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    Colpitts oscillator stability analysis

    Hi,

    I "designed" a collpits oscillator in base configuration according to a textbook [1] depicted in Fig. (Bild) 1a (it's in german, sorry ). My design/siumulation does not use a quartz crystal.
    I simulated the oscillator in LTspice with a PMBT2222A [2] NPN BJT from Nexperia. I set the emitter resistance R_E to 20k, and the circuit operates fine. The change of R_E leads to a loop gain (Vs in the textbook) of about 10, and a quality factor of the whole circuitry Q_B of about 66.

    Concerning the loop gain of about 10, which is significantly larger than 1, the circuitry should certainly start oscillating.

    My question is, is there an analytical way to determine the stability in any way? Further, is there a way to determine the turn-on time, which the oscillator needs until reaching steady state? The analysis should preferable include the correct transistor, if possible.

    I'm also curious about the graph in the right of Fig. (Bild) 2 in [1], where the hatched region is "The area in which experience has shown that optimum quality values can be achieved for the coil and the oscillating circuit (no-load quality)". Where do I get such an information, except from this textbook?


    [1] https://books.google.at/books?id=u0s...B6hmer&f=false

    [2] https://assets.nexperia.com/document..._PMBT2222A.pdf

    BR
    stenzer

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    Re: Colpitts oscillator stability analysis

    Ulrich Rohde has an in-depth analytical textbook about oscillators.I recommend it to follow..The Design of Modern Microwave Oscillators for Wireless Applications : Theory and Optimization by Ulrich L. Rohde
    But I'd rather say that analytical approximations are very tedious and mostly erroneous.Modern circuit simulators today such as ADS and AWR's MWOffice give very quickly the exact results.
    Because oscillators are chaotic and nonlinear behaving devices therefore calculation will not set its place as wanted.



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    Re: Colpitts oscillator stability analysis

    A high L:C ratio takes more cycles to grow to a steady state from power-up.
    It also rings for a longer time after shut-off.
    The reason is that it usually has higher Q and greater 'inertia'.

    When L:C is low, or ohmic resistance is considerable, then it takes fewer cycles to reach steady state. Voltage amplitude tends to be reduced. Oscillations die out quickly if gain is insufficient.



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    Re: Colpitts oscillator stability analysis

    Yes, there it is, looking at the graph in the Elemente book link (looks like page 211).

    Click image for larger version. 

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    The graph relates frequency to Zo...
    and Zo is determined by the L:C ratio (or rather the square root). The dotted lines seem to indicate that 1MHz suits a Z value of 1000, and therefore L:C ratio of 1 million.

    Where a schematic contains an LC tank, or LC filter, etc., the L:C ratio is usually high, greater than a thousand.



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    Re: Colpitts oscillator stability analysis

    Hi,

    thank you for your replies!

    @ BigBoss: Thank you for the book suggestion, it is available in my university library. I will have a look.
    Until now I used LTspice for the simulations. There are trail versions of AWR's MWOffice and Keysight's ADS available. I will try ADS to simulate the oscillator.

    @ BradtheRad: Thank you for the hints regarding the L:C ratio.
    Regarding the graph, I was curious where if it is an empirical one and is it possible to calculate its margins?

    BR stenzer



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    Re: Colpitts oscillator stability analysis

    Quote Originally Posted by stenzer View Post
    @ BradtheRad: Thank you for the hints regarding the L:C ratio.
    Regarding the graph, I was curious where if it is an empirical one and is it possible to calculate its margins?
    The hatched area is the region that generally works for low voltage, low current circuits (I think). The upper and lower limit are approximate (obere Grenze, untere Grenze).

    Usually you want an LC combination which operates on the amount of current which is available. That way it creates sufficient voltage swings.

    Low current is associated with high L, low C.
    The combination yields high reactive impedance, which pairs up naturally with high neighboring resistances in the circuit.

    High current is associated with low L, high C.
    Yields low reactive impedance, which pairs up naturally with low neighboring resistances.



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    Re: Colpitts oscillator stability analysis

    Books, which for me are the reference when designing oscillators, are:
    --Discrete Oscillator Design: Linear, Nonlinear, Transient and Noise domains--Randall Rhea
    --Oscillator Design and Computer Simulation--Randall Rhea
    --RF and Microwave Transistor Oscillator Design--Andrei Grebennikov

    All these books have dedicated chapters for stability of self-oscillations.
    On top of unique analysis of oscillators, these books have very practical examples.



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