Optocoupler ac model ltspice

Question

I am trying to plot the bode diagram of a flyback converter on LTspice. This is the first time that I do this and before trying to plot my flyback converter, I would like to plot the bode diagramm of a flyback whose I know the answer in order to see if I am able to do it correctly. So I took an example from the book "Switch mode power supplies" (amazing book) written by Christophe Basso.

Here is the example:

I have some troubles to understand how the optocoupler is modelized. The parameters of the optocoupler model are the following :

• CTR (CTR = 2)
• Fp which is probably the frequency of the pole of the transfer function of its model (Fp = 6k)

As Christophe Basso wrote it in its book an optocoupler has a parasitic emitter collector capacitor. So I did the following model :

Nevertheless, It probably miss something ... as I do not get how to have a 1st order transfer function with a pole :

$$H_{opto}(s) = \frac{G_{0}}{1+\frac{s}{wp}}$$

Thank you very much and have a nice day !

Answer 1

The optocoupler 1st-order model is a simple current-controlled current source whose output is decoupled by a parasitic capacitor. This is what has been represented in the post. This capacitance needs to be characterized and accounted for when adopting the compensation strategy. The below circuit shows how to extract this parasitic element. More details can be found in the APEC 2018 seminar that I taught in San-Antonio (TX):

When realizing a type 2 compensator (1 pole at the origin, 1 zero and 1 pole) with a TL431, you form the second pole by decoupling the feedback pin of the controller to ground via a capacitor. This is \$C_2\$ in the below picture:

However, it is important to realize that the optocoupler pulling the FB pin to ground adds its parasitic capacitance to the capacitor already in place. It does not add a second pole (at least in low frequency) but simply shifts the original pole: \$\omega_p=\frac{1}{R_{pullup}(C_2||C_{opto})}\$. As such, once the type 2 pole position has been determined and a capacitance calculated, the final value connected to the controller must account for the optocoupler capacitance. For instance, assume you calculated a 4-nF total capacitance and the opto already contributes 2 nF, then the final capacitor will be 2 nF. As indicated in the comment, I was originally considering the optocoupler pole as an added one but it is not the case as explained in the above lines. The extra block X4 can thus be omitted.