Post by AMSA on Sep 18th, 2014, 7:55am
Hi AnilReddy,
I am using a very low value of inductance. Well, the problem that I am facing is this:
I am using a method very popular that can be found in several applications notes from several manufacturers and some books (for example Basso) and it consists on selecting the desired closed loop crossover frequency of the converter and based on that we calculate the components values to put around the error amplifier. These controllers are named as type 1, 2 and 3. The type 3 is the one most used in dc-dc buck converter (my dc-dc is a buck) and that is because the buck converter has double pole (LC filter) and ESR zero (capacitor). However, my converter, because of some losses doesn't present any kind of frequency response shape when compared to the typical buck frequency response (a peak @ LC ressonance frequency and a transition from a -40dB/dec roll-off to -20dB/dec roll-off @ ESR zero of the capacitor).
I have designed the type 3 controller using a VCVS where the components were calculated based on that K-factor approach (which is nothing more or less than the nicholas method, I think) that I mentioned above.
I got some values for the R and C components and I simulated the frequency response and I got a nice shape of the controller.
Now some warnings:
The two zeros that the controller has are to be placed in the double pole of the LC filter and the two poles (the third is at the origin) are to be placed on the ESR zero. To be honest I don't see that typical peak on that double pole, that doesn't mean that he's not there, in fact they are there but we don't see the peak (because of the losses - Q factor) - I THINK. The other problem is with the ESR zero. He's at very high frequency because the ESR is very low, I'd say < 0.5Ohm (?) - we are talking about MOM RF Caps (UMC 130nm). So, if they are at very high frequency it is logical to bother about them? If yes, well, we just need to calculate the components to get the desired values based on the K-factor approach.
That said, what's the problem. The components values are very low (of course), resistors included! Is that the problem? I think it might have some influence. How to overcome? More current? (Symmetric OTA, 2-stage Miller with a class A, AB or whatever on the output, to give more current?) Regardless that, I notice that when I simulate with the VCVS the shape of the frequency response is nice but when I simulate with the Symmetrical OTA, for example, the shape is nice until he finds the zero's he can't "follow" the same shape as the based VCVS controller VCVS.
After that I thought that inserting a VCVS with unity gain on the output of the Symmetrical OTA could help me figure out if I have some problems with the impedance that the OTA see, because OTAs can't provide much current to resistive load. The result I got was that after that he can follow the VCVS based controller after those zeros, however he suddenly cuts off (start to roll off quickly) before he finds the two high frequency poles and that happens around the GBW frequency of the Symmetrical OTA.
You can get a better picture here:
The green one is the SYMMETRICAL OTA frequency response. It seems to me that he can't provide much current so he goes "down".
The question about the current is because the low values of the components that I am getting (you can see that on the VCVS picture). But I think that those values are the necessary one (and that's because are the values that the k-factor method gives) in order to comply with the required frequency response shape of the controller.
The open loop frequency response of the Symmetrical OTA is this one:
You can see there the crossover frequency (gain-bandwidth product), and PM.
I know that the gain is very low and I don't know if this is the suitable OTA to implement the controller but I had to start somewhere. I didn't found much info on this, how to design the OTA for error amp/controller PID/etc.
To finish, one details, yet regarding the load effect (the current that the OTA can't provide).
I designed another controller, now based on the values that I found in one application note where the values of the components are higher. Resistors in the kOhm range (except one of them that is located in the input of the amplifier) and the capacitors around nF). The results were very nice, as you can see in here:
But one thing that confuses/confused me was that now, the OTA starts to fall (we can say it has the same symptom(???) as the other controller) way before the 100MHz of GBW.
Any help and or suggestions are welcome.
Thanks you very much in advance.
Kind regards.