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Does RHP zero in boost/buck-boost always exist?

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bhl777

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Hi All,

Do we always have the low frequency right half plane zero at boost and buck-boost conveter?

More specifically, the existance of RHPZ seems to be related to CCM/DCM and also the control mode. Can any one clearify the following questions?

(1) can I say RHPZ only exists in CCM, but not DCM? Intuitively, it seems like DCM always has a tri-state time interval, which can be used as the OFF time when necessary during the load transient.

(2) does RHPZ also exist when we have variable frequency mode control? For example, contant off time control has been used in Boost and buck-boost. There is a similar question asked in this forum but no conclusive answer was posted there.

https://www.edaboard.com/showthread.php?304551-Constant-off-time-boost-converter-has-no-Right-Half-Plane-Zero

Thank you!
 

Hi,

For Q1:
RHPZ exists in both boost- and buck-boost-derived CCM and DCM converters. The power-stage inductance determines the frewuency at which it exists. In DCM, it exists at a very high frequency beyond our highest frequency of interest such that it's effect doesn't affect our feedback loop. This is because of the low-value inductance used in the power stage. In CCM, because the inductance is heavy, it shows up at a frequency lower than our switching frequency and actually dwells within the vicinity of our desired crossover frequency.

For Q2:
Yes. Like I already mentioned above, it exists in all boost- and buck-boost-derived converters and the frequency at which it exists is determined by the power stage inductance. Its existence has nothing to do with the control mode.
 

It always exists in the sense that the thing you must do to produce more voltage (turn on the low switch) briefly reduces the output voltage. That's an RHP zero.


However a current mode control loop implemented on a boost doesn't have an RHP zero I believe. And if that's wrapped by a voltage loop with a lower bandwidth the remaining impact of the RHP zero should be almost nothing.
 

(1) can I say RHPZ only exists in CCM, but not DCM?
Yes. In DCM, there is no RHPZ.

(2) does RHPZ also exist when we have variable frequency mode control? For example, contant off time control has been used in Boost and buck-boost. There is a similar question asked in this forum but no conclusive answer was posted there.
When operating in CCM, the RHPZ always exists, no matter what sort of modulation scheme you use. I have also seen others report that constant off/on time control mitigates the RHPZ, but it's simply not true. The RHPZ is built into the boost circuit itself. The controller can add poles/zeros onto the overall transfer function, but it can't remove existing ones (can't cancel a RHPZ since a RHPP is unstable).

RHPZ exists in both boost- and buck-boost-derived CCM and DCM converters. The power-stage inductance determines the frewuency at which it exists. In DCM, it exists at a very high frequency beyond our highest frequency of interest such that it's effect doesn't affect our feedback loop. This is because of the low-value inductance used in the power stage. In CCM, because the inductance is heavy, it shows up at a frequency lower than our switching frequency and actually dwells within the vicinity of our desired crossover frequency.
Show your work. The concept of poles/zeros existing above the switching frequency makes no sense (in the context of state space averaging). It's like trying to describe the frequency response of a digital filter outside its nyquist bandwidth.

However a current mode control loop implemented on a boost doesn't have an RHP zero I believe.
The CMC loop itself has no RHPZ, since the CMC loop governs the inductor current, not the output current/voltage. But if we look at the response of the output, the RHPZ pops up, regardless of whether a CMC loop is used.
And if that's wrapped by a voltage loop with a lower bandwidth the remaining impact of the RHP zero should be almost nothing.
Assuming you mean the bandwidth of the voltage loop is lower than the RHPZ. That's typically the only way to deal with it.
 
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There's actually a RHPZ in DCM boost and buck-boost converters but it exists at a frequency higher than the range we are concerned with. It is not that it doesn't exist. It is just out of the way. That's why it's not considered. Somewhere high up in frequency sits the RHPZ in DCM boost converters, sincerely.

You can calculate the frequency that it exists for DCM with the same formula that you do for CCM. One thing you'd realize is that that frequency is always outside our consideration range of frequencies.

- - - Updated - - -

...
Show your work. The concept of poles/zeros existing above the switching frequency makes no sense (in the context of state space averaging). It's like trying to describe the frequency response of a digital filter outside its nyquist bandwidth.
...
How do you mean show your work? I'm not the OP.

For boost: ((1-D)^2)*R/(2*pi*L) = frhpz.

For Buck-boost: ((1-D)^2)*R/(2*pi*D*L) = frhpz.


Those are the frequencies where the RHPZ exists for the corresponding converters. Those expressions have nothing to do with the feedback loop. They are just components of the power stage transfer functions. If you make a bode plot of these converters' control-to-output transfer functions, they'll show up at these frequencies, whether in CCM or DCM.

For you to say that it does not exist is not correct.

One thing you have to understand is that the expressions we write are approximations. Because it is not written in expression for the transfer functions that you have seen for DCM modes does not mean that they do not exist. It just means that for the sole reason that they are out of the way, (1-s/wrhpz) --> 1.
 

looking at those equations, they only come into play when Rload is very large and the duty cycle D is very large & L is large - under these conditions - you will be in CCM - so your formulae apply - but really right hand plane zero comes into play only when CCM entered into - and your equations show this will be only for R>>1 and D approaching 1, with a large L.

For DCM there is no RHP issue, if you are operating under CrCm, i.e on the boundary between DCM & CCM then yes if you try to increase the power point you will have RHP issues - but if you stay inside a fully DCM window - no RHP issues ... your formulae tend to confirm this ...

Common sense reinforces this, under fully DCM, over one complete cycle the o/p power goes up for an increase in D, under CCM over one complete cycle o/p power does not go up for an increase in D...
 

We are saying two different things here. You are concerned about the existence of an issue. I am concerned about the existence of the RHPz -- be there an issue or not.

I have explained in my post that it exists at very high frequency in DCM that it does not pose a threat. But for the question whether it exists? Yes it does.

Just put in known DCM boost or buck-boost parameter values for the variables in the equation. Whatever value you get, that the frequency that the RHPZ exists.

My point is that it also exists in DCM but you don't have an issue with it.
 
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I have a few questions that I'd like to ask on this:

When we say that a RHPZ exists in boost and buck-boost converters, what is being looking at, the power stage or the close-loop converter?

When we analyze the transfer function, do we consider a continuum of a parameter values or the worst case value?

looking at those equations, they only come into play when Rload is very large...
Actually frhpz is higher for converters with higher values of Rload.

but really right hand plane zero comes into play only when CCM entered into
This statement is with the consideration of closing the loop. I'm considering the inherence of the RHPZ in the power stage.

Common sense reinforces this, under fully DCM, over one complete cycle the o/p power goes up for an increase in D, under CCM over one complete cycle o/p power does not go up for an increase in D...
I do not understand what you mean here but you don't increase this D. This D is already the maximum value for the converter.
 

Respectfully - I cannot agree with you.

I have to disagree with this too.

The thing that makes a boost converter increase voltage has the side effect of decreasing voltage in the short term. That’s a RHPZ. Under all circumstances and control schemes.

DCM doesn’t make a difference. If the loop asks for more voltage the next switch cycle will spend more time with the low side switch on, thus more time while the load is draining the output cap before the indicator charges it again. Again, that’s an RHPZ.
 

But no - not in DCM, in DCM when the D is increased a little the total power to the load goes up in that cycle, because time where the current would otherwise be zero - is now active time - therefore no RHP zero, inside that same cycle the peak input current is bigger and the total current to the load ( & o/p cap) is also bigger - you are confusing with CCM ...

- - - Updated - - -

Respectfully your formulae only apply when the combination of RL, D & L combine to put you in CCM...
 

I just found this paper by Texas Instrument online: it confirms the existence of RHPZ in DCM boost converters.

Google "under the hood of a DC/DC boost converter. The information is on page "3-9".
 

hi - just read it - you refer to equ 18 & 19 in that paper - the so called RHP zero is in fact formed from the output load and the ESR & ESL in the output cap AND the boost choke - it is barely a zero - it merely flattens out the gain response as you now have an inductive divider at high frequencies. There is no RHPZero in the sense that increasing on time in DCM gives a delayed response - it doesn't - as somewhat hazily pointed out in the preceding text - although the writer does conflate DCM and CCM operation at times ...
 

hi - just read it - you refer to equ 18 & 19 in that paper - the so called RHP zero is in fact formed from the output load and the ESR & ESL in the output cap AND the boost choke - it is barely a zero - it merely flattens out the gain response as you now have an inductive divider at high frequencies.

The RHPZ is showed in equation 19. It has nothing to do with all the parameters you mentioned above. It is shown as (1 - s*D/(2*fsw)). Anything outside this is not a function of the RHPZ. Do not confuse the low-frequency gain and pole with RHPZ.

(1 - s*D/(2*fsw)) is the RHPZ exactly like I said. It is there but somewhere far away that it's effect may not be felt.

There is no RHPZero in the sense that increasing on time in DCM gives a delayed response - it doesn't - as somewhat hazily pointed out in the preceding text
This statement again is considering a closed-loop converter not the power stage alone as it should.

although the writer does conflate DCM and CCM operation at times ...
I do not want to comment on this. But I haven't seen it anywhere on this paper.

- - - Updated - - -

Meanwhile, where did you see the inductive divider?
 
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No - I am not considering a closed loop converter - than would be irrelevant anyhow - I'm putting it as simply as can be - In DCM if you increase the D you see the effect immediately - inside a cycle, of increased o/p power - this is not classic RHP zero - where there is a dip in o/p power results from the initial increment in D.

The "zero" alluded to in the paper is the result of the boost inductor and the load and any effect of the ESR/ESL in the output cap - forming a divider with flat gain as the freq rises - you can see that in the graphs.

You have ignored equ 18 - which forms a large part of equ 19 - either way


All converters have this "zero" if they have any series inductance any where and some output load and or caps with ESR / ESL - that does not mean they have a classic RHPZ delayed response - far from it ...
 

Yes, I ignored equation 18 because there's nothing in it that has an effect on the RHPz. The effect of equation 18 is only felt by the low-frequency gain and the pole.

Anyways, I think we are now on the same page. At least we are in agreement with my point in post No.2

Hi,

For Q1:
RHPZ exists in both boost- and buck-boost-derived CCM and DCM converters. The power-stage inductance determines the frewuency at which it exists. In DCM, it exists at a very high frequency beyond our highest frequency of interest such that it's effect doesn't affect our feedback loop. This is because of the low-value inductance used in the power stage. In CCM, because the inductance is heavy, it shows up at a frequency lower than our switching frequency and actually dwells within the vicinity of our desired crossover frequency.
...

Meanwhile, I expressed frhpz as ((1-D)^2)*R/(2*pi*L) which would mean that the the expression for the RHPz is (1 - s/(((1-D)^2)*R/L)).
I can explain why the expression for the RHPz is given as (1 - s*D/(2*fsw)) instead of (1 - s/(((1-D)^2)*R/L)), should anyone want me to.
 

But no - not in DCM, in DCM when the D is increased a little the total power to the load goes up in that cycle, because time where the current would otherwise be zero - is now active time - therefore no RHP zero, inside that same cycle the peak input current is bigger and the total current to the load ( & o/p cap) is also bigger - you are confusing with CCM ...

Switching cycles don't matter. The RHPZ may be above the switching frequency, but its still there.

From Akanimo's source:
"In DCM, and because of the relatively smaller
inductor, the RHP-zero frequency extends to
beyond the switching frequency with negligible
inpact at typical loop crossover frequencies "
 

Oh dear, big strong TI made a statement in an application note! Nothing we can do except breathlessly parrot it.

The TI AN gives one citation for their claim, which can be found here. I've skimmed over it, and it apparently claims a new method of deriving state space models. It's an interesting concept that I'll have to spend more time on. But I can't find anywhere where they make the same claim as the TI AN.
 
Guys this isn't rocket science.

Assume the lower switch stays on for X time meaning it turns on at time 0 and turns off at time X. While the lower switch is on the output voltage decreases. Output voltage hits its lowest point at time X.

If we increase X the output voltage spends more time decreasing and bottoms out at a lower voltage than the previous cycle (before the switch turns off and it rises again). That's an RHPZ in DCM.
 

asdf44 - sorry wrong, in DCM there is always dead time - if you use more of the dead time in raising the current you get more output on the falling current - therefore no delayed action response in true DCM therefore no classical RHP zero in DCM - please think about it carefully ...
 

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