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Stability analysis for hysteretic switched mode LED driver is pointelss?

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Hi again,

Ok thanks.

I asked about that cap because it could play a crucial role in the stability.

I was out late last night partying so im a bit overtired this morning, unfortunately. I rarely go out anymore but when i do i like to party heartily :)

At my second look at this circuit it seems like the main stability issue will be how the LCR output reacts with the duty cycle AND frequency of the switch. This is unlike the regular buck because with a regular buck the frequency is constant and known at all times. It appears that we might first model this as a frequency controlled switch being controlled by the input source voltage because the output load is constant. We then have to think about the aliasing between the switch frequency and the plant reaction. For some values of frequency we may not even get the right output. Although this would be rare if it even happened once for a power supply during normal operation it could mean the lights dim, which we certainly dont want. Keeping the output capacitance as low as possible would help prevent any aliasing though because the switch would have to switch too fast to interact strongly with the plant reaction, and that means it would only be able to interact mildly for sub harmonics of the plant, which would not be as bad.
This leads me to believe that it would help to simply look at the points where there is strong or mild aliasing and see what it does to the output. This is what i believe an averaged model would show us. We then might take steps to avoid the worst operating areas, if they in fact ever can happen because after all the very low output capacitance of LED's means the plant main frequency is going to be very high. I'll try to look into this more though today or tomorrow. Right now im tired out and drinking coffee :)
In the mean time maybe you have some more thoughts on this stability issue too. I will also draw up a more simplified schematic showing the basic operation only, without focusing on individual part peculiarities with the exception that the switch frequency will have an implied limitation on how high it can go.

BTW, it couldnt hurt to start with a time domain analysis could it? We could look at the most critical operating points that way at the least, and try to determine if those operating points could ever be reached due to the limitations on the switching frequency. Obviously there has to be limitations on that or else the MOSFET would be forced to switch too fast and that would consume too much power.

Here's a simplified schematic.
BTW, do we have to use an N channel MOSFET? We then have to assume that the output of the SR latch is higher than +Vcc .
 

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Hi again,

Ok thanks.

I asked about that cap because it could play a crucial role in the stability.

I was out late last night partying so im a bit overtired this morning, unfortunately. I rarely go out anymore but when i do i like to party heartily :)

At my second look at this circuit it seems like the main stability issue will be how the LCR output reacts with the duty cycle AND frequency of the switch. This is unlike the regular buck because with a regular buck the frequency is constant and known at all times. It appears that we might first model this as a frequency controlled switch being controlled by the input source voltage because the output load is constant. We then have to think about the aliasing between the switch frequency and the plant reaction. For some values of frequency we may not even get the right output. Although this would be rare if it even happened once for a power supply during normal operation it could mean the lights dim, which we certainly dont want. Keeping the output capacitance as low as possible would help prevent any aliasing though because the switch would have to switch too fast to interact strongly with the plant reaction, and that means it would only be able to interact mildly for sub harmonics of the plant, which would not be as bad.
This leads me to believe that it would help to simply look at the points where there is strong or mild aliasing and see what it does to the output. This is what i believe an averaged model would show us. We then might take steps to avoid the worst operating areas, if they in fact ever can happen because after all the very low output capacitance of LED's means the plant main frequency is going to be very high. I'll try to look into this more though today or tomorrow. Right now im tired out and drinking coffee :)
In the mean time maybe you have some more thoughts on this stability issue too. I will also draw up a more simplified schematic showing the basic operation only, without focusing on individual part peculiarities with the exception that the switch frequency will have an implied limitation on how high it can go.

BTW, it couldnt hurt to start with a time domain analysis could it? We could look at the most critical operating points that way at the least, and try to determine if those operating points could ever be reached due to the limitations on the switching frequency. Obviously there has to be limitations on that or else the MOSFET would be forced to switch too fast and that would consume too much power.

Here's a simplified schematic.
BTW, do we have to use an N channel MOSFET? We then have to assume that the output of the SR latch is higher than +Vcc .


My dad say's and I quote " If you can party and post the next day, you DIDNT party hard enough" LOL, he also said something about a place called woodcock or something, but it went over my head a bit.
 
Could use P type if req'd. BTW, is that a working sim you have there with the SR latch?....would be great to run that.
 
After seeing the OP's many page threads on stuff like this, and him not accepting any ones opinions but his own, I'd be asking one question of him..... "what does your manager say?":p:banghead::sorry:
 
ive worked in places, where if i suggested to the manager that we delay shipment of an hysteretic led driver because we first need to do bode plat stability analysis, they would sack me on the spot.
 
Hi again,

LG:
Ha ha, i think he meant "Woodstock". Even though i posted today i'm really tired out, but trying to wake up a little more somehow.
You would not believe the number of spelling errors i have made today that i had to go back over and correct before posting.

Flyback:
It should be a working sim, although i did not try it yet, but now that you mention it i think i will try that.
The basic operation is simple of course, the SR latch is just there to 'remember' the states of the comparators and either keep the MOSFET on or keep it off. So it should work the same for getting to the basic operation themes of these kinds of converters. Might be a little tricky getting the solution to converge...we'll just have to try it.

shortbus:
Well these are some more in depth topics here. They require more thought and more work, and ultimately some assumptions that may come into question depending on the application and the desired want of detail. I am skipping some details that would be particular to a given exact topology in favor of the overall theory and overall analysis. If the reader wants to go into more detail they have to specify that and that it is, or modify the results so far to reflect the particular application.
So in other words we are more or less just discussing this anyway, so different opinions will come in as to the exactness and applicability. We'll just have to see how it plays out in time.
 
ive worked in places, where if i suggested to the manager that we delay shipment of an hysteretic led driver because we first need to do bode plat stability analysis, they would sack me on the spot.


Then the issue is as an engineer do you.

1) stick to the principle of correct engineering practice

2) Do your job, collect the pay and say nothing even if its wrong

3) worry about it all and post knowing it wont change anything

4) Grow a set and go see your Bosses Boss, lay it down and put a well thought out offer on the table :D

Me I would go work for myself or choose 4. But all along you have posted so many anti things about the people you work for, and now they also grow TULIPS! I still dont get that please explain, at the moment you dont fit my logic and it drives me nuts when that happens, so please just for me explain what TULIPS have to do with the price of fish and your job.
 
To be honest, I was looking for someone to come forward and say, that converter is a couple of comparators, no stability analysis needed.
 
Hi,

I would like very much to say that, but there is the issue of the aliasing we would have to at least look into. With very very small output capacitance though i would think it would be stable because the MOSFET switching speed allowed could probably never reach a high enough frequency to matter. So it's a matter of looking at the output capacitance vs the MOSFET switching frequency. It would be nice to be able to say, "This design works as long as the switching frequency is 2 times less than or two times higher than the natural frequency of the plant." Two times higher probably doesnt matter, but who knows, maybe another design uses a large output capacitance like 1000uf and that could mean keeping the switching frequency higher would be better so it never gets close to the resonant frequency of the plant.
Might be interesting to look at these different cases.
 
I didnt think the cap size was relevant?...the inductor current is being controlled between 2 levels by the comparators..thats it I thought?
 
Hello again,

Well the Rs, inductor, capacitor, and load R make up the plant, and if that resonates at a frequency F1 and we happen to be switching at that same frequency, we can get some strange operation. It may or may not be damaging to the circuit, but it may alter the light output which is not a desirable feature either.
I'll try to do some definite analysis soon and see what i can find out.

I've updated the simplified schematic because i left out the two "one shots", and obviously i flipped one of the comparator inputs so i fixed that too.
The "one shots" are made as simple as possible just for illustration, and are needed because what we really need is for the latch to switch once at the time the level changes to one of the preset values (comparator voltage references) and then maintain that state until the opposite preset value is reached. Without the one shots the latch will see a "set" input forever for one example which means the circuit wont 'oscillate'.

So now the circuit operation is as follows...
When the inductor current is lower than 1 amp the MOSFET turns on and stays on until the inductor current goes above 1.5 amps at which time the MOSFET turns off, and the cycle repeats as the current ramps down below 1 amp again. I believe this is the operation you wanted to look at.
There would be other ways to get this operation too without using one shots, such as using a single comparator with, well, he he, hysteresis, but for now it's good enough just to establish a base line kind of operation. The switch points are very well defined, the plant characteristics are not too well defined but im pretty sure that with no output capacitor we can assume a high frequency resonant frequency for the plant. Adding a capacitor though would help us understand what happens if we should ever be so unlucky as to actually switch at the same frequency, or perhaps near the same frequency. The assumed operation is that the inductor and output load (and anything else involved in the output such as the Rs and sense resistor) create a 'ramp' of current, but if we run at the wrong frequency we could end up with a sinusoidal waveform or half or part of a sinusoidal waveform, which them perhaps not average to the same current level as we are assuming for correct operation (average of 1 amp and 1.5 amps is 1.25 amps). We'd also want to look at the peak currents to see if they go higher.

In the above im just trying to give you an idea about what i would like to get out of this analysis: if anything can go wrong, and if so, how wrong can it go.
For noise analysis we probably would assume that there is random noise present which averages to zero and that it is not enough to wreck the normal operation.
 

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I thought when you control an inductive current in this way, you cancel the pole due to that inductor,,and get a simple, first order system, rather than a resonating LC response, no matter what the cap size?
 
Hi,

Well if you could prove that mathematically then you would not have to 'think', you would 'know' :)

If that is true we'd like to be able to show it with some math. But think about this, how well are we really 'controlling' that current? We are only measuring two points along the current waveshape, and it is normally sawtooth, but what happens when that waveshape changes to sinusoidal? We are still only measuring two points, so we no longer have complete control over the peak current (remember that turning off the switch does not always guarantee that the current goes down when driving a resonate circuit, while when driving a first order circuit it will go down).

I am starting to think that there could be several 'modes' to the operation, which we probably wont see due to the very small output capacitance. Each mode could lead to a different average current output. How much different though is the real question...is it enough to make a big difference and make the design look terrible, or not.
 
I thought when you control an inductive current in this way, you cancel the pole due to that inductor,,and get a simple, first order system, rather than a resonating LC response, no matter what the cap size?
That would seem to be true. If you are controlling the loop of an LC circuit using the capacitor output voltage, then the output voltage will continue to rise after the inductor switch opens because there is current still flowing in the inductor through the flyback diode (the resonant effect) which then requires second-order compensation to stabilize the loop. If you are controlling the loop using the inductor current, then the current starts to fall the instant the inductor switch opens. The resonant capacitor voltage continues to rise as before, but that is not in the control loop so has no effect on the loop stability.

As long as the switch response time is much less then the rise and fall time of the inductor current, it would appear that the circuit is inherently stable, the same way a bang-bang house thermostat control is inherently stable since the house thermal time-constant is much larger than the thermostat response time.
 
That would seem to be true. If you are controlling the loop of an LC circuit using the capacitor output voltage, then the output voltage will continue to rise after the inductor switch opens because there is current still flowing in the inductor through the flyback diode (the resonant effect) which then requires second-order compensation to stabilize the loop. If you are controlling the loop using the inductor current, then the current starts to fall the instant the inductor switch opens. The resonant capacitor voltage continues to rise as before, but that is not in the control loop so has no effect on the loop stability.

As long as the switch response time is much less then the rise and fall time of the inductor current, it would appear that the circuit is inherently stable, the same way a bang-bang house thermostat control is inherently stable since the house thermal time-constant is much larger than the thermostat response time.


Hi,

I think you are both forgetting about the DIODE (the Schottky diode).

Remember that the current is on the RISE when the switch opens, because the current is ramping up and when it exceeds 1.5 amps that's when the switch opens. When the switch opens (conventional) current has been flowing left to right in the inductor, the inductor will then continue to conduct through the diode. So current does not stop when the switch opens, it just finds another path and the output circuit becomes a passive LCR circuit with stored energy in both inductor and capacitor. Remember that when a pulse is applied to an LCR circuit if there is little damping the circuit resonates for a little while with waveshape as an exponentially damped sinusoid, and that's only with one single pulse that starts and then stops at some point and never returns.

How bad this works out to be in real life though would depend on how much capacitance we have and how much damping. The LED's have little capacitance, so there is probably not much of a problem, and that also probably means lots of damping which then means no resonant effect.
 
MrAl, that was just to be a reference to how much his threads are to a BillyMayo thread. They, in some ways are quite a bit similar. Already have there mind made up and drag it out hoping some one will agree with them.
 
Hello again,

shortbus:
Ok, i'll keep that iin mind, thank you.

others:
Operating params: L=100uH, R=4 Ohms, Cout=1uf, Vcc=10v (note R is used to replace the LED's as their resistance shouldnt vary too much, too much to worry about for now that is)

At 50 percent duty cycle, the waveform through the LED's looks nearly sinusoidal. It's not though. Nice thing is, it does not shoot up above the inductor current peak. Bad thing is, it is varying quite a bit anyway, from 1.1 amps to 1.4 amps, although for LED's that's not necessarily bad.
There is one catch, and that is if the input goes too low the circuit will start to behave like a low frequency LED blinker except the LED's will not go completely off, they will just have their current vary from around 1 amp to 1.5 amps. That would make them appear to dim, then brighten, then dim again, etc. A good addition to the circuit then would probably be a low voltage detect, or allow the LED's to 'blink' to show that the batteries are running down.

A simplification to this circuit for this kind of analysis is to just hit the inductor with a duty cycle that forces the current to vary between 1 amp and 1.5 amps. That has to be done with various input voltages, and the load can be varied to look for problems with low or high loads, and the capacitance can be varied too. It looks like higher capacitance might actually help, although i have to look at this more yet.

Despite the wild looking nature of the circuit, it is starting to look pretty tame. Even when the plant goes to a damped sinusoidal response it isnt as bad as originally thought with the peak sinusoidal being limited. Of course this means the LED brightness varies, but it will normally vary quite fast, faster than a human can see, unless the input voltage is allowed to go below some threshold where the LED brightness will vary quite a bit and very slowly, easily observable by any human.
 
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