Periodic Steady-State Analysis for DC-to-DC Converters

In "Spectre RF by any other name ...", a non-RF application for Spectre RF's periodic steady-state analysis was introduced. An example of using periodic steady-state analysis [PSS] to simulate the dynamic performance: THD and SFDR, of a switched-current Digital-to-Analog Converter [DAC] was presented. In this append, we will look at using periodic steady-state analysis for another non-RF application, switching regulator simulation. Switching regulators are the core of switched-mode power supplies [SMPS] and are interesting because they are used in most power supplies, including the high efficiency power supplies required mobile applications.

Let's begin by considering a simple switching regulator design, a buck-down converter for converting from 12V to 5V, shown in Figure 1. The design is a voltage-mode, continuous conduction mode switching regulator. The control block: reference voltage generator, error amplifier and compensation, drives a pulse-width modulator: ramp generator, comparator, and switch. The output of the switch is filtered by an LC tank and feedback to the control block. The duty cycle of the pulse-width modulator determines the output voltage of the regulator. The inductor and capacitor non-idealities [self-resonance frequency, ESR, ...] are modeled but not shown. Finally an EMI filter has been included in the design.

Figure 1: Buck-Down Converter schematic

First, let's look at the dynamic response of the regulator. After settling the start-up transient, the regulator operates at the frequency of the ramp generator. When operating at steady-state, the dc level is 5.002V and there is ripple on the regulated output voltage, ~+/-7mV. The transient response of the regulator is shown in figure 2.

Figure 2: Buck-Down Converter transient response

 

While transient analysis can be used to verify the overall performance of the circuit, it is difficult to analyze the circuit's performance in the time domain using transient analysis, for example, consider the challenge of trying to simulate the phase margin and gain margin of the control loop. Ideally we would like to be able to use simulation to improve the buck-down converter design in the same way that using ac, noise, stability analysis can be used for design of linear circuits. However, linear analysis can not be directly applied to switching regulator designs so we need to find a new methodology for analyzing the switching regulator. Since the switching regulator has a periodic steady-state, we will apply the periodic steady-state analysis technology in Spectre RF. In this case, a source is used to generate the ramp so driven periodic steady-state analysis is used. The complete setup for PSS analysis is shown in Figure 3.

Figure SEQ 3: PSS Analysis setup

 

Since a switching regulator has fast changing time domain waveforms, the Shooting Newton [time domain] periodic steady-state engine was selected. If the Harmonic Balance engine is used, then a large number of tones would need to be selected in order to correctly represent the voltage at the output of the comparator and the switch output since these waveforms are nearly square waves. In this case, the stabilization time [tstab] is equal to the transient simulation time. In practice, a shorter stabilization time would be used to reduce simulation time. Allowing the circuit to settle to close to steady-state will help convergence. For this test example using a tstab of 2-3us should be sufficient.

Figure 4: Buck-Down Converter periodic steady-state response

 

The plots for periodic steady-state response show the switch drive signal, net015 [0-12V], the output of the Switch, Switcher Output [-0.8V-12V], the buck converter output after the LC tank, Regulated Output [4.995V-5.009V]. Plots of the transient and periodic steady-state response match if overlayed and the average output from transient analysis and periodic steady-state analysis are consistent, 5.002V. In the next append, we will look at performing periodic small signal analysis to analyze the converters performance. If you have any questions about this append or would like more information, please let me know!

Arthur Schaldenbrand