Formula for Right Half Plane Zero in a Boost Converter 4

[DHambley]

Lloyd Dixon gave us this equation long ago for the corner frequency of the RHP zero for a Boost converter:

F = (1/2pi)* R/L * (1-D)^2/D
= (1/2pi)* R/L * (Vi/Vo)^2/D

Other app notes from TI give this equation:

F = (1/2pi)* R/L * (1-D)^2
= (1/2pi)* R/L * (Vi/Vo)^2
There's no D (duty cyle) in this denominator!

National Semi gives this formula:

F = (1/2pi)* 1/L * (Vin*D)/Iin

Well, these three just don't match! Any thoughts on who's right? I've always used the first formula above.

DH

 

[sreid]

Switching Power Supplies By Keith Billings (Earlier Edition) had a good description and equation that worked for me but my copy grew legs and walked off. The book also has good sections on magnetics especially powered iron cores and litz wire. I'd buy another copy but I don't have a need these days.

http://www.amazon.com/Switching-Pow...=sr_1_2?ie=UTF8&s=books&qid=1225660671&sr=1-2

 

[Fluorescence]

Sorry to throw in my ten pennorth, but this is an interesting post and others may be inspired to answer..

I was thinking of some practical method of geting the RHPZ corner frequency.

I was thinking that it must be measurable from an actual boost converter (simulation or real).
Can we say If it wasn't measurable then it wouldn't matter?

-But i wonder how to isolate this measurement from others in the converter.

I reckon to make a boost SMPS and use no compensation...ie just the feedback divider.

Switch from no load to full load and see how long it takes to stabilise out at the full load. -either that or put a watch on the boost diode current and time how long before the current goes from no load current to full load current.

.....in that timing i thought would be an indication of the corner freq of the RHPZ.

then you can check this with the formulae.

 

[DHambley]

Flou, The zero is actually pretty measurable. The plot from our phase-gain analyzer shows the effects of the RHP-zero approximately where the first equation (I'll call it the "Dixon" equation) sais it should be. That is, a rising gain and a drooping phase. The duty cycle in the present configuration is high, like 80%, so that the "missing" (1/duty) in the TI equation would only mean a 25% difference in corner freq'. The actual 3dB point is kind-of hard to determine with all of the other noise on the bode plot, so it's hard make out this 25% difference.
DH

 

[sreid]

Since my "Billing's Book" apparently "Packed-Up and Went Home" an my memorys fade, remind me

1) Does the RHP Zero exist for both continuous and discontinuous switching?

2)The RHP Zero shifts frequency [f] with changes in the
Vin Level and the question is; f decreases as Vin decreases? And this results in conditional stability conditions?

 

[Renovator1]

hgldr - I've always gone with Lloyd's equation, too. Those Unitrode seminars are excellent reference material for anyone that designs SMPS. That said, you are asking for trouble if you let a boost or flyback derived converter go into CCM; make sure the PWM chip you are using can't go to 100% but regardless there will be a load current which will cause the converter to go to max duty cycle which, perversely, will cause the output voltage to drop. To see this sort of nastiness in action on your phase/gain (Bode plot) analyzer just keep loading the converter down until the output voltage suddenly drops to zero.

Thus, while you can predict the location of the RHP zero, unless the converter operates with a fixed or only slightly varying load, you don't ever want to encounter it in the field - the converter will get stuck in the above described metastable state.

 

[DHambley]

Renovator,
Yes, it's true that designers new to SMPS's need to educate themselves of these issues with CCM, some of which you've pointed out. There are many applications for which CCM is used in flybacks and boost converters. I don't believe anyone is asking for trouble by doing so, unless they don't know what they're doing.
DH

 

[Renovator1]

You *can* run a boost/flyback in continuous conduction mode (just to differentiate between critical conduction mode - which is actually ideal), but there will be some combinations of input voltage, duty cycle and load resistance that are unstable. Of course, the last sentence you wrote sums it up perfectly, "...unless they don't know what they're doing."

That said, as you have a phase/gain analyzer at your disposal *you* probably know what you are doing... Most people don't bother buying one of those things just for the heck of it

 

[DHambley]

The thing people need to be aware of is what you wrote, "there will be some combinations of input voltage, duty cycle and load resistance that are unstable". This came to light on my particular project.
The flyback which I'm working on works fine (28V input with typical O/V, U/V, and other input spikes) but my customer now changed their parameters and they need it to work if the input droops to 6V. That's where the CCM is occuring and thus, the lively RHPzero came to life. I had to dust off an old textbook to analyze it.

 

[Renovator1]

Oh, boy... 6V to (presumably) over 28V on the input? That's gonna be a tough nut to crack!

Hey, I found yet another equation to determine the RHPZ frequency:

F = (Rl * Vin^2)/(Lsec * Vout * (Vin + Vout))

Where Rl is the load resistance and Lsec is the secondary inductance of the flyback transformer (if L is in uH then F is in MHz)).

This is from Marty Brown's "Practical Switching Power Supply Design" which, to be frank, over-simplifies a lot of the math but actually is a decent reference for some of the practical aspects. Getting a bit long in the tooth, though, just like the old standards for SMPS design by Billings and the late Pressman.

 

[sreid]

For those that missed it, "Respect the Unstable."

http://flyingv.ucsd.edu/krstic/teaching/143b/GSBode.pdf

 

[Fluorescence]

hello,
Renovator1 i also use the Marty Brown book, in fact its my favourite reference....-with his flyback examples he always uses opto feedback with TL431.

I dont know how he gets his compensation done though because the following article:

http://powerelectronics.com/mag/50107.pdf

...seems to suggest that control loop compensation with TL431/opto is different to the equations he proposes.

 

[sreid]

Even more beautiful, "Fundamental Limitations on Control Design."

http://www.control.lth.se/~kja/limitationsparis4s.pdf

 

[gabisuciu]

Z=(1/2pi)* R/L * (Vi/Vo)^2
I used several times this formula with good results.
It also results from a mathematical small signal process description.

 

[treez]

i assume you wish to solve it....

so i suspect you can do this by putting a small cap on the lower feedback divider resistor and gradually upping it until the No_load to Full_load switching works OK.

eventually the duty cycle will be prevented from changing that quickly that the "channel" through the boost diode is not "strangled" off too quickly.

 

[cabraham]

For the boost topology, RHPZ radian freq = R*((1-D)^2)/L. There is no "D" in the denominator. The D in the denominator is for the buck-boost (flyback) topology only. Divide by 2*pi to get Hertz freq.

I always use CCM when the load current is large enough. If one understands the intricate details of SMPS operation, CCM is no problem at all. In DCM, the stresses on the parts due to high peak currents and voltages are substantial. CCM offers lower noise and higher efficiency.

The downside to CCM is the RHPZ which forces the servo loop to roll off to unity gain at a lower freq than if DCM were used. In DCM there is no RHPZ. Thus CCM offers lower bandwidth than DCM.

Overall, I use DCM when the output current is small. Noise and stress are not an issue in that case, and DCM offers higher bandwidth. For large output currents, I always use CCM. Otherwise noise and peak stresses are excessive as well as losses.

Remember that the boost converter has no short circuit protection. An additional FET will be needed to shut off power in the event of an output short.

Claude

 

[DHambley]

Cabraham,
The boost and flyback can both be modeled to be the same topology and thus, the same response. You can convert the flyback model to a boost by scaling the transformer to a 1:1 so that the inductance (as seen at the primary) is equal. Since the topologies can be scaled to be the same model, one response equation can't have the 1/D missing while the other equation keeps it.
Dixons equation has 1/D for a boost. The 1/D which you pointed out as being for a flyback, would also be true for a boost.

DH

 

[cabraham]

hgldr,

Check any reference and you will find that what I posted is correct. If we take the xfmr-isolated flyback and scale the xfmr to 1:1, what we get is an *inverting buck-boost* topology, NOT a straight boost converter.

They are different. A boost is a member of the *general* flyback family, but the transfer function is quite different. The boost during the switch on time relies on the output cap to power the load. The inductor is energized via the input and to ground via the switch. When the switch is turned off, the inductor de-energizes into the output cap and load. But, the input source is conducting the inductor current. A portion of the per cycle energy is provided by the input power source, during the switch off time.

A buck-boost, however, does not have this direct input to output energy transfer. During the on time, the switch closes and the input source energizes the inductor while the output is disconnected from the input and inductor just like the boost. The cap holds the output. The big difference is that during the switch off time, the input is disconnected from the output. The inductor de-energizes through the diode and output load and cap.

With a buck-boost, all of the per cycle energy is stored in the inductor during the on time, and released to the output during the off time. The input never transfers energy directly as in the case with the boost converter.

The boost and buck-boost have differing transfer functions, because the "transfer" is different. The unitrode/TI archive of app notes, Natl Semi, Linear Tech, and every university says so. The transfer functions for various SMPS topologies has been studied, modeled, and tested to death.

Believe me, I wouldn't lie to you. Best regards.

Claude

 

[DHambley]

CCM or DCM, you can indeed model the frequency responce of a boost and flyback using the proper voltage ratios. If you model the secondary voltage of the transformer during the energy transfer of a boost to be proportionate to the secondary of the flyback (NOT the input switch voltage), then the energy delivered to the load as a function of duty cycle, is the same for both topologies. Energy continuing to flow from the source for a boost is modeled as a DC offset. This account for the 1/D or no 1/D in the DC models.
However, the issue is the Frequency of the zero, not the 1/D in the DC responce euqation. This has nothing to do with the 1/D in Dixons equation.

 

[cabraham]

Please examine the Tex Instr app note SLVA061, "Understanding Boost Power Stages ...". The small signal transfer functions differ. The buck-boost has the "D" in the denominator, and the boost does not. There is nothing to debate. BR.

Claude