Transconductance Amplifier used as SMPS Error amplifier

[grizedale]

Hello,

The transfer function of a normal voltage error amplifier as used in a SMPS is easy to derive.

But how do you do it, if the error amplifier is a transconductance amplifier as in the LTC1871 current mode controller.

https://www.linear.com/docs/Datasheet/1871fe.pdf


OR,
If you do not know how to do the transfer function, do you know which is the pole frequency and zero frequency of the compensation components as on page 31 of the LTC1871 datasheet?....and is this Type 2?

 

[mtwieg]

The derivation is just as simple as with a voltage amplifier. The transfer function for a transconductance error amp is just the load impedance multiplied by transconductance. In that figure, there is a pole at 0Hz, a zero at about 1.06KHz, and another pole at around 154KHz.

 

[grizedale]

Thanks,

I can see how you calculated the pole and zero...though i cannot see how you calculated the pole at 0Hz.

......i think the mystery is that a transconductance amplifier has an extremely huge input impedance, so the resistance of the upper divider resistor is insignificant.....this is bizarre because normally the upper divider resistor has a big effect on the gain of a normal voltage type error amplifier.

Do we say that for a transconductance amplifier, putting say a series RC network across the upper divider resistor has no effect on the transfer function?

For a voltage error amplifier, the transfer function is simply Z(feedback)/Z(in)......

For a Transconductance amplifier, are you saying that is Z(out) * Transconductance?

 

[FvM]

i cannot see how you calculated the pole at 0Hz

A transconductance amplifier with capacitive load implements an integrator (=pole at 0Hz).

i think the mystery is that a transconductance amplifier has an extremely huge input impedance, so the resistance of the upper divider resistor is insignificant

It's far from being insignificant. The divider is simply working as such V2 = V1*R2/(R2+R1). In a inverting feedback amplifier configuration, there's no low side resistor R2.

 

[grizedale]

So in a transconductance error amplifier, should we treat the output divider as an attenuation stage?

It just seems to me strange that the output divider has no part in the transfer function of the transconductance error amplifier.

And surely an error amplifier must have negative feedback, so the OTA's compensation components just going to ground seems counter-intuitive?

And regarding the origin pole......does it meet the 0dB axis at a frequency of 1/(2*PI*RC(Cc1+Cc2)) ?

 

[FvM]

It just seems to me strange that the output divider has no part in the transfer function of the transconductance error amplifier.

Who says it hasn't? It surely has, the same as amplifier gm.

And surely an error amplifier must have negative feedback.

It hasn't, it's simply open loop. Unlike with an OP circuit, the gain depends on gm.

does it meet the 0dB axis at a frequency of 1/(2*PI*RC(Cc1+Cc2)) ?

gm/(2*PI*(Cc1+Cc2))