Stability analysis for hysteretic switched mode LED driver is pointelss?

[Flyback]

Hello,
Can you confirm that a Bode plot stability analysis for a switched mode LED driver based on the ZXLD1360 IC (schematic as per page 2 of the datasheet) is pointless?

That is, ZXLD1360 based LED drivers are intrinsically unstable, its just that the instability is bounded by the comparators?
So can you confirm that the phase and gain margins (if produced) would indicate instability, and so would be pointless?


**broken link removed**

 

[steveB]

I don't think it would be pointless if it is done in the correct way. Usually, stability analysis of switched converters requires averaging and linearization to get a representative linear system to analyze for stability, sensitivity, robustness, frequency response, etc.

Is it worth the trouble? I'm not sure if it is or is not. Often to be sure that it is not needed (and pointless from that point of view) you need to do the analysis. Either that, or you can subject the design to rigorous environmental testing and experimentally change component values to be sure the design is robust and stable in the sense that you require.

Of course if the product exists, recommended circuits and guidelines are given, and the product is field tested, you probably don't need to go crazy doing any of this because the manufacturer has probably already done it for you (assuming you trust them).

 

[Flyback]

But if something's unstable by nature then surely stability analysis is less than useful?

 

[steveB]

That's why I say that it must be done the correct way, and you need to do the analysis for the aspect of the system that is not unstable. So, the system can be switching between two unstable conditions (hysteresis, bang-bang, astable are some words often used here), but the average behavior can still be stable and under good control. Hence, there are mathematical techniques that can be used to reveal the particular aspects of the system that are amenable to linear stability analysis. This then become one of many tools to help understand and design the system.

So, I would say that it can be very useful for understanding and design optimization, and can reveal things that can't be learned in any other way. However, it is not always necessary to do this type of analysis to make a useful practical system. The example you show, perhaps it is not particularly useful, but I think you could do it. For more advanced control of DC/DC converters, it is very helpful to do this type of average model and linearization to develop system models that can be studied using standard linear analysis tools.

 

[Flyback]

We appear to agree that it is unstable, so do you agree that Bode plot stability analysis would indicate a phase margin of zero degrees and a gain margin of zero?...after all, the hysteretic converter referred to is essentially an oscillator, the oscillation is in the buck inductor current.

The gain at 180 degrees for an oscillator is one.....ie, the right value for continuing oscillations....ie instability.
Surely a bode plot analysis is just going to show theoretical instability?

Despite thousands of bode plot analyses being carried out and depicted in PWM controller datasheets and application notes, I have never seen one single example of a bode plot analysis being carried out for a hysteretic buck converter of the type as ZXLD1360.
I would say that as long as the internal comparators act as comparators, and there is enough "delta" signal voltage on the current sense pin so that the signal doesnt get drowned in noise, then the device will operate correctly , as it should.?

 

[steveB]

I've never seen one example of a bode plot analysis being carried out for a hysteretic buck converter either, and I've never tried to do it myself, so I can't comment too much more on it. I can't argue with the fact that it seems the device will operate correctly over a very wide range of conditions and should be robust.

I suspect the analysis of an "averaged system" will end up looking simple and stable, while the actual system is an alternating type of unstable system. I'm not sure that this type of unstable system would have the classic bode plot gain of 1 with 180 degree phase shift.

 

[MrAl]

Hello there,

But if something's unstable by nature then surely stability analysis is less than useful?

If you want to call this system 'unstable' then why not call the regular buck circuit unstable too?

If stability analysis has somehow become obsolete then that's news to me

For switching circuits we usually resort to an 'averaged' model, where the switching action is modeled as being so high in frequency that any ripple becomes insignificant, and that leaves us with a linear equivalent for the switching action, and this linear circuit can then be analyzed just like any other linear circuit.

Before you try to suggest that the averaged model is not the real circuit, i know that it is not exactly the real circuit, but the averaged response is exact so we can still use it for stability analysis.

Some averaged models are fairly complicated to generate, but the buck isnt one of the complicated ones, it's quite easy really.
We could do a simple buck to show you how to proceed and then you could apply that to your circuit if you like.

 

[Flyback]

surely the only thing that could destroy the operation of the hysteretic zxld1360 buck is the comparator ?
So basically as long as the input to the signal to the comparator does not get drowned in noise then we're fine?

 

[MrAl]

Hi,

I have to wonder why you are so worried about this circuit, what brought you to think about this?

I also realized that the simplest averaged model example is probably a switch in series with a resistor, where the switch is turned on and off in a regular fashion like in a PWM circuit. For a 'regular' averaged analysis we assume the switch on/off frequency is very high as compared to other responses in the system. The on/off switching action makes the total resistance look higher.

For a resistor Rs and knowing the duty cycle DC the averaged response is then:
RTotal=Rs/DC

so for a 1k resistor and duty cycle DC=50 percent, we'd have:
RTotal=1000/0.5=1000*2=2000

so the resistance looks twice as high. For a 25 percent duty cycle we'd have:
RTotal=1000/0.25=1000*4=4000

so the resistance now looks four times as high.

This makes sense because if we break the circuit for half the time the average current halves, and if we break the circuit for 75 percent of the time the average current quarters. If there are other parts in the circuit we must take those into consideration too though.

You can note that once we convert to the averaged model we loose the ripple information (the micro time information), but that's not what we are after in this kind of analysis anyway. If this was part of a larger system we would make sure that the switching action was fast enough to consider using an averaged model, and then we would replace it with a resistance of Rs*DC for the stability analysis. Often the duty cycle changes as part of the system response so DC becomes a function of frequency.
This is like displaying the response of the circuit on an oscilloscope, then looking at the scope from very far away...we just see the major response we dont see the tiny changes.

A complete application example would be a tunable low pass filter. The frequency range would be limited to much less than the switching frequency of the switch itself but would also depend on any post filtering.

Interestingly, the normal buck circuit with voltage regulation turns into a linear voltage regulator when we move to the averaged model. We could then do a root locus for example and come up with very useful data about the stability of the circuit.

 

[large_ghostman]

OMG another Led crusade can you confirm means: this is what I think but I dont want to look like a tinned meat sandwich.
I wouldnt mind but he has even stopped liking posts! only reason I used to answer was for the points

 

[Flyback]

I thought the "Likes" icons had gone...till now,
Anyway, supposing your gaffer told you that he was launching a production batch of 5 million ZXLD1360 based LED lamps into full production..without having done the bode plot stability analysis...they will be immediately shipped to customers.
He will not be swayed. He will not do Bode plot analysis.
He will launch the 5 million into production.
He will simply ensure that the current sense signal voltage is not drowned by noise. ie that this signal is big enough to mean that it doesn't get drowned by noise.


The company could go bust if a large number of this batch go unstable and fail.
Do you report him to his superior?
Or do you not?

 

[large_ghostman]

I thought the "Likes" icons had gone...till now,
Anyway, supposing your gaffer told you that he was launching a production batch of 5 million ZXLD1360 based LED lamps into full production..without having done the bode plot stability analysis...they will be immediately shipped to customers.
He will not be swayed. He will not do Bode plot analysis.
He will launch the 5 million into production.
He will simply ensure that the current sense signal voltage is not drowned by noise. ie that this signal is big enough to mean that it doesn't get drowned by noise.


The company could go bust if a large number of this batch go unstable and fail.
Do you report him to his superior?
Or do you not?

No dont report. Do a plot yourself though and keep it quiet, you report you get put on the s h i t list and might get sacked. You are better to wait until someone says " anyone bothered to plot this?" then pipe up.
I am learning fast that sometimes keeping your head down when you think you hear thunder is a good way to avoid the bullets

 

[Flyback]

ok, but you plot it, and you show instability, because after all, its an unstable system..thats how it works, its essentially an oscillator, and in the world of smps, oscillatory behaviour is classed as instability.

Supposing you do the alternative analyses explained by other posters here, which somehow gets away from showing a "Normal" hysteretic converter as being unstable, and shows instability in the actual operation , even though the 5 prototype units were fine.....what do you then say?

What do you then say?

 

[large_ghostman]

ok, but you plot it, and you show instability, because after all, its an unstable system..thats how it works, its essentially an oscillator, and in the world of smps, oscillatory behaviour is classed as instability.

Supposing you do the alternative analyses explained by other posters here, which somehow gets away from showing a "Normal" hysteretic converter as being unstable, and shows instability in the actual operation , even though the 5 prototype units were fine.....what do you then say?

What do you then say?

Then you stick it all in a email to your boss, you say. Boss look I am fretting over this, I cant sleep I am loosing weight and I have even been driven to bugging the hell out of people on the internet because I am so upset about it, could you please take a look at these plots (or insert other test here) and reassure me please, Sooth my brow and take my pain away, please please tell me it will all be ok, Or Boss I am gonna CC this email to your Boss and include my terms and contract for your job!
Best regards (fill in name here).


OR

Just send him the test results, if he does nothing then simply wait, when it goes the same way the pear did you then go get a T SHIRT printed with TOLD YOU SO on the front and a copy of the plot or whatever on the back.

 

[steveB]

Before a design goes into production, you would want to do some due diligence to make sure the design is robust. Usually, this involves doing as much analysis as you can, and then testing the hell out of the product to find out its failure modes and to make sure that it will not fail under the operating and storage conditions specified.

If I were an engineer in that situation, I would do the analysis on my own, even if it meant my own time had to go in. This would be as much an issue of self preservation as it is an altruistic gesture for the company. Bottom line is, ... if the product fails with that production level, it can cripple the company, hurt stock owners, and I and my fellow coworkers may lose our jobs. Also, doing the analysis is a good learning experience and I often do such exercises on my own anyway just to learn.

If my own analysis revealed a problem, then I would report the problem. Otherwise, I would not mention my work and just sleep a little easier at night.

But, this analysis is a secondary issue. The main question is whether the product/device has been subjected to real world failure mode testing. Have you beaten the crap out of it to find out what makes it break? If you haven't, then you will find out that answer from field data on the real product, which might end up being very costly.

For reference, any design work I've ever done on Navy contracts has always required a detailed stability and sensitivity analysis. Never have we been allowed to say, "hey the system is not linear", or "it can't be linearized", or "it is inherently unstable and hence a stability analysis can't be done or is not meaningful". There is always something that can be done, and we have to do whatever can be done mathematically, even if it is only approximate. But, after all this due diligence design work, the Navy then goes and beats the crap out of the system. This last "gate" is the critical one because mistakes can be made in an analysis but real data does not lie.

 

[MrAl]

ok, but you plot it, and you show instability, because after all, its an unstable system..thats how it works, its essentially an oscillator, and in the world of smps, oscillatory behaviour is classed as instability.

Supposing you do the alternative analyses explained by other posters here, which somehow gets away from showing a "Normal" hysteretic converter as being unstable, and shows instability in the actual operation , even though the 5 prototype units were fine.....what do you then say?

What do you then say?

Hi,

You need to do the analysis first, then anything else comes later. If the converter works then it wont come out as unstable, but you cant always throw a definition at something and expect it to hold for every case under the sun. There could be special circumstances that alter the interpretation of 'instability'.

You also seem to be confusing oscillation with total instability. If the oscillation is bounded then it's not unstable. So the oscillation has to be controlled that's all.

Maybe if you draw up a little circuit with comparators we can take a look.

 

[Flyback]

Here is circuit in LTspice

 

[steveB]

By the way, I should mention that one of the problems I've seen, that can sneak up on you, is after you have tested and analyzed and proved the design is robust, later some "bean counter" will decide to swap a critical component for an "equivalent" part that is much cheaper. I've seen this happen many times.

The problem is that not all properties of a part are fully captured by its specifications. Hence, a re-qualification of the product should be done. But, usually it is not done because of the cost and time needed, which sometimes leads to disasters, which I've witnessed a few times.

 

[MrAl]

Here is circuit in LTspice

Hi again,

I took a quick look and that looks like a good 'drawing', thanks for doing that so i can clearly see what you are talking about.. I'll see if i can take a better look tomorrow sometime as i dont think i'll get a chance to do it tonight. In the mean time though, what is that "C1" part doing there?

We'll have to handle this a little different than with a standard buck.

 

[Flyback]

Woops, C1, yes, I forgot to delete it.....at least its not connected....well you can connect it if you want, and filter the LED current.