SLUAAL2 Application note

Figure 1-23 Type 2 Compensator with Fast Lane

Equation 51.

G_{c} (s) = |\frac{V_{f b} (s)}{V_{o} (s)}| = \frac{R_{f b} C T R}{R_{L E D}} (\frac{1}{(C_{v} + C_{f}) \cdot R_{u p}} \frac{1 + R_{v} C_{v} s}{(1 + \frac{s R_{v} C_{v} C_{f}}{C_{v} + C_{f}}) s} + 1)

Equation 40.

\begin{array}{l} Assuming C_{f} < < C_{v}, G_{c} (s) further simplifies to \\ G_{c} (s) = \frac{R_{f b} C T R}{R_{L E D}} (\frac{1}{C_{v} \cdot R_{u p}} \frac{1 + R_{v} C_{v} s}{(1 + s R_{v} C_{f}) s} + 1) \end{array}

Equation 41.

This can be written as G_{c} (s) = G_{o} (\frac{\frac{ω_{L}}{s} + 1}{1 + \frac{s}{ω_{p 1}}})

Equation 42.

where G_{o} = \frac{R_{f b} C T R}{R_{L E D}} (1 + \frac{R_{v}}{R_{u p}}) ω_{L} = \frac{1}{(R_{v} + R_{u p}) \cdot C_{v}} ω_{p 1} = \frac{1}{R_{v} \cdot C_{f}}

Here $ω_{L}$ is low frequency inverted zero and $ω_{p 1}$ is a high frequency pole, CTR is current transfer ratio of optocoupler.

Note:

During the full load to light load transition, the current through the optocoupler LED needs to be able to vary more than $\frac{I_{f b}}{C T R}$ to regulate the output voltage. Here I_fb is maximum current provided by the FB pin. So, $R_{L E D} \leq \frac{V_{o} - V_{r e f} - V_{L E D}}{(\frac{I_{f b}}{C T R})}$ where V_ref and V_LED are reference pin voltage and optocoupler LED drop when the current is conducing.
The shunt regulator starts sinking current only when reference pin voltage reaches the V_ref. During startup, make sure that the voltage appeared across the shunt regulator does not exceeds the absolute maximum cathode to anode voltage. Otherwise, the voltage can be destroyed. In cases where LLC output voltage is higher than abs max of shunt regulators, Type 2 compensator without fast lane is recommended. Here Zener diode is used in the fast lane to clamp the voltage.