how to understand the current mode has one pole?

[batistuta]

current mode single pole

hi, all
as we all known, in current mode control dc/dc converter, after add a inner current loop, the control to output transfer function only have one pole(1/2*pi*R*C),(compare to voltage mode control) the pole caused by inductor(L) dissipared...
how to understand this??? through physical insight...
thanks.

 

[VVV]

current mode transfer function

It's not that easy to understand, but imagine this: you have a current source, in series with a resistor and also in series with the load resistor. Under these conditions, the voltage across the load resistor is simply the current times the output resistor. As you can see, the resistor in series with the current source plays no role in the output voltage. Of course, the voltage across the series resistor will change with the current, but the OUTPUT voltage will not be affected by the series resistor (as long as the current source has compliance).

What happens if you replace the resistor in series with the current source with another device, say an inductor? The output voltage will still be determined by the output resistance times the current of the source, irrespective of the value of the inductor. Of course, there will be voltage drop across the inductor, depending on how fast the current of the current source changes.

So if you have a current source, any impedance in series with it will not matter.
In other words, it can be anything, including a short-circuit. That simplifies things.

What happens if you connect a cap across the load resistor now? Well the cap and the output resistor form an impedance that is connected to a current source (in series possibly with another impedance, which we have seen does not matter, so we can short it out). That gives you a single-pole response.

Since current-mode control effectively controls the current through the inductor, the inductor no longer has any effect on the transfer function, so "its like it's not there", or shorted out.
So all you are left with is the output cap and the load resistor, which will give you a single-pole response, as stated above. Of course, the ploe frequency shifts with the load resistance.

 

[batistuta]

perfect...vvv, thank you! i got the idea...
in simple model, assume iL(t)=iC(t)...( inductor current equal to control current), neglect artidicial ramp and inductor current ripple, we can see in the model, inductor is series with the current sourceiC(t)
so it does not contribute pole to transfer function. seems dissppared..
in accurate model, not neglect current ripple, we can see in the transfer function there are two poles and one zero, just like duty cycle control.... but these two poles are seperated, accroding to low Q approximation, one is at 1/R*C, the other is nearly the switch frequency or above switch frequency(relate to its duty cycle)...

am i right ????

 

[VVV]

I am not sure I understand the question. You are probably referring to what is knows as "nodulator pole" or "modulator phase lag".
This comes about because when the outer control loop (the voltage loop) changes its output to call for more or less current, the inner loop (current loop) cannot respond instantaneously. That is because there are delays in the comparator, transistor, etc. All these delays add up. In the freqeuncy domain these delays translate into another pole at some higher freqeuncy.

For more details see "Modulator phase lag" on page 5-9 of this appnote: **broken link removed**

 

[batistuta]

thanks.vvv