
In the majority of system measurements, the reference point for the measurement is the initial steadystate periodic operating point. Since in a typical design project, the designer runs several thousand simulations, being able to reduce the amount of CPU time required to get the system into steady state pays off in time saved for the engineer. If the time to reach steady state can be reduced from 10 minutes to 10 seconds, the time savings runs into hundreds of hours over the life of a project.
Because SIMPLIS can run so many simulations in a relatively short period of time, the SIMPLIS POP analysis makes serious simulation analysis feasible for switching power supply systems. Without POP, only a cursory set of simulation analyses can be run in the practical time allowed. POP, however, makes possible exhaustive system performance characterization during the design process. As a result, the majority of design errors can be detected very early in the design process. Detecting errors before the design has been committed to hardware means that the design errors are least expensive in time and money to correct.
Because of the speed and accuracy with which the piecewise linear SIMPLIS POP analysis can find steady state means, SIMPLIS AC analysis is possible based on the following twostep process:
A Power Factor Corrector (PFC) converter dramatically shows the amount of time POP can save when simulating a converter to steadystate. Because this converter has a slow control loop response time, the transient simulation must be run for a long time to allow the converter to settle into steadystate. The POP analysis can reduce the time required to reach steadystate by orders of magnitude.
A zip archive of the PFC converter schematics and supporting files can be downloaded here: simplis_500_pfc_examples.zip. The zip file contains four schematics which are identical, except for the analysis modes and the initial conditions. These models are larger than the SIMetrix/SIMPLIS Intro size restrictions. For an evaluation license for the full version of SIMetrix/SIMPLIS, contact SIMPLIS Technologies.
The PFC converter examples have the following characteristics:
The PFC converter schematic is pictured below:
The first simulation run on this converter is a SIMPLIS transient analysis, where the converter is simulated through a softstart cycle and the output voltage is allowed to settle. The simulation stop time is set to 1s, which is long enough to allow the output voltage to settle after the softstart is complete.
The converter has relatively few large energy storage elements, primarily composed of the output capacitor, boost inductor, softstart capacitor and voltage loop compensation capacitors. Because the converter transitions through a softstart cycle, these major energy storage elements are initialized to the following values:
Circuit Element  Initial Condition 
Output Capacitor 
163V 
Boost Inductor 
0A 
Softstart Capacitor 
860mV 
DCInput Transient Analysis Waveforms 
Elapsed Time : 158s (2min , 28 s.) 
The SIMPLIS POP analysis greatly speeds up the simulation time by actively forcing the converter into a steadystate. In this example, the initial conditions for the three main energy storage elements ware taken from the steadystate portion of the transient simulation data. These initial conditions are:
Circuit Element  Initial Condition 
Output Capacitor 
400V 
Boost Inductor 
1.66A 
Softstart Capacitor 
3V 
Compensation Capacitor C2 
920mV 
The initial condition for the voltage loop compensation capacitor C2 is added to ensure the converter is in a switching state when the simulation starts. The POP analysis requires the circuit to continuously switch in a periodic manner, and without this initial condition, this particular model can stop switching, which causes POP to fail.
The steadystate waveforms for the POP analysis are shown below. Note the output voltage has converged to a steadystate and there is no visible settling on the waveforms. This simulation only took 1 second to complete, compared to the transient example which took 2min., 28 seconds.
DCInput POP Analysis Waveforms 
Elapsed Time : 1s. 
One of the greatest rewards for designing a converter model which succeeds in SIMPLIS POP analysis is the ability to run an AC analysis directly on the transient model. There is no need to derive a AC model for the topology under study as SIMPLIS provides the AC response for the timedomain circuit model.
The overall loop gain of the PFC converter is shown below. This simulation took 1second to run after a successful POP analysis.
DCInput AC Analysis Waveforms 
Elapsed Time : 1s. 
From the AC analysis, the PFC converter has the following control loop measurements:
Measurement 
Value 
Loop Crossover Frequency 
11.6 Hz 
Phase Margin 
48.6 degrees 
Gain Margin 
29.9 dB 
A summary of the elapsed time to reach steadystate for each DC Input Analysis mode is shown in the table below.
Analysis Mode  Elapsed Time 
Transient 
158s, ( 2 min. 28 s. ) 
POP 
1s. 
The example zip file simplis_500_pfc_examples.zip contains two schematics configured for an AC line input. One schematic ( simplis_500_pfc_ac_input_tran_example.sxsch ) is configured to run the transient analysis, and the other ( simplis_500_pfc_ac_input_pop_ac_example.sxsch ) for a POP analysis.
Converters with AC inputs will only POP under very specific circumstances. These requirements are:
If these requirements are met, the POP analysis will be successful and the resulting AC analysis can be run on the model. In the circuit examples, the first condition is met by choosing the line frequency to be 50Hz. The switching frequency is 100kHz, which is effectively the 2000^{th} harmonic of the line frequency.
Because the POP trigger frequency is 2000 times lower than the DC input case, the simulations with an AC input source take considerably longer to complete than the DC input case. Even so, the POP analysis is faster than the transient ( on either AC or DC inputs ) and, after the POP analysis is successful, the SIMPLIS AC analysis can be performed on the converter model, with an AC input line.
As with the DC input case, the major energy storage elements are initialized.
Circuit Element  Initial Condition 
Output Capacitor 
163V 
Boost Inductor 
0A 
Softstart Capacitor 
860mV 
Compensation Capacitor C2 
970mV 
ACInput Transient Analysis Waveforms 
Elapsed Time : 148s (2min , 18 s.) 
After running the transient analysis, the SIMPLIS POP analysis is run on the model. In this example, the initial conditions for the three main energy storage elements ware taken from the last data point of the transient simulation data. These initial conditions are:
Circuit Element  Initial Condition 
Output Capacitor 
400V 
Boost Inductor 
40mA 
Softstart Capacitor 
3V 
Compensation Capacitor C2 
880mV 
The steadystate waveforms for the POP analysis are shown below. Note that instead of POP using the switching frequency as the POP trigger, the AC line frequency is used. As with the DC input case, the output voltage has converged to a steadystate and there is no visible settling on the waveforms. This simulation only took 43 seconds to complete, compared to the transient simulation on the same model, which took 2min., 18 seconds.
ACInput POP Analysis Waveforms 
Elapsed Time : 43s. 
The overall loop gain of the PFC converter operating under AC line input is shown below. This simulation took 1 min., 46 seconds to run after a successful POP analysis. Note that this simulation time is much longer than the DC input case because the converter is using the line frequency of 50Hz as the POP trigger source.
DCInput AC Analysis Waveforms 
Elapsed Time : 106s. 
The AC Analysis results for a DC and an AC line source are nearly identical.
AC and DCInput AC Analysis Waveforms 

A summary of the total elapsed time to reach steadystate for each line source type and analysis mode are shown in the table below.
Line Source  Analysis Mode  Elapsed Time 
DC 
Transient 
128s. 
DC 
POP 
1s. 
AC 
Transient 
118s. 
AC 
POP 
43s. 
© 2015 simplistechnologies.com  All Rights Reserved