You can see from the entire expansion that all three of the effects are
there. And one of the most interesting one is the cross modulation term.
Here you can see that the amplitude of one signal affects the amplitude of
another.
73
Bill wa4lav
At 09:42 PM 1/1/2004 -0500, rfdude@COMCAST.NET wrote:
That is incorrect. If you wish to look over the math you will see the
process that actually produces these products. There are actually 3
effects caused by the odd terms. Harmonics, IMD products and cross
modulation. These are produced simultaneously and if you filter out one or
some it does not affect the others. Frequency Mixing is performed by the
even order terms of the polynomial. You are using simply a binomial
expansion and not a complete Taylor expansion of the non-linear
characteristic curve.
73
Bill wa4lav
At 02:12 AM 1/2/2004 +0000, rfdude@COMCAST.NET wrote:
Bill wrote:
*IMD is caused by the odd order terms of the polynomial ( output
voltage/input voltage) of a device. The harmonics of these can terms ( 3rd,
5th etc harmonics) can easily be filtered but the near by IMD products
cannot since they are KHz or less from each other. Many think IMD is due to
frequency mixing of harmonics but it is not, the additional frequencies are
created in the device with out the aid of harmonics.
......................................................................
Just to set the record straight: IMD products ARE the mixing terms of the
the "harmonics" with the "fundamental(s) (correct for the lowest order IMDs)".
For example for a two tone case, F1 and F2, the first close-in-band IMDs
are: 3*F2squared-F1 and 3*F1squared-F2, (F2squared is the 2nd harmonic of
F2, and so on....). Ignoring the amplitude term, this leads to the 3rd
order IMD products: 2F2-F1 and 2F1-F2.
The harmonics are part of the picture and are generated when the
fundamentals are raised to the higher power(s) of the binomial expansion.
The lowest order IMDs are created when the harmonics are mixed with the
fundament(s). For higher order IMD terms it is the mixing of also the
harmonics among themselves. These are the cross terms of the binomial
expansion.
Only the cross term of the quadratic gives the desired beat products
because none of the terms are raised to a higher power (n=1) (no
harmonics are involved). All the other cross terms of the binomial are
part of the IMD baggage.
So harmonics are part of the picture in generating IMDs.
Wonder why we use a "switch" for mixing instead of a true multiplier?
Well that another whole story.
kb3bf, chris
> IMD is caused by the odd order terms of the polynomial ( output
> voltage/input voltage) of a device. The harmonics of these can terms (
3rd,
> 5th etc harmonics) can easily be filtered but the near by IMD products
> cannot since they are KHz or less from each other. Many think IMD is
due to
> frequency mixing of harmonics but it is not, the additional
frequencies are
> created in the device with out the aid of harmonics. If you are
interested
> in the math behind IMD and harmonic distortion and frequency mixing (
> algebra and trig.) I can attach to an email notes that one of my students
> put together from one of my classes. It is rather large for some reason
> because I could not get it published to PDF without going to total bit
map.
>
> 73
> Bill wa4lav
>
>
> At 01:12 AM 1/2/2004 +0100, you wrote:
>
> >----- Original Message -----
> >From: "Bill Fuqua" <wlfuqu00@uky.edu>
> >To: <bill@wjschmidt.com>; "AMPS" <amps@contesting.com>
> >Sent: Friday, January 02, 2004 12:00 AM
> >Subject: Re: [Amps] 3.5 kV 2A REGULATED Power Supply: Schematic ?
> >
> >
> > > At 04:50 PM 1/1/2004 -0600, Dr. William J. Schmidt, II wrote:
> > > >Class A has less little IMD, class B has a lot. C would be
really nasty
> > > >if not
> > > >for output filtering (good tank circuit)
> > >
> > > C will have lots of IMD regardless of tank circuit. The tank
circuit only
> > > eleminates
> > > harmonics.
> >
> > ** not only eleminates ( most of ) harmonics, when cleaning up up
the sine
> >( RF ) as a f(Q ) of the tank.
> > I always believed IMD was included ! What am I missing Bill ?
> >
> >Hpy 2004 to all.
> >
> >jos on4kj
> >
> >f> 73
> > > Bill wa4lav
> > >
> > >
> > >
> > > _______________________________________________
> > > Amps mailing list
> > > Amps@contesting.com
> > > http://lists.contesting.com/mailman/listinfo/amps
> > >
> > >
>
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