Reps Reps Reps : Slope Compensation

My recommended weekly list of do it yourself reps (for power electronics guys) is :

Apply the Extra Element Theorem (EET, Middlebrook) to a real circuit
Derive the expression for the Right Half Plane Zero in a Boost regulator
Derive the expression for required linear slope compensation in a generic regulator (m1, m2, m)
Derive the equations for operation of a flyback converter
Derive the equations for operation of a forward converter

This is all about fitness - keeping your confidence level high and being confident enough with the algebraic jugglery that you can try out new what-if scenarios without getting paralyzed by the analysis.

Looking back over my professional life, I can see that, despite my memory, I haven't had much success or confidence in building systems or sub-systems of any significant depth. I think one problem is a lack of chunks. Sure, I remember facts, but the how to build isn't there.. Why? I think I failed to generate chunks by failing to spend sufficient time with a particular system and due to the poor quality of my sleep, especially in the early days of my career. As I've said often, energy and the ability to concentrate are the keys to the quality of like. Time management follows naturally.

Anyways, enough ranting - I want to give you a chunk, but how..
How can you always pull out the formula for the gain of the perturbation in duty-cycle out of thin air, like I gave you one for EET? We need a mnemonic..

Here's what's happening. You start with inductor current at I, with no perturbations, it ends up at I after going up with a slope of m1, then down with a slope of m2 after peaking at Ip. This is the same with or without slope compensation. In that ideal case, the duty cycle is D. And, you'll agree m1*D = m2*D' (where D' = 1 - D).

Real case, you had a perturbation that changed the Ip to Ip + delta_I. That also changed D to D1 (D + d).

In the next cycle, D2 is D - d2 and you want an expression for d2.

I2 = I + m1*D1*Ts - m2*D1'*Ts -- has to be true - nothing to do with Ip changing because all that's captured in D1
Now write an expression for D1 in terms of I, Ip + delta_I and the m's. Juggle it to get Ip + delta_I on the LHS. (Starting value = I, ending value = Ip + delta_I, slope is m1 + m - coz, when you implement the peak-current mode thing, the slope-comp is part of it)
Do the same for D2.
No eliminate I2, I, Ip and delta_I by keeping Ip + delta_I together - maybe just call it Ip2 and use m1*D = m2*D'

Sound easy, but how to create a mnemonic?
When you start off writing the equations, these are the LHS's to begin with :

m1*D = m2*D'
I2
D1
D2

So, if you can think of a better mnemonic, let me know..
Sherlock : A process of elimination will lead you to the jackpot and you'll strick Gold - as if you had the M1Das touch. Get it? Then, "I also did two" - I2D1D2" - " I too did two". Too lame? :)