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What is Cf in OpAmp circuits? OpAmp design books?

Discussion in 'Electronic Design' started by Frank, May 20, 2004.

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  1. Frank

    Frank Guest

    Hi everyone,

    The circuit below was posted as a reply to a question I asked back in
    February (Thanks for all the tips!). Other projects have taken a
    higher priority up until now and I'm getting back to this one.

    Showing my analog ignorance, I admit I don't know what the capacitor
    Cf is for. From what I've read, is it supposed to provide some sort
    of stability to the circuit? The problem is I can't find any
    information on calculating the best value for this capacitor. I'm
    assuming it's something fairly small in the pf range. The circuit is
    basically set and left alone, not varying the values at any frequency
    at all.

    Any pointers? I can do the math.

    Also, any good books on OpAmp circuit usage?



    Please use a fixed-spaced font to view.

    Vin --+--->| Regulator |------------------------+-->
    | +-----+-----+ |
    | |Adj \
    | | CF R2
    | | +---||------+ \
    | | | | /
    | | | /| | |
    | | | /-|---+----+
    | +-------------+----< | |
    | | \+|---+ \
    | \ \| | R3
    \ Rb | \
    R1 \ | /
    \ / | |
    / | | ---
    | --- | Gnd
    | Gnd |
    | K x Vref |
    | +----+
    | Vref ( < 5V ) |
    | | |Rh
    | | +-----+
    | | Radj | | Variable
    /---/ zener or +-------| | Pot
    / \ TL431 | |
    --- 2-wire <===============| |
    | interface +-----+
    | |Rl
    --- |
  2. Tim Wescott

    Tim Wescott Guest

    Cf slows down the response of the op-amp, to keep the circuit from
    oscillating. It doesn't really matter that you _want_ the circuit to
    sit still when left alone, if it's inherently unstable it'll burst into
    song on its own no matter how hard you don't touch it.

    You need to set Cf high enough so that the gain around the loop from the
    'adj' pin of the regulator, through the regulator's internal
    compensation, through the op-amp and back to the 'adj' pin, is
    significantly less than 1 at the frequency where the phase is shifted by
    180 degrees.

    You don't know how the regulator is compensated, and furthermore
    different regulators from different manufacturers or different times
    will be compensated differently. I'd suggest that you dink around with
    the values of Cf until you find the value that just makes it oscillate,
    then install a Cf that's at least 10 times that amount. I'd probably
    bump it up to 100x if the capacitor didn't get too large, especially if
    I were designing for production.
  3. Joel Kolstad

    Joel Kolstad Guest

    At that point (ringing) it's just underdamped but you may still have some
    reasonable phase margin, no? You're suggesting critical deamping?
    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?)
    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. :)
    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
  4. Tim Wescott

    Tim Wescott Guest

    By the time it's really ringing the phase margin is no longer
    reasonable. A second order system with a 63 degree phase margin is
    critically damped; with a 45 degree phase margin your damping ratio is
    about 1/2 and you'll just be showing ringing.

    I wouldn't design for 45 degrees phase margin unless I had a high level
    of trust in the system components; I don't feel that a regulator could
    be trusted to this level, and the set of all possible regulators that
    might be put into the circuit _certainly_ can't be trusted.
  5. Joel Kolstad

    Joel Kolstad Guest

    Aw, c'mon, those overclocker guys haven't even broken a sweat at a 20% hike
    in Vcc!

    Just kidding. :)
    Nice to know I'm not alone!
    That is impressive.

    I like your 'oscillating power supply' feedback fix; I'll definitely give it
    a try some time. What order feedback networks do you usually place pads
    down for on the PCB? I've gone through Pressman's book on switch-mode power
    supplies, and while there are a few things I disagree with him about in his
    feedback compensation chapter, he did manage to convince me that 2nd order
    network (a pair of zeroes and poles) can be useful.
    I have the typical engineer paranoia that the cookbook approach isn't going
    to work at just the point where it needs to to prevent the airplane from
    falling out of the sky, and hence understanding what's going on is
    That's a spot-on reason a lot of truly good books get bad reviews, in my
    opinion -- someone who doesn't yet have the background to understand them
    inadventently purchased them and now they're pissed. What's strange is that
    usually I can recognize such situations in my own book-buying endeavors and
    then just refrain from reviewing them!
    The same can be said of many Prompt Publications books. I'm pretty sure
    they and Tab will print just about anything that's vaguely technically
    related so long as they're covinced it'll sell -- quality of the work not
    I'd certainly be interested!

  6. Terry Given

    Terry Given Guest

    Nice reply, Tim. If the regulator doesnt oscillate (Murphy pretty much
    guarantees this to be the case when your (very good) design technique
    requires it), then try a load step - R + FET + pulse generator. Switch the
    load on and off, and look at the output voltage - If you get an RC-like
    exponentially decaying under- or over-shoot (load on & off respectively)
    then its stable. As you increase Cf, the time constant will increase
    (amplitude probably will increase too).

    This time constant is directly related to the crossover frequency of your
    closed-loop control system. What time constant do you need? well, thats up
    to you, but is often governed by the load changes you expect to see in
    practice (pentium VRMs see > 20A load changes in a few 10s of ns - these
    circuits tend to have bloody short time constants)

    If instead of a nice exponential decay you get ringing (usually with an
    exponentially decaying envelope) then your circuit is exhibiting closed-loop
    oscillations, and Cf needs to be increased. If you make Cf small enough, you
    may well get a lovely sine wave superimposed on your DC voltage.....

    dont forget to test your supply with a variety of loads, and at a variety of
    temperatures. Tims rule-of-thumb "Find Cf that just works then use 10x" is a
    great way of empirically designing compensation networks, as it provides you
    with plenty of margin to soak up load & device variation over time,
    temperature and sock colour.

    It turns out that stability analysis of closed-loop control systems is
    actually fairly difficult - many EE grads cant do it at all. And very few
    books on power supplies tell you how to do it, either. A class in control
    systems theory might help, but they often talk about mechanical and chemical
    control systems, and handily ignore opamp/psu control loops. And then when
    you do find an article on psu loops, they always seem to miss out crucial
    bits of information...*sigh* Or some maths nut implements an H-infinity
    controller or some other stupid, mathematically evil thing, leaving you
    still wondering how the hell to calculate Cf....

    If you really want to learn how to do it for opamps, read Jerald Graeme's
    book "optimising op amp performance" ISBN 0-07-024522-3 - he explains it all
    clearly and carefully. If your maths is good, go for Jiri Dostals
    "Operational Amplifiers" ISBN 0-7506-9317-7, but its a lot harder read (Bob
    Pease swears by this book)

  7. Terry Given

    Terry Given Guest

    Hi Joel,

    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!

    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)

    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.
    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
    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.


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

    Terry Given Guest

    Hi Joel,

    in hindsight I would consider it downright stupid. Numerical solutions are
    shitloads faster, and avoid algebraic mistakes (easy when inverting 4x4
    matrices analytically)
    Alas, mr P doesnt quite give enough info....
    I normally use Zf = C||(R+C). It may be a good idea to drop a C across the
    top resistor of the voltage divider (usually only used in voltage mode
    buck-derived converters). I always work in smt, and it costs nothing to
    leave an smt part off, but is a real pain to add one that isnt there.
    never read a prompt publication. probably wont now.
    I'll post it soon (I'll add good/bad comments to the spreadsheet, which I
    keep to recall who borrowed what - sometimes people dont return books, and I
    have to hunt them down and kill them)

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