Bill,
I found you attatchment, thanks for sending it.
There is nothing wrong in using the binomial expansion in representing a switch
function. The binomail will include the terms of the taylor expansion when you
define the function that shows the I(V) property of your mixer element.
In the end I see the same terms you have with the taylor series expansion. It
may be a matter of semantics but a periodic function squared (or higher power)
leads to an harmonic. If you don't agree please tell me why. I would like to
set the record straight.
Also I do not understand what you mean by:
"It is just that in doing the math we
expand the terms a little bit at a time."?
thanks
chris kb3bf
> You know this misconception probably has come from the trig identity
> generally used to expand (Cos A + Cos B)^3.
> Which is the same one I use. However, it could be done with different
> identities. These processes are taking place simultaneously.
> It is not that a pair of terms are squared to produce a second harmonic and
> then multiplied by the fundamental. It is just that in doing the math we
> expand the terms a little bit at a time.
>
> 73
> Bill wa4lav
>
>
>
> At 09:48 PM 1/1/2004 -0500, rfdude@COMCAST.NET,amps@contesting.com wrote:
> >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
> >>> > > >
> >>> > > >
> >>> >
> >>> > _______________________________________________
> >>> > Amps mailing list
> >>> > Amps@contesting.com
> >>> > http://lists.contesting.com/mailman/listinfo/amps
>
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