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.....
