Benefits to a 2^{nd} Stage LC output filter for flyback：

- Lower total capacitance needed to achieve output voltage ripple objective
- Reduce overall footprint of the output filter compared to 1 stage output filter
- Lower output voltage ripple more dramatically

Problems introduced by a 2^{nd} Stage LC output filter for flyback:

- Re-adjust the compensation network to re-establish control loop stability
- Additional small signal model analysis to find the poles and zeros

Using the PWM Switch method to analyze the stability and output setpoint tolerance issues introduced by a 2^{nd} Stage LC output filter, one needs to do the impedance reflection to simplify the input to output model. To analyze the small signal model for Flyback converter, start by reflecting the load and filtering caps (impedance) on the secondary side to the primary side.

The Fig. 1 shows the simplified Flyback Converter with multiple outputs

Fig. 1 Flyback Converter with multiple outputs

The Fig. 1 illustrates a simplified Flyback converter with 3 outputs. With the reflected impedance, a Flyback converter turns into a Buck-Boost Converter. Z1, Z2 and Z3 are the output impedances for the three outputs, respectively. And we can get the following equations:

Recalling basic operations for a Flyback converter, energy is transferred when the main switch M1 is turned off. The link between the primary side and the secondary side is the flux inside the magnetic core. The illustration is shown in Fig. 2.

Fig. 2 (a) Fig. 2(b)

As shown in Fig. 2(a), for a single output configuration, the M1 is on. Current Ip flows through the primary side winding as flux f increases. Since the diode is reverse-biased, there is no current flowing through the secondary side winding. When the M1 is turned off, as shown in Fig. 2(b), to keep the flux remain unchanged, the diode is now forward-biased and conducting. Then the following equations apply.

Based in the equation (9), the output impedance for each output can be reflected to the primary side by multiplying a coefficient and in parallel. With the reflected impedance, a Flyback converter turns into a Buck-Boost converter. A Flyback converter with multiply outputs can be simplified into a buck-boost with several loads in parallel, as shown in Fig. 3.

Fig. 3 Simplified Buck Boost Converter with multiply loads in parallel.

With the loads reflected from the secondary side to the primary side, a Flyback converter can be analyzed as a buck-boost converter. This practice can greatly ease the analytical work for the applications in which a second stage LC filters are used at each output for reducing output voltage ripple.

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