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Colpitts oscillators

Discussion in 'Electronic Design' started by Joel Koltner, Jan 7, 2008.

  1. Joel Koltner

    Joel Koltner Guest

    I've did some troubleshooting of a common-collector 3rd-hamornic crystal
    Colpitts oscillator this weekend, discovering that my emitter inductor (used
    to force harmonic operation) was too big, thereby sometimes allowing
    oscillation at the fundamental rather than the harmonic. In tracking this
    down, I re-read the relevant sections of Matthys's "Crystal Oscillator
    Circuits" and Hayward's "Radio Frequency Design." The two of them have
    somewhat different focuses, but I find it interesting that when it comes to
    the two capacitors in the "Colpitts network" Matthys says, "There is no
    requirement for any specific ratio of C1 [the base-emitter cap] to C2
    [emitter-ground cap]." While arguably an entirely true statement, in contrast
    Hayward spends plenty of time discussing the ratio, even going so far as to
    create a graph of the oscillator's loop gain and phase as a function of one
    capacitor's value vs. the other, with the intent of letting you choose a gain
    that's not too much bigger than one so as try to minimize output waveform
    distortion.

    Anyone have some thoughts on this? I have a suspicion that Hayward addresses
    the topic because he's trying hard to keep the transistor in small-signal
    (active) mode as much as possible, where Matthys right off-the-bat says that
    you can expect your transistor to be off ~80% of the time, saturated ~10% of
    the time, and operating actively ~10% of the time.

    Matthys also suggests that the C2 (base-emitter) cap should generally be
    "between 40-70pF," whereas Hayward likes 100pF (and generally prefers larger
    caps... which I suspect reflects his emphasis on oscillators down at HF
    whereas Matthys often wanders into VHF territory).

    I'm interested in whether those of you who design such oscillators tend to do
    it more from heuristic techniques (I have another book which suggests very
    heuristical approaches, e.g., "make the ratio of C2:C1 about 4:1") and expect
    to do a bit of tweaking on a bench vs. simulating the entire thing in SPICE
    first and expecting that it'll work just ducky on a bench. Also... when
    you're looking at a Colpitts oscillator, what do you tend to "see?" The most
    "natural" representation to *me* of the various configurations are:

    Common base: Transistor thought of as a gain=1 emitter follower, and you're
    chasing loop gain. Hayward uses this point of analysis (and points out that
    it is, of course, an arbitrary choice.) I can see it readily as a negative
    resistance too.
    Common collector: Transistor thought of as a negative resistance, and with a
    few quick network transformations you're back to an RLC network where the
    transistor's negative R cancels our the load R. (Plastonek takes this
    approach. Matthys does loop gain analysis with just a bit of hand-waving
    thrown in. Hayward points out that all the topologies are really the same,
    you're just shifting the ground reference around...)
    Common emitter: Classic loop gain approach, with transistor base being a
    resistive load and the collector being a current source driving a pi network.
    Everyone seems to do it this way, since it's perhaps the most intuitively
    obvious topology and it's easy to analyze.

    I also find it interestingly the Hayward's book -- aimed at hams -- seems to
    have one of the most comprehensive discussions of all this. The Art of
    Electronics only has a page on it!

    ---Joel
     
  2. ehsjr

    ehsjr Guest

    Joel Koltner wrote:

    You expected something different? AOE covers a wide
    range - Hayward is focussed. However, I must admit
    to wanting more sometimes where AOE whets the appetite
    instead of offering a full meal. Not a negative comment
    on AOE, just a recognition that it is not intended to
    be an in depth treatise on all things electronic.

    Ed
     
  3. Rich Grise

    Rich Grise Guest

    .
    Personal preference - the one guy likes to run his oscillators class A,
    while the other guy is partial to class C. ;-)

    Cheers!
    Rich
     
  4. Phil Hobbs

    Phil Hobbs Guest

    For a Class C oscillator, you're better off changing the bias so that
    the amplitude limiting happens by cutoff and not saturation. Your
    close-in phase noise will be much better. It sounds as though M. is
    assuming that anyone who wants a quiet oscillator will use ALC.

    Cheers,

    Phil Hobbs
     
  5. Joerg

    Joerg Guest

    AoE isn't an RF book. There are very few good RF books and IMHO the best
    are from the ham radio community. I could recommend a some really good
    ones but except for the ARRL Handbook the ones here aren't in English.

    SPICE and theoretical approaches are fine but at the end of the day
    you'll have to fire up the old Weller and experiment. Find out the
    boundaries, stability ranges etc. I found that transistor models for
    SPICE aren't the cat's meouw when you approach the UHF range and above.

    I got myself a few BFP620 with the last Digikey round. Hopefully the
    project load will ease up some. Can't wait to get my hands onto those
    because their ft is a screaming 65GHz. Yeehaw!
     
  6. Joel Koltner

    Joel Koltner Guest

    I guess I did... they spend so much time on op-amps and filters, it's only a
    hop, skip, and a jump to oscillators. At least as far as basic operation
    goes -- I wouldn't expect Win to delve into phase noise, how everything
    starts getting a lot "messier" if you toss a PLL into the mix, etc.
     
  7. Joerg

    Joerg Guest

    Same here, they covered them in Basic Electrical Engineering for us, 1st
    or 2nd semester. But let's face it, fresh grads coming out of
    universities these days only see that weird component X1 in their
    circuit, connected to two pins of their DSP, along with a couple of
    capacitors that they have picked by rote from a table in the datasheet.
    That's it. The most they might ever do in oscillator design is pick a
    Fox can from the Digikey catalog. IME Clapp, Colpitts, Hartley and such
    certainly fall into the RF (= weird) category for most engineers.

    Sometimes I wonder who is going to write such books once others have
    followed Doug and left the earth.

    Probably the first thing is going to be a pulse amp. Got to be careful
    though. Once Vce goes above 2.3V ... poof. An ever so slight overshoot
    can send them off the cliff. OTOH it is incredible how cheap RF
    transistors have become. IOW the good old days are right now.
     
  8. Jim Thompson

    Jim Thompson Guest

    Us old farts will always be employed ;-)

    ...Jim Thompson
     
  9. Joerg

    Joerg Guest


    Hey, I'm not that old. Yet. But I believe companies like Tektronix,
    Intel or HP should build subsidized nursing homes with electronics labs
    in there. Seriously. "Yo, Leroy, we've got this new kid here. Can you
    put your teeth in and explain a sampling circuit to him?"

    I was pretty shocked when neighbors were over with their girls. Both
    attend schools in SoCal and I, having been educated overseas, just
    couldn't believe it: I did not know that they are being plagued with
    tons of liberal arts stuff instead of EE, med, or whatever their goal
    is. Why are they doing that? I thought this stuff was taught at the high
    school level and then that's it.
     
  10. Joel Koltner

    Joel Koltner Guest

    Yeah, but unfortunately you're not always going to be around... at least on
    this particular plane of existance. :)
    My wife has a cousin who graduated from high-school a year or so ago. It was
    one of those "charter" high schools, with an eye towards those interested in
    arts. I was amazed that as a senior in high school they'd still give her A's
    on reports even though they had a fair number of misspelled words and
    grammatical errors! It's hard to blame a kid for not learning a lot when so
    little seems to be asked of them... at least when it comes to "traditional"
    learning -- I'm sure most kids today are far more "educated" than we ever were
    when it comes to stuff like the history of discrimination, diversity, etc...
    It's a cultural shift that says "everyone must go to college." Yet I don't
    really think that any significantly different percentage of kids are all that
    *interested* in what college has to offer than they ever were, so as a result
    you see courses getting watered down because it looks bad for a college to be
    failing, say, a third of their students.

    ---Joel
     
  11. Jim Thompson

    Jim Thompson Guest

    Joerg, You just don't understand... "science" is by "consensus" now
    :-(

    ...Jim Thompson
     
  12. Joerg

    Joerg Guest

    That's one reason why a lot of our church members are now home-schooling
    their kids.

    The other fact that constantly amazes me is how many kids go to college
    without having given thought to what they want to become some day. My
    parents would have read me the riot act.
     
  13. Joerg

    Joerg Guest

    Ah, now I get it. Like global warming?
     
  14. Jim Thompson

    Jim Thompson Guest

    Yep.

    We're about to have tar-and-feathering around here. The school
    "educrats" showed "An Inconvenient Truth" to students without any
    contrasting opinions.

    They also ignored December 7.

    Hell is about to break loose.

    ...Jim Thompson
     
  15. Howard Swain

    Howard Swain Guest

    Hi Joel,

    I use "Colpitts" for oscillators with one inductor and 2 capacitors (no crystal).
    I always think of them as having the transistor in common base.
    The gain of the transistor is a large-signal Gm.

    This approach was described by Kenneth Clarke in "Design of Self-Limiting
    Transistor Sine-Wave Oscillators" in IEEE Trans. on Circuit Theory, vol 13,
    (March 1966), pp 58-63.
    It is also described in Communication Circuits: Analysis and Design
    by Kenneth Clarke and Donald Hess (1971).

    Clarke derives the large signal Gm by using Bessel functions.
    Then it is a simple matter to derive the loop gain and conditions for oscillation.
    As well as the relation ship between DC emitter current and the peak voltage
    on the tank.
    The oscillator will limit by having the e-b junction cut off much of the time.
    As a result of this technique, I designed for a desired voltage level on the tank.
    And, of course, a desired voltage on the load.
    So, I designed oscillators based on these derived equations and did neither
    a heuristic nor a SPICE techinique.

    A much simpler (though slightly less accurate) version of this technique is
    described in Planar Microwave Engineering by Thomas H. Lee (2004).

    There seem to be 2 main ways to add a crystal to a Colpitts oscillator.
    One is to simply replace the L with the crystal operated slightly above
    series resonance. I think this is usually called a Pierce oscillator.
    I've never designed one of those. If I had to, I'd try to do it the
    same way as above, though.

    The other is to insert the crystal between the emitter and the junction of the
    two capacitors. I think this is usually called a Butler oscillator.
    The crystal is operated at series resonance; I resonated the case
    capacitance out with an inductor. Here, the L-C tank of the base Colpitts osc.
    selects which overtone you are using from the crystal.
    I biased the transistor for linear operation and used hot-carrier
    diodes to limit elsewhere. Again, it was possible to design for desired
    signal and power levels.
     
  16. Joel Koltner

    Joel Koltner Guest

    Hi Howard,

    "I use "Colpitts" for oscillators with one inductor and 2 capacitors (no
    crystal)."

    Ah, good point -- I was being a little imprecise in my terminology.

    "This approach was described by Kenneth Clarke in "Design of Self-Limiting
    Transistor Sine-Wave Oscillators" in IEEE Trans. on Circuit Theory, vol 13,
    (March 1966), pp 58-63."

    Thanks for the reference.

    "So, I designed oscillators based on these derived equations and did neither
    a heuristic nor a SPICE techinique."

    ....and I take it your as-built results were reasonable close to those
    predicted by the design equations? Hayward uses some "rules of thumb" that
    are intuitively reasonable and says they generally work out to within 2dB of
    what he actually builds, which is pretty impressive for avoiding the slow road
    to a proper large-scale gm discussion.

    "A much simpler (though slightly less accurate) version of this technique is
    described in Planar Microwave Engineering by Thomas H. Lee (2004).

    That one's sitting on the shelf... thanks again.

    "There seem to be 2 main ways to add a crystal to a Colpitts oscillator.
    One is to simply replace the L with the crystal operated slightly above
    series resonance. I think this is usually called a Pierce oscillator."

    Yes. In Hayward's examples he sticks with replacing the inductor in a common
    collector Colpitts with a crystal and calling it a Pierce whereas most other
    examples (including Matthys) seem to use the common emitter (or some generic
    inverting logic gate), so I'm thinking that "Pierce" covers pretty much any
    particular topology where you just swap the inductor for a crystal and figure
    you'll be operating a little above series resonance.

    "I've never designed one of those. If I had to, I'd try to do it the
    same way as above, though."

    The design techniques seem to get a little bit more cut-and-try when you go to
    a harmonic oscillator... :) AFAIK Matthys is the only one who still attempts
    to give some reasonably mathematical design approaches.

    "The other is to insert the crystal between the emitter and the junction of
    the
    two capacitors. I think this is usually called a Butler oscillator.
    The crystal is operated at series resonance; I resonated the case
    capacitance out with an inductor."

    I'm tempted to try building a Butler myself -- series resonant approaches seem
    to be preferred over parallel resonant ones, presumably because the case
    capacitance doesn't become a part of the frequency determining elements (i.e.,
    only the motional L and C matter).

    Your post has been quite helpful, Howard -- much appreciated.

    ---Joel
     
  17. I'd like to know where in the Constitution it says, "the government is
    hereby granted the authority to take away your earnings to pay other
    people's bills"?

    Thanks,
    Rich
     
  18. Joel Koltner

    Joel Koltner Guest

    Speaking of crystals... I've found Jack Smith's article on measuring a
    crystal's equivalent circuit model parameters as linked to here:
    http://www.cliftonlaboratories.com/ ...useful Jack's a surprisingly
    productive guy... he has the cover story in QEX this month to boot!

    Similarly, just a few months ago Wes Hayward wrote up "An Oscillator Scheme
    for Quartz Crystal Characterization" here: http://www.w7zoi.net/tech.html
     
  19. You must be much younger than you appear.

    What's wrong with just getting a higher-level education, such that you
    can make _informed_ decisions, rather than just a couple of years of job
    training and basket-weaving?

    Thanks
    Rich
     
  20. Joel Koltner

    Joel Koltner Guest

    I think that was already a given at the time they wrote it, so no one thought
    specifically to write it down. :)

    Are you a universal healthcare supporter, Rich? When people start going down
    the path of "universal healthcare is socialism!" -- which, to a certain
    extent, sure, it is -- I like to point out to them how much other socialism
    we've had in this country for many decades if not centuries...
     
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