Bill,
I am not sure a single taylor series expansion can apply for your mixing case.
Ideal mixing is based on multiplication, but let's skip this case because it
seldom applies, other than in a Gilbert Cell (very poor dynamic range).
Switching is the next ideal form of mixing, and that cannot be described by a
single continous function; it has to be broken up.
In a non-ideal switch such as a Schottky diode, the local oscillator (LO)
swings the mixer diode from reverse bias to forward bias. The currents are
discountious at V=0, since the reverse current is dominated by drift current,
and the forward current is based on themoionic emission (just like a field
emitter in vacuum device). It would be diffusion current in a pn diode, but pn
diodes are seldom used for mixers, since they are too slow.
The same case would apply for the strong LO biasing in a vacuum tube grid, and
on the regimes defining the plate current from the grid voltage. The whole LO
cycle must be taken into account.
The taylor series expansion would be broken up in the non linear discountinous
regions. However I am not sure what implication this may have without redoing
the math.
I'll let you predict the outcome from the workout.
chris
> At 02:12 AM 1/2/2004 +0000, rfdude@COMCAST.NET wrote:
>
> >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.
>
> As long at the non-linear function is continuous and and can be described
> by a polynomial (Taylor Series). The mixing of second harmonics and
> fundamentals does not take place.
> For example, I can have a second order (squared term) which will produce
> mixing between the two original frequencies and second harmonics of the two
> frequencies. Even though I have increased the second harmonic content from
> none to some or a lot it has no effect on the IMD products. Just look at
> the math. So I say that the production of the IMD products and second
> harmonics are independent and thus it is no mixing of the second harmonics
> and fundamentals.
>
> 73
> Bill wa4lav
>
>
_______________________________________________
Amps mailing list
Amps@contesting.com
http://lists.contesting.com/mailman/listinfo/amps
|