# In SMPS , why does peak current mode control have lower gain for inner loop compared to average current mode control?

This has been bothering me for a while.

In some of the design notes of power management ICs , it is mentioned that peak current mode control has 'lower gain - wider bandwidth' inner loop compared to that of average current mode control. Why is it so?

Quote from a design note-

"Peak current mode control has a low gain, wide bandwidth current loop which generally makes it unsuitable for a high performance power factor corrector since there is a significant error between the program signal and the current." Application note for UC3854 Power factor correction

Thanks

• Link to the design note in question? Because (A), I'm interested, and (B) the answer may be in there and you're just missing it. – TimWescott Dec 16 '18 at 21:07
• Added the link to design note. – Divya K.S Dec 17 '18 at 6:38

Te real reason is : There is always peak to average error for peak current mode control. You are controlling the peak current not average current. At the zero crossings, due to the big inductance ( used for CCM), the slope V/L = di/dt , V is very low and inductance is very big,therefore the slope of the current will be slow. Which also means that the peak current tries to catch up to hit the reference set point, but it cannot because V is very low and in doing so, the average input current is distorted at zero crossing. Therefore with peak current mode control you have more crossover distortion. And remember there is a ramp in peak current mode control, which actually limits the duty cycle at the zero crossings ( the ramp is not helping actually, it is working against us). Llyod Dixon talks about this in Unitrode seminar notes. Also Christophe Basso talks about this in his textbook. The solution to remove the peak to average error is to make the inductance bigger so that the current ripple is lower. But, if you make L bigger at the zero crossing, the di/dt will be even slower. PCMC was abandoned for this reason in PFC. Average current mode control (CCM) and constant ON time boundary mode are quite famous for Power factor correction

• Yes. I understand the above reasoning. My doubt is about gain and bandwidth consideration. How do they play a role in comparing PCMC with average current mode control? – Divya K.S Dec 25 '18 at 18:02
• I do not have a correct answer for it. Please take a look at average current mode control analysis done by Dr. Ray Ridley : researchgate.net/publication/… Usually for PFC applications PCMC and average current mode control (ACMC) are approximated as 1st order ( power stage) transfer functions in the low frequencies ( 1-2kHz). ACMC needs 2 compensation networks ( one for voltage loop), 1 for current loop. PCMC needs just 1. This is another good reference : maximintegrated.com/en/app-notes/index.mvp/id/3939 – Venkat Karthik Dec 28 '18 at 9:34

I think this is very closely related to the unity-gain of operational amplifiers.
That is, I think the SMPS you're talking about uses op-amps to tame their system.

Op-amps has a bandwidth that is related to their unity-gain frequency and closed loop amplification which can be seen in the graph below.

Yes, that's right, real op-amps are designed to have one dominant pole, and you as an engineer can choose where on the slope you want your op-amp to operate in.

The equation for the bandwidth is the following:

$$\large\omega_{\text{bandwidth}}=\dfrac{\omega_{\text{unity-gain}}}{A_{\text{closed loop}}}$$

As usual there is always a trade-off, either you have high bandwidth and low amplification, or you have low bandwidth and high amplification. You can however cascade amplifiers to increase the bandwidth, or use better op-amps, both of which costs more money. It's all about trade-offs upon trade-offs.

In your case they are talking about "peak current mode" which is something that should be dealt with fast. Fast means high frequency, high frequency means high bandwidth, high bandwidth means low amplification. And this is why there is lower gain for peak current mode control.