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V5px, V6px and beyond are working prototypes of my nonlinear SMPS model that that lifts the restriction of averaging from frequency domain SMPS simulations. These initial prototypes are restricted to Voltage Control applications. My intent is to lift that restriction in a subsequent model enhancement.The circuit modeling follows Vorperian's concept [1] of introducing equivalent circuits for the PWM modulator and the switch leaving the remainder of the converter as is. The PWM modulator and switch model nonlinearities by sourcing voltages at frequencies outside the external stimulae. With the restriction of averaging lifted the model becomes applicable at arbitrary frequencies across the spectrum up to and beyond the UHF band where EMI is studied, At frequencies below Fsw the model should produce the same results as the averaged switch.This initial version of the modulator and switch is limited to voltage mode control and continuous conduction. It retains the assumption of small disturbances compared to steady state operation but the derivations make limited use of that assumption.The test bench is the same buck converter Mike Donnelly used to demonstrate TDFS Loop Stability Analysis. I have replaced the switch assembly with an equivalent circuit derived by the methodology Vatche Vorperian documented in his May 1990 paper [1]. I drive the switch with a PWM modulator that sources the Fourier transform of the pulse sequence..The key to coding the models is the use of VHDL-AMS spectral source quantities to formulate Fourier transforms involving products and ratios of waveforms. By this mechanism the models present all the characteristics of the non-linear components in the DC-DC converter. swdrive continues to be derived as a closed form expression of the modulator output but now includes the combined steady state and transient drive signals. The switch model outputs a theoretically correct formulation of the switch outputs, the voltage at the common terminal and the current sourced out of the active terminal.Potential applications:1) Response at high frequencies to arbitrary disturbances including finite pulses, white noise, AM radio, X-Ray radiation...2) Analyze susceptibility to electromagnetic interference (requires modeling of that interference).3) Rad-Hard testing (requires modeling of that interference),4) Generation of RF interference (e.g., by modeling the choke magnetics).This version is under test to determine its accuracy and faithfulness to the actual switching characteristics.[1] See Vorperian's "Simplified Analysis of PWM Converters Using Model of PWM Switch Part 1" in the May 1990 issue (Vol. 26, No. 3) of the IEEE Transactions on Aerospace and Electronic Systems.

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PWM Modulator - VCVS - corrected

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PWM Modulator - VCVS-------------------------------------------------------------------------------------This is a structural representation of the language-based behavioral model found in SMSSA_modulator_v6p4. It is constructed from delay lines, summing and subtraction points, spectral quantity generatots (i.e. AS signal sources, passive R-C elements and Voltage-controlled voltage sources acting as high gain amplifiers and an integrator. It implements the same modulation expressions as v6p4 . All components are available from LTspice or any other Spice derivative.All formulas have been developed rigorously except for the final dependence of the switch drive output on the control voltage. The assumptions of a periodic Vctl and the scaling applied to that voltage. These factors have been adjusted t o match results below 1/2 Fsw as simulated with the TDFS mechanism developed at Mentor by Mike Donnely.Voltage-Controlled Voltage Sources act as ideal hi-gain opamps with infinite bandwidth, infinite Rin and zero Rout. Fixed AC sources account for the nonlinear behavior of the modulator. They are phase-shifted to 180 degrees to produce an in-phase result after three stages of summing points.

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Nonlinear SMPS AC Analysis - Buck Converter - V5p2.2

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V5px is the culmination of my goal to construct a nonlinear SMPS that can be analyzed in the frequency domain without averaging out the switching cycle variations. The circuit modeling follows Vorperian's concept [1] of introducing equivalent circuits for the PWM modulator and the switch leaving the remainder of the converter as is. The PWM modulator and switch model nonlinearities by sourcing voltages at frequencies outside the external stimulae. With the restriction of averaging lifted the model becomes applicable at arbitrary frequencies across the spectrum up to and beyond the UHF band where EMI is studied, At frequencies below Fsw the model should produce the same results as the averaged switch.

This initial version of the modulator and switch is limited to voltage mode control and continuous conduction. It retains the assumption of small disturbances compared to steady state operation but the derivations make limited use of that assumption.

The test bench is the same buck converter Mike Donnelly used to demonstrate TDFS Loop Stability Analysis. I have replaced the switch assembly with an equivalent circuit derived by the methodology Vatche Vorperian documented in his May 1990 paper [1]. I drive the switch with a PWM modulator that sources the Fourier transform of the pulse sequence..

The key to coding the models is the use of VHDL-AMS spectral source quantities to formulate Fourier transforms involving products and ratios of waveforms. By this mechanism the models present all the characteristics of the non-linear components in the DC-DC converter.

swdrive continues to be derived as a closed form expression of the modulator output but now includes the combined steady state and transient drive signals. The switch model outputs a theoretically correct formulation of the switch outputs, the voltage at the common terminal and the current sourced out of the active terminal.

Potential applications:

1) Response at high frequencies to arbitrary disturbances including finite pulses, white noise, AM radio, X-Ray radiation...

2) Analyze susceptibility to electromagnetic interference (requires modeling of that interference).

3) Rad-Hard testing (requires modeling of that interference),

4) Generation of RF interference (e.g., by modeling the choke magnetics).

This version is under test to determine its accuracy and faithfulness to the actual switching characteristics.

[1] See Vorperian's "Simplified Analysis of PWM Converters Using Model of PWM Switch Part 1" in the May 1990 issue (Vol. 26, No. 3) of the IEEE Transactions on Aerospace and Electronic Systems.

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Buck Converter with Vorperian Switch v2.1

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Norm's aliasing demo - Mike's topology

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This example demonstrates the TDFS (Time Domain Frequency Sweep) Loop Stability Instrument Model. It is used to compute the open-loop transfer function of an operating (closed-loop) switching power converter. There is no need for state-average or continuous equivalent models for the modulator section of the design, as normally needed for frequency-domain (or "AC") analysis. Rather, the actual circuit component models can be used directly, because the open-loop transfer function is computed from time-domain simulation results.In this case, the converter is operating at 200kHz switching frequency, and is converting the 12V DC input to a regulated 5V output, while supplying a 5A current to the 1 Ohm load resistor. The TDFS measurement instrument indicates that the open-loop gain crossover frequency is at 26 kHz, and the phase margin is just under 60 degrees. This verifies that the opamp-based lead-lag compensator is providing adequate stability margin under these operating conditions.Note that the TDFS instrument model characterizes the open loop transfer function by injecting a small sinusoidal stimulus signal in series with the loop, and then measures the complex ratio of the return signal to the injected signal, is described in:D. Venable, “Testing Power Sources for Stability”, Venable technical paper #1, Venable Industries.The companion example, "Step-Down (Buck) DC to DC Converter - Switching", shows the line and load transient response of this converter design. Another companion example, "Step-Down (Buck) DC to DC Converter - Continuous", uses a state-average model of the switching (or modulator) section of the converter, so it supports traditional "AC" or frequency-domain analysis.

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Ripple Free Buck

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This design starts from a copy of Mike Donnelly's "TDFS Loop Stability for Step-Down DC to DC (Buck) Converter - Switching". I've inserted a moving average filter between the output capacitor bank and the output to the load. With the averaging window with set equal to the 5us switching period, the steady state switching ripple is completely cancelled. The price is a 2.5us delay imposed by the filter's linear phase response.As with Mike's example, the converter is operating at 200kHz switching frequency, and is converting the 12V DC input to a regulated 5V output, while supplying a 5A current to the 1 Ohm load resistor.The TDFS measurement instrument generates a Bode plot for the open-loop transfer function that compares the gain crossover and phase margin to the original values of 60 degrees PM @ a 26 KHz gain crossover.Note that the TDFS instrument model characterizes the open loop transfer function by injecting a small sinusoidal stimulus signal in series with the loop, and then measures the complex ratio of the return signal to the injected signal, is described in:D. Venable, “Testing Power Sources for Stability”, Venable technical paper #1, Venable Industries.

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SMSSA Theory - Test rev 2 Baseline

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This example demonstrates the TDFS (Time Domain Frequency Sweep) Loop Stability Instrument Model. It is used to compute the open-loop transfer function of an operating (closed-loop) switching power converter. There is no need for state-average or continuous equivalent models for the modulator section of the design, as normally needed for frequency-domain (or "AC") analysis. Rather, the actual circuit component models can be used directly, because the open-loop transfer function is computed from time-domain simulation results.In this case, the converter is operating at 200kHz switching frequency, and is converting the 12V DC input to a regulated 5V output, while supplying a 5A current to the 1 Ohm load resistor. The TDFS measurement instrument indicates that the open-loop gain crossover frequency is at 26 kHz, and the phase margin is just under 60 degrees. This verifies that the opamp-based lead-lag compensator is providing adequate stability margin under these operating conditions.Note that the TDFS instrument model characterizes the open loop transfer function by injecting a small sinusoidal stimulus signal in series with the loop, and then measures the complex ratio of the return signal to the injected signal, is described in:D. Venable, “Testing Power Sources for Stability”, Venable technical paper #1, Venable Industries.The companion example, "Step-Down (Buck) DC to DC Converter - Switching", shows the line and load transient response of this converter design. Another companion example, "Step-Down (Buck) DC to DC Converter - Continuous", uses a state-average model of the switching (or modulator) section of the converter, so it supports traditional "AC" or frequency-domain analysis.

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SMSSA Theory - Test rev 2

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This example demonstrates the TDFS (Time Domain Frequency Sweep) Loop Stability Instrument Model. It is used to compute the open-loop transfer function of an operating (closed-loop) switching power converter. There is no need for state-average or continuous equivalent models for the modulator section of the design, as normally needed for frequency-domain (or "AC") analysis. Rather, the actual circuit component models can be used directly, because the open-loop transfer function is computed from time-domain simulation results.In this case, the converter is operating at 200kHz switching frequency, and is converting the 12V DC input to a regulated 5V output, while supplying a 5A current to the 1 Ohm load resistor. The TDFS measurement instrument indicates that the open-loop gain crossover frequency is at 26 kHz, and the phase margin is just under 60 degrees. This verifies that the opamp-based lead-lag compensator is providing adequate stability margin under these operating conditions.Note that the TDFS instrument model characterizes the open loop transfer function by injecting a small sinusoidal stimulus signal in series with the loop, and then measures the complex ratio of the return signal to the injected signal, is described in:D. Venable, “Testing Power Sources for Stability”, Venable technical paper #1, Venable Industries.The companion example, "Step-Down (Buck) DC to DC Converter - Switching", shows the line and load transient response of this converter design. Another companion example, "Step-Down (Buck) DC to DC Converter - Continuous", uses a state-average model of the switching (or modulator) section of the converter, so it supports traditional "AC" or frequency-domain analysis.

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