On Tue, 03 Jul 2007 15:02:59 -0700, Keith Dysart
<Keith.Dysart@gmail.com> wrote:

>On Jul 3, 4:19 pm, John Fields <jfie...@austininstruments.com> wrote:
>> On Tue, 03 Jul 2007 12:05:52 -0700, Keith Dysart
>>
>>
>>
>>
>>
>> <Keith.Dys...@gmail.com> wrote:
>> >On Jul 3, 2:07 pm, Keith Dysart <Keith.Dys...@gmail.com> wrote:
>> >> On Jul 3, 12:50 pm, John Fields <jfie...@austininstruments.com> wrote:
>>
>> >> > On Mon, 2 Jul 2007 23:03:36 -0700, "Ron Baker, Pluralitas!"
>>
>> >> > <t...@aint.me> wrote:
>>
>> >> > >"John Smith I" <assemblywiz...@gmail.com> wrote in message
>> >> > >news:f64hg5$d3j$1@nnrp.linuxfan.it...
>> >> > >> Radium wrote:
>>
>> >> > ><snip>
>>
>> >> > >Suppose you have a 1 MHz sine wave whose amplitude
>> >> > >is multiplied by a 0.1 MHz sine wave.
>> >> > >What would it look like on an oscilloscope?
>>
>> >> <snip>
>>
>> >> > >What would it look like on a spectrum analyzer?
>>
>> >> > | |
>> >> > | | | |
>> >> > --------+--------------------+-------+------+----
>> >> > 100kHz 0.9MHz 1MHz 1.1MHz
>>
>> >> > >Then suppose you have a 1.1 MHz sine wave added
>> >> > >to a 0.9 MHz sine wave.
>> >> > >What would that look like on an oscilloscope?
>>
>> >> <snip>
>>
>> >> > Tricky!!!
>>
>> >> > It looks like AM but it isn't, it's just the phases sliding past
>> >> > each other slowly and algebraically adding which creates the
>> >> > illusion.
>>
>> >> > >What would that look like on a spectrum analyzer?
>>
>> >> > | |
>> >> > | |
>> >> > -----------------------------+--------------+----
>> >> > 0.9MHz 1.1MHz
>>
>> >> > --
>> >> > JF
>>
>> >> But if you remove the half volt bias you put on the
>> >> 100 kHz signal in the multiplier version, the results
>> >> look exactly like the summed version, so I suggest
>> >> that results are the same when a 4 quadrant multiplier
>> >> is used.
>>
>> >> And since the original request was for a "1 MHz sine
>> >> wave whose amplitude is multiplied by a 0.1 MHz sine
>> >> wave" I think a 4 quadrant multiplier is in order.
>>
>> >> ...Keith-
>>
>> >Ooops. I misspoke. They are not quite the same.
>>
>> ---
>> That's right. They can't possibly be because the first instance
>> _was_ multiplication and the second instance addition.
>
>Quite counter intuitive, I agree, but none-the-less true.
>To convince myself, I once created an Excel spreadsheet
>to demonstrate the fact.
>
>It along with some other discussion and plots are available
>here http://keith.dysart.googlepages.com/radio5
>
>> >The spectrum is the same, but if you want to get exactly
>> >the same result, the lower frequency needs a 90 degree
>> >offset and the upper frequency needs a -90 degree offset.
>>
>> ---
>> That makes no sense since the frequencies are different and,
>> consequently, the phase difference between the signals will be
>> constantly changing.
>
>To get exactly the same results, if, at time t0, the phases
>for the signals being multiplied together are 0, then at
>time t0, the initial phases for the signals being added
>must be 90 and -90.

---
OK, but that's just for the single slice in time where the circuit
reactances for both frequencies are complex conjugates, and cancel,
leaving only pure resistance for both signals to drive at that
instant.


--
JF