Type II and type III compensation

[AMSA84]

Hi guys, I have one question:

I have read around some technical white papers and in some books that the type II is suitable for a phase boost of 90º and for converter operating in current-mode and CCM. However, there is two white papers from two manufacturers that says that this compensator can be used to compensate converters that have a large capacitor ESR at the output.

I am designing one converter that has this kind of ESR, a capacitor with relative high ESR (500mOhm). So this means that I can use the type II without problems?

There is one more thing:

In this technical paper: https://www.ti.com/lit/an/slva662/slva662.pdf page 5, we can read:

Note that this type of compensator always has a net negative phase, and it cannot be used to improve the phase of the power stage. For this reason, Type II compensators cannot be used for voltage-mode control in CCM where there is a large phase drop just after the resonant frequency.

I don't understand. Can someone explain me?

Thanks and regards.

 

[mtwieg]

Hi guys, I have one question:

I have read around some technical white papers and in some books that the type II is suitable for a phase boost of 90º and for converter operating in current-mode and CCM. However, there is two white papers from two manufacturers that says that this compensator can be used to compensate converters that have a large capacitor ESR at the output.

I am designing one converter that has this kind of ESR, a capacitor with relative high ESR (500mOhm). So this means that I can use the type II without problems?

What matters is where the zero formed by the capacitor ESR is. If it's at or below your intended crossover frequency then it will help add some phase boost and a type II may work.

There is one more thing:

In this technical paper: https://www.ti.com/lit/an/slva662/slva662.pdf page 5, we can read:

Note that this type of compensator always has a net negative phase, and it cannot be used to improve the phase of the power stage. For this reason, Type II compensators cannot be used for voltage-mode control in CCM where there is a large phase drop just after the resonant frequency.

I don't understand. Can someone explain me?

Thanks and regards.

A voltage mode converter in CCM will have (at least) a double pole, which will give a sharp phase lag near 180 degrees above that resonant frequency (neglecting any zeroes due to capacitor ESR as above). The negative feedback will contribute another 180 degrees, meaning it will be very near instability (your phase margin is basically zero). So to increase phase margin you need a circuit with a positive phase response at some frequency. A type I compensator (an integrator) always -90 degrees, so it would never work in this case. A type II (a PI) can have near 90 degrees of phase boost, but that is relative to the -90 degree baseline of the type I, so the actual phase response of a type II is always negative. A type III (PID) has up to 180 degrees of phase boost, so its overall phase can be up to +90. That's why the type III is suitable for CCM voltage converters.

 

[AMSA84]

Thanks for the reply.

Well, the ESR value is around 0.5Ohm and my crossover frequency is around 10MHz so it is a bit lower than the ESR zero. This way it means that the Type II cannot be used?

The capacitor ESR is around, say 50MHz. The crossover frequency is around 10MHz The switching frequency is well above the 50MHz of the ESR. Which kind of controller is best suitable?

 

[mtwieg]

I think you must be confusing MHz with kHz? What frequency is the ESR zero?

 

[AMSA84]

My ESR zero is around 50Mhz.

 

[mtwieg]

So you're using a 6.4nF output capacitor? Is this for some sort of monolithic CMOS converter?

 

[AMSA84]

Yes it is.

I'd like to ask another thing. From discrete components, we use opamps to implement the compensator. However, since we are dealing with monolithic converter, the compensator will be implemented using an OTA amplifier.

If you look at page 4 and page 6 we can notice that the way the components around the amplifier are placed differently. Now, I wonder why is that?

Does anyone know why we have to connect the components that way (page 4) when we are using an OPAMP and in the other way (page 6) when using an OTA? It is mandatory?

 

[mtwieg]

I suggest you try to derive the transfer function of the circuit in figure 3 for an OTA instead of an opamp, it will come out completely different and not be what you want.