[Amps] Non-linear subharmonics was: Nonsense, AL-1500 parasitic

[jeff millar]

The reference to gain at f/2 is there...near the top of the second
reference...

    For proper operation, the capacitance must be decreased
    when the input voltage is maximum and increased when the
    input voltage is minimum. In other words, the pump signal
    frequency must be exactly double the frequency of the input signal.

The statement makes the point that a circuit with non-linear reactance can
have gain at f/2.  The the author goes on to generalize

    A parametric amplifier that is not phase-sensitive, referred to as
    a NONDEGENERATIVE PARAMETRIC AMPLIFIER,
    uses a pump circuit with a frequency higher than twice the input signal.
    The higher-frequency pump signal mixes with the input signal and
    produces additional frequencies that represent both the sum and
    difference of the input signal and pump frequencies.

This statement makes the point that a circuit with non-linear reactance can
have gain at any frequencies lower than the pump frequency.

Steve's point about noise helps to understand how the subharmonic gets
started. quoting from his email...

    As best I remember the article I read, the argument goes that
    if anything (even noise, maybe) causes f/2 to appear in a circuit,
    then IMD between f/2 and f produces 3f/2, then both f and 2f
    with 3f/2 produce f/2 and so on, so it can become stable and self
    sustaining if the circumstances are right. The same analysis can
    apply to f/3 etc.

This describes how any oscillation gets started.  In other words, a circuit
with gain starts out with zero signal and then a bit of noise occurs that
gets amplified and filtered and feeds back....leading to a build up of self
sustaining oscillation.  In familiar oscillators, a filter ensures that gain
and oscillation occurs at a single frequency.

It's valid to call a parametric frequency divider a sub-harmonic generator
because the frequency of oscillation isn't controlled in by a filter, but by
the mixing of oscillation, harmonics of the oscillation and the pump
frequency.

Michael Tope provided a reference
(http://smirc.stanford.edu/papers/JSSC99JUN-hamid.pdf) that shows a
subharmonic generater using a mixer and gain.  That circuit looks a lot more
like a classic oscillator than a parametric amplifier, but the same
principle applies.

Also recently on this list, Peter Chadwick provided a reference to a book
that covers the subject

    Parametric dividers can be made with a varactor: see
    Manassewitsch, Frequency Synthesisers, Theory and Design,
    second edn., p376 et seq.:
    One would expect a power dependency in the effect.
    Carrier storage devices can also be used to make a divider -
    see Manassewitsch again.

jeff, wa1hco

----- Original Message -----
From: "Ron" <w8ron@stratos.net>
To: "jeff millar" <wa1hco@adelphia.net>
Cc: <W8JI@contesting.com>; "'Amps'" <amps@contesting.com>
Sent: Monday, May 20, 2002 10:43 PM
Subject: Re: [Amps] Non-linear subharmonics was: Nonsense, AL-1500 parasitic


> I read these pages and couldn't find a reference to the f/2 discussion.
> It seemed to discuss injecting energy into a resonant cavity using a
charge pump
> running at twice the cavity frequengy and also injecting it at other
frequencies
> to obtain mixing products.
>
> Second, Steve's comment about "any thing (even noise) getting into the
amplifier
> is an invalid argument in that any ligitmate signal that enters the
amplifier is
> a mixing product and we already discussed that.  If it were noise ....well
noise
> is random and so the harmonics and mixing products would be noise and
randon as
> well.
> ---
> Ron