Managing output voltage ripple on a power supply is one of the ways to meet emissions regulatory requirements. An effective implementation of a 2^{nd} stage LC filter does require additional analysis and adjustments to make the power supply stable. Flyback converter designs that implement a 2^{nd} stage LC filter can use less filtering capacitance and get less voltage ripple on the output load. A 2^{nd} stage LC filter versus additional output capacitors to reduce voltage ripple is a lower cost solution and improves the system reliability, since less capacitors are used. However, the remedy of the 2^{nd} stage LC filter introduces instability in the output regulation without re-adjusting the compensation network. To solve this output regulation problem, a robust design should derive a small signal model of the switching power converter. The derivation will identify the poles and zeros of the switching power supply in a closed loop control system, so one can gain some intuition about the total system behavior and later optimize the compensation network.

Fig.1 Flyback converter using 2^{nd} stage LC filters

There are three popular ways to derive a small signal model for Flyback:

- State Space Averaging method introduced by Middlebrook;
- PWM switch modeling from Vorperian;
- Averaged Switch method from Robert Ericsson.

The State Space Averaging method has been used for modeling many PWM converters and has been proven to be a useful tool in designing a stable loop. However, since the State Space Averaging method utilizes the parameters like the current signal inside the inductor and the voltage across the capacitor, people need to re-do the derivation work if any other active components are added. This feature makes the State Space Averaging method not convenient to model the Flyback converter with 2^{nd} stage LC filter.

The PWM switch modeling method linearizes the switching components into small signal model. PWM switch modeling can be initiated once the circuit looks like Figure 2a. As shown in Fig.2(a), the Flyback converter is firstly configured into Buck-Boost by reflecting its secondary side to its primary side through impedance reflection. The 3 terminal PWM switch network (a-c-p terminals; active-common-passive terminals) in Buck-Boost can be replaced with already existing linearized models in either CCM or DCM (Figure 2(b)) operating conditions. By plugging in these already derived linearized models, a small signal model of the Flyback converter power train is ready for finding the pole(s) and zero(es) in close loop.

Fig.2(a): Configuring Flyback into Buck-Boost

Fig.2(b): PWM Switch Modeling in Buck-Boost

There are two ways of modeling Flyback converter using Averaged Switch method. One way is to reflect the load to the primary side and then replace the FET and diode with perturbed and linearized models as we did using PWM switch. This approach seems less attractive since it takes extra effort to derive the Averaged Model while the PWM switch models are readily available for plug-in. The other way of modeling is to derive the Averaged Model directly without impedance reflections. However, the model derived using this approach is more complicated than the model derived using PWM switch, which makes it not a good choice for modeling Flyback. Thus, the PWM switch modeling is most efficient option for modeling a Flyback converter with 2^{nd} stage LC filter. Compared to the more straight-forward PWM Switch method, both averaged switch methods require more steps or more complication to find the small signal model to find the pole(s) and zero(es) for flyback.

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