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# zero in boost converter feedback loop

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#### mengghee

##### Full Member level 3
hello everybody,

there is a circuit diagram in one of my old thread. and it was a feedback loop of a simple boost converter. there is a capacitor parallel with the feedback resistors cz1. and in the explanation it says that it is there because the circuit requires a zero. what is a zero ? and why is it needed ? and also ... what is the configuration of the error amplifier in that circuit ? thank you very much ..... the link is below

thank you

regards,
mengghee

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A zero (also called a transmission zero) corresponds to a frequency that makes the loop transfer function zero. The frequency of the zero is where this occurs. First order zeros are of the form $1 + s/\omega_z$ where $\omega_z$ is the zero frequency. The transfer function for a zero is around 0dB below the zero frequency and increases +20dB/decade above the zero frequency. The phase of the zero is approximately 0° below $\omega_z/10$ and 90° above $10 \omega_z$, between these limits it incrases at 45°/decade.

Note that the zero adds phase (up to 90°) into the transfer function. The zero is used to add additional phase into the loop gain transfer function so that the overall tranfer function phase is increased and moves away from -180°. Moving away from the -180° increases the phase margin of the system which improves stability.

Best regards,
v_c

### mengghee

Points: 2
v_c,

I am sorry, but i am struggling to understand what u are trying to tell me. is there any other way you can explain the purpose of zero refering to the circuit diagram in the link and without touching too much on control system ? i am not very good in control system. in fact very poor.

regards,
mengghee

and also what affect it has on the circuit ?

Well, you are right -- it is indeed a control system and the terminology related to it uses control system jargon. I cannot think of any way to explain it now without using these terms. One thing I can say is that the R's and C's added to the compensation network, alter the time delay (phase) characteristics of the overall system and this phase is very critical to the stability. Basically, you don't want any noise frequency to go around the loop and experience a 180 degree phase change. Why because since the error amplifier is in the inverting configuration it adds another 180 degrees (that makes it 360) and now you are constructively adding to the noise.

So let's say a 1mV noise signal at some frequency say 200kHz in the loop. Let's say the gain in the system at 200kHz is 20dB (factor of 10) and the total phase is 360. If this signal is injected in the loop, it will experience a gain of 20dB and since the amplified signal is in phase with the original signal, the new signal will be amplified by 10 every time it goes around the loop. The signal might grow pretty quickly and might saturate devices or lead to sustained oscillations.

Well I don't know if this is better -- I cannot think of anything great right now.

I think you might want to take a look at the Fundamental of Power Electronics by Erickson & Maksimovic. They explain this pretty well although they will also be using some control system terminology.

Best regards,
v_c

### mengghee

Points: 2
thanks V_C,

It is much better though i still haven't get a grip of it. well i have been reading on many papers and websites, application notes etc. have yet to understand the control system part. i have to admit i am a bit too slow. I don't really understand the bit where usually i see a bode plot, gain vs frequency. i have learnt bode plot before and i did quite understand it from my second year in uni. the thing which i don't understand is ... how do we get the bode plot ? what is the gain ? what frequency ? where does all of them come from ? frequency of what ? gain of what ? sigh* sigh* thanks

regards,
mengghee

To understand the basics of the Bode plot, I suggest that you take a look at a book on control systems. Also the book that I mentioned before does an excellent job of introducing the Bode plot since that is used later in the book to look at the loop gain of dc/dc converters.

The loop gain transfer function consists of the linearized transfer function of the converter (that's the dc-dc converter itself) and the transfer function of the error amplifier and driver circuit.

I suggest that you take a look at this reference **broken link removed**
It is going to take some time to understand many of the basic concepts before putting it all together and to make it make sense to you. So I don't think there is a quick solution to this.

Here's another reference that is a bit more basic **broken link removed**

Best regards,
v_c

Added after 1 hours 48 minutes:

Also look here https://focus.ti.com/docs/training/catalog/events/event.jhtml?sku=SEM401002

Points: 2