DC/DC Regulator Design Questions

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I'm using the TPS54560 regulator from TI which has a built in switch. I'm reading equations 45 and 46 in the datasheet and trying to figure out how those equations were derived. I'm really scratching my head on the derivation/explanation for these two. I'd love some help here!

Thanks.

[T3sl4co1l]

45 is just the geometric average (which is more relevant to ratiometric figures than an arithmetic average, though they produce nearly the same result for close inputs, say within 10% of each other) of modulator pole and half the switching frequency (which, IIRC, is the RHP zero of the peak current mode controller).  So you want to have cutoff below that dangerous zero, and the other part, the pole, suggests how much.

46 takes the cutoff frequency and voltage gain and, based on the error amp characteristics (i.e., Gm), turns that into a resistance.  The figure 2*pi*f_co*C_OUT is the conductance of the filter cap at the desired cutoff frequency, taken as a ratio with the power stage transconductance.  In other words, the dimensionless ratio which is the loop gain from C_OUT back to the power stage.  This, in turn, is multiplied by another dimensionless ratio, V_OUT / V_REF, which is the voltage gain of the system.  Finally, 1/gmea is the appropriate scaling factor that brings it back to units of ohms.

FWIW, in my opinion, it's hardly worth calculating compensation values.  You'll only end up tweaking them later anyway.

Tim

[jakeypoo]

5A built in switch? Very nice.

Just my 2 cents, use the WEBENCH tool to get your part values. You can go in and change your L and C values and it will spit out values for compensation components. But like Tim said, you end up tweaking those if you need to anyway.

WEBENCH usually over specs things like voltage and power ratings of external components, so then you can go and select your preferred inductor and diodes.

[tree]

I understand that you'd tweak the values, but these formulas give you a nice starting spot. I'd like to be able to understand them if possible since the datasheet doesn't explain them.

I understand that equation 45 represents the geometric mean, but I guess I should have phrased my question differently. For instance, I know where Fco1 arose from, but have no idea where Fco2 came from. Why do you use fp(mod) and HALF the switching frequency to compute Fco2?

I had figured out how to derive equation 46 last night right before I fell asleep, but I don't understand why Fco was used in that equation. By extension, I have no idea why fp(mod) was used in 47, although I understand how to compute the value of C5.

EDIT: I think the reason why Fp(mod) is used to compute C5 is so that you place a compensation zero at approximately the output pole (or as the datasheet refers to it, modulator pole).

[T3sl4co1l]

I don't remember the entire analysis, but this might give some ideas;
http://www.ee.bgu.ac.il/~pel/pdf-files/conf45.pdf
As PWM rises (and, in turn, Vo/Vi or loop gain, in a typical BCM range converter), the number of pulse widths produced begins to bifurcate repeatedly.  The onset of the first bifurcation happens to come out as a RHP zero, or something like that, and is a limiting factor in the loop response of peak current mode converters (because, after passing that zero through the feedback loop equation, it can become a RHP pole).

Or, put differently: the onset of chaos results in an apparent alternating duty cycle.  Every other cycle, meaning, the resulting ripple occurs at Fsw/2.

Tim

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Which question are you answering, Tim?

This shows that what you said is a bit over my head.

[T3sl4co1l]

Oh, regarding the Fsw/2 part.

Don't feel bad, I've not done the analysis myself.  And like I said, I don't really care, because I just compensate them by hand anyway.

Tim

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I've been playing around with it at the bench as well, but it'd be nice to understand the formulas. Thanks for your help.