Hi Joel,

Joel Kolstad said:

At that point (ringing) it's just underdamped but you may still have some

reasonable phase margin, no? You're suggesting critical deamping?

a critically damped (delta = 0.71) 2nd order circuit has a single "ring"

with about 20% overshoot, followed by almost no undershoot and settling to

the steady-state value; the rise time is quite a bit less than a first-order

response. By the time delta = 1, the 2nd order cct looks just like a 1st

order ie RC response. As delta increases above 1, the "time constant" of the

pseudo 1st-order response gets longer and longer (and the 1st-order

approximation gets more and more accurate, IIRR).

Watch a pentium get real pissy if you give it a 20% overshoot! Ultimately

though *YOU* get to choose the response that best suits your app, so choose

wisely. Usually its a tradeoff between response time and overshoot. If

response time aint critical, damp the crap out of it! I once worked on a

400W flyback converter with a crossover frequency of 1Hz - a moving coil

meter faithfully displayed the step response!

The way I was taught to do it was based on analyzing a 2nd order simplified

(plenty of small parasitics left out) small-signal model amplifier and

'noticing' that the placement of Cf tended to make it dominant. For

something much more complex, it seems debatable whether or not it's even

worth analyzing analytically instead of just SPICEing it. (Too bad

pole/zero analysis tends to be somewhat broken in SPICE3... I wonder if

Kevin fixed his?)

Kevin will love me for saying this, but a transient test is gemnerally the

way to go in spice. I have not had much success using spice TF analysis, and

so gave up on it years ago (quite probably it works fine under certain

circumstances, but I had wasted enough time so did something that worked,

and havent looked at it since. I bet its great for all-passive circuits like

LC filters).

I have tackled the analysis of 3rd and (once, never again) 4th order

systems, analytically. The 3rd-order system wasnt too bad (well, dozens of

pages of maths, bloody hard to ensure I hadnt made any ****-ups) and I got

closed-form design expressions. The 4th order system didnt decompose nicely,

so I couldnt analytically find the roots, but luckily god invented matlab

. The exercise was painful enough I just do that stuff numerically now,

with a decent maths package (mathcad, matlab)

I sometimes do opamp circuit simulation using a VCVS with a gain of 1e9, ie

an almost perfect opamp. Then I use a 1st order laplace block to simulate

GBW, followed by the device macromodel (which is usually very close to the

laplace block version), but only when I need to show the effect of the opamp

on cct performance (active filters etc)

Linear Technology's application notes advocate the 'apply step to error

input, examine shape of output response, iterate with compensation as

needed' approach to design.

the best thing about this approach is you dont need horribly expensive test

gear like network/frequency-response analysers etc. I came up with a

decidedly crude method a few years ago. If smps oscillates, measure the

oscillation frequency - this is your current (pun unintentional) crossover

frequency. It is trivial to analyse the error amp circuit, its the rest of

the smps thats poxy to analyse. If Fcross isnt acceptable, fiddle with your

error amp gain only (leave phase the same - piece of piss to do in spice)

until Fcross is where you want it (more gain = higher Fcross, less = lower).

Once Fcross is where you want it, re-design your error amp for the SAME gain

at Fcross, but much more phase boost, thereby stoppping the oscillations. It

bloody well works, too. I havent actually tried fiddling with gain alone to

move Fcross, its always been good enough for me, but the theory is sound.

All i ever do is stick in the right number of components, so the values can

be twiddled at will - actually I calculate them all, and then see how it

behaves; sometimes I screw up, and produce power oscillators, at least until

the 2nd round of R,C calcs as outlined above, but no pcb changes.

Sad commentary on some of the people who purchased that book (this is an

Amazon.Com review):

"Get yourself a decent OpAmp "cookbook", you'll learn far more from a "this

is how they did it" approach than this author's methodology. "

---Joel Kolstad

Well, I have read a lot of electrical/electronic engineering books (I have a

technical library with about 700 books in it), and JG's is pretty darned

good (I bought it because bob pease recommended it). Cookbooks are OK if you

are only interested in making their circuit work, without any real

understanding - its more akin to training (think dogs) than educating. give

me education every time.

I did a job a while ago that required an inverting sallen-key bandpass

filter. The "cookbook" equations set R1=R2=R, C1=C2=C and give equations for

Wo, Q, BW and centre-band gain, and they work, BUT Q,BW and centre-band gain

are interdependant. I wanted to do BETTER (high gain, low Q), so went back

to the original design equations (derived them myself, its easy really),

which are a whole lot messier than the cookbook equations. Sure enough, with

a little algebra I came up with a set of closed-form equations that allow me

to choose Wo, Q and gain, then calculate all the R's and C's. I got quite a

bit more gain than the cookbook solution.

Oh, and what if there is a typo in the cookbook? switching ones brain off

and following a proof by blatant assertion is usually a great way of

producing a sub-optimal design. what if the circuit you want isnt in the

cookbook? say its an existing product, designed by someone who died in a car

crash (cant ask them, unless you ouija board has a set of greek &

mathematical symbols), it works perfectly but you need to change some

parameters for a new product?

I think it would be fair to say that whoever posted that was not highly

skilled in the art of electronics, and probably couldnt follow the maths. If

you can, off the top of your head, analyse a 2nd order circuit in the

laplace domain, then you can tackle pretty much any real-world problem, and

will easily follow JG's mathematical reasoning. get it on interloan from

your local library, and have a read - you will be pleasantly surprised.

In general, any book published by TAB books is for hobbyists (who dont

understand much of anything, especially maths), and are desperately lacking

in useful information (read a book by Irving Gottlieb and you'll see what I

mean) - often they are just cobbled together out of bits of app notes. Mind

you, Walt Jung's books are damn good. I have his opamp and data converter

cookbooks, and a dozen or so analog devices app books he has contributed to.

I just read that idiots (eDICKent) review on amazon - what a moron!

obviously he is a piss-poor engineer. If he cant understand JG, I would

recommend suicide as a viable career alternative as he is way too stupid to

be of any use as an engineer.

Actually, I'll rescind that harsh career recommendation - about 2/3 of the

money I have earned as a consultant engineer has been fixing circuits

"designed" (often straight out of cookbooks-for-dummies) by idiots like that

guy. eDICKent, please keep fucking up product designs, I want a large

swimming pool :}

look at the review after him: (copied from amazon.com)

This book is an excellent treatment of this subject that is intuitive and

not overly theoretical. It draws together a lot of material available in

magazines and on vendor websites, but not available in book format. The

author starts with the traditional op amp symbol, and derives Black's

classic feedback model for various configurations (inverting, non-inverting,

etc) of the op amp. A generalized expression for the closed loop gain is

eventually obtained where the numerator is the ideal closed loop gain, and

the denominator contains the frequency response that can be analyzed with

the aid of the Bode plot. Practical design issues are logically addressed

using this simple formalism including bandwidth, phase compensation for

input and output capacitances, power supply by-pass requirements,

distortion, etc. Care is taken to indicate what conclusions apply to all op

amp configurations, and which address specific design issues. As a writer,

the author is very pointed in his approach and thorough with his analyses;

and will not win any awards for fiction suited for a general audience.

However, I highly recommend the book to anyone trying to learn how to use op

amps in a systematic way

I couldnt have put it better myself. ten bucks says eDICKent wouldnt

recognise noise gain if it leapt up an bit him on the ass.

Cheers

Terry

PS if you are interested, I can post a list of the books i do have.....