Clarify Frequency Multiplication

[Klaus Jensen]

Linear mixing of two generated frequencies is the electronic
equivalent of mathematical "addition". This can be easily
demonstrated in function generator software.

What then is the software equivalent of "multiplying" two sinewave
frequencies together?

For example, multiplying 30Hz by 60Hz to (presumeably) derive 18KHz.
And what does the resulting signal look like?

I am aware of "multiplier" IC's, but want to do this in software as a
purely mathematical function.

Klaus Jensen

[Phil Allison]

"Klaus Jensen"

>
> Linear mixing of two generated frequencies is the electronic
> equivalent of mathematical "addition". This can be easily
> demonstrated in function generator software.
>
> What then is the software equivalent of "multiplying" two sinewave
> frequencies together?
>
> For example, multiplying 30Hz by 60Hz to (presumeably) derive 18KHz.

** Oh no it don't.

> I am aware of "multiplier" IC's,

** Then go find out what they ACTUALLY do.


... Phil

[Robert Baer]

First, it helps to know what 2 times 3 is..better brush up on your math.
Second, it helps what the term "multiplying" means in this context.
Then you might have a chance..

[Bill Sloman]

Think trigometry.

http://en.wikipedia.org/wiki/Trigonometry

cos (A + B) = cos A . cos B - sin A .sin B

cos (A - B) = cos A . cos B + sin A . in B

Whence sin(A).sin(B)= 0.5 . Cos(A-B) - 0.5 Cos(A+B)

The product of a 30Hz sine wave and a 60Hz sine wave (as generated by
sticking them into the X and Y inputs of a four-quadrant multiplier)
is the sum of a 30Hz cosine wave and 90Hz cosine wave - which is to
say a pair of phase shifted sine waves.

Your 18kHz represents a rather comic misapprehension.

--
Bill Sloman, Nijmegen

[Phil Allison]

"Klaus Jensen"

> Linear mixing of two generated frequencies is the electronic
> equivalent of mathematical "addition".

** In electronics, "linear mixing" is normally just called "summing".

Egs: summing amplifier, summing stage etc

The idea of "linear mixing" likely comes from the world of recording and
live sound.

Egs: mixing desk, mixing engineer, the mix etc

Every sound mixing desk contains numerous summing amplifiers which take
inputs from each channel and sum them.



.... Phil

[Phil Allison]

"Bill Slowman"

> Your 18kHz represents a rather comic misapprehension.

** Wanna put the code scribbling newb out of his misery by defining what a "
frequency multiplier " actually is ?

Tip: think whole numbers ...




... Phil

[John Larkin]

If you mathematically multiply two sine waves (or use an analog
multiplier) you get the sum and difference frequencies, as Sloman
points out in his usual obnoxious way.

There's no simple or even fundamental way to multiply two frequencies.
The result would depend on your units of measure.

In Hz, 30 * 60 = 1800

but if you think of those same sine waves in radians,

(30 * 2 * pi) * (60 * 2 * pi) = 71057

which is not the same thing.


--

John Larkin Highland Technology Inc
www.highlandtechnology.com jlarkin at highlandtechnology dot com

Precision electronic instrumentation
Picosecond-resolution Digital Delay and Pulse generators
Custom timing and laser controllers
Photonics and fiberoptic TTL data links
VME analog, thermocouple, LVDT, synchro, tachometer
Multichannel arbitrary waveform generators

[Bill Sloman]

On May 18, 2:07 pm, "Phil Allison" <phi...@tpg.com.au> wrote:
> "BillSlowman"

A frequency multiplier is a non-linear device - such as a four
quadrant multiplier - that exploits the trignometric relationships
that I pointed out generate sum frequencies. The newb's 30Hz
multiplied by 60Hz to get 90Hz is a trivial case.

If you want high multiples of the driving frequency, you use a part
that converts a sine wave into an approximation to series of Dirac
spikes, whose Fourier transform contains equal amplitudes of every
harmonic of the fundamental up to a limit set by the width of the
spike.

Since the Dirac spike has zero width by definition, it transforms into
an infinite number of harmonics, each with a with vanishingly small
amplitude.

Step recovery diodes generate edges with fall times down to about
100psec - which is to say, harmonics up to 10GHz. They are real and
useful.

http://en.wikipedia.org/wiki/Step_recovery_diode

--
Bill Sloman, Nijmegen

[Bill Sloman]

On May 18, 4:33 pm, John Larkin

<jjlar...@highNOTlandTHIStechnologyPART.com> wrote:
> On Fri, 18 May 2012 17:15:31 +1000, Klaus Jensen
>

> <klausjen...@promark.com> wrote:
>
> >Linear mixing of two generated frequencies  is the electronic
> >equivalent of mathematical  "addition". This can be easily
> >demonstrated in function generator software.
>
> >What then is the software equivalent of "multiplying" two sinewave
> >frequencies together?
>
> >For example, multiplying 30Hz by 60Hz to (presumeably) derive 18KHz.
> >And what does the resulting signal look like?
>
> >I am aware of "multiplier" IC's, but want to do this in software as a
> >purely mathematical function.
>
> >Klaus Jensen
>
> If you mathematically multiply two sine waves (or use an analog
> multiplier) you get the sum and difference frequencies, as Sloman
> points out in his usual obnoxious way.

What's obnoxious about spelling out the fundamental trignometrical
basis of what's going on? Does it bruise you sensitive ego by
reminding you of the classes you skipped because you were too busy to
see their relevance?

> There's no simple or even fundamental way to multiply two frequencies.
> The result would depend on your units of measure.
>
> In Hz,  30 * 60 = 1800
>
> but if you think of those same sine waves in radians,
>
>         (30 * 2 * pi) * (60 * 2 * pi) = 71057
>
> which is not the same thing.

Give John another life-time or two and he'll discover dimensional
analysis.

--
Bill Sloman, Nijmegen

[Phil Allison]

"Bill Slowman"

>
> > Your 18kHz represents a rather comic misapprehension.
>
> ** Wanna put the code scribbling newb out of his misery by defining what a
> "
> frequency multiplier " actually is ?
>
> Tip: think whole numbers ...


A frequency multiplier is a non-linear device - such as a four
quadrant multiplier - that exploits the trignometric relationships
that I pointed out generate sum frequencies. The newb's 30Hz
multiplied by 60Hz to get 90Hz is a trivial case.

** Oh dear, I thought I was handing Bill a piece of cake.

But he turned it into a big, brown, smelly turd.

Making EXACTLY the same "comic" mistake as the fuckwit code scribbler.



... Phil

[John Larkin]

On Fri, 18 May 2012 07:52:52 -0700 (PDT), Bill Sloman
<bill....@ieee.org> wrote:

>On May 18, 4:33 pm, John Larkin
><jjlar...@highNOTlandTHIStechnologyPART.com> wrote:
>> On Fri, 18 May 2012 17:15:31 +1000, Klaus Jensen
>>
>> <klausjen...@promark.com> wrote:
>>
>> >Linear mixing of two generated frequencies  is the electronic
>> >equivalent of mathematical  "addition". This can be easily
>> >demonstrated in function generator software.
>>
>> >What then is the software equivalent of "multiplying" two sinewave
>> >frequencies together?
>>
>> >For example, multiplying 30Hz by 60Hz to (presumeably) derive 18KHz.
>> >And what does the resulting signal look like?
>>
>> >I am aware of "multiplier" IC's, but want to do this in software as a
>> >purely mathematical function.
>>
>> >Klaus Jensen
>>
>> If you mathematically multiply two sine waves (or use an analog
>> multiplier) you get the sum and difference frequencies, as Sloman
>> points out in his usual obnoxious way.
>
>What's obnoxious about spelling out the fundamental trignometrical
>basis of what's going on?

Calling a basic misunderstanding a "comic misapprehension."

[tm]

"John Larkin" <jjla...@highNOTlandTHIStechnologyPART.com> wrote in message
news:4nrcr7tjv7rrfbie2...@4ax.com...

> On Fri, 18 May 2012 07:52:52 -0700 (PDT), Bill Sloman
> <bill....@ieee.org> wrote:
>
>>On May 18, 4:33 pm, John Larkin
>><jjlar...@highNOTlandTHIStechnologyPART.com> wrote:
>>> On Fri, 18 May 2012 17:15:31 +1000, Klaus Jensen
>>>
>>> <klausjen...@promark.com> wrote:
>>>
>>> >Linear mixing of two generated frequencies is the electronic
>>> >equivalent of mathematical "addition". This can be easily
>>> >demonstrated in function generator software.
>>>
>>> >What then is the software equivalent of "multiplying" two sinewave
>>> >frequencies together?
>>>
>>> >For example, multiplying 30Hz by 60Hz to (presumeably) derive 18KHz.
>>> >And what does the resulting signal look like?
>>>
>>> >I am aware of "multiplier" IC's, but want to do this in software as a
>>> >purely mathematical function.
>>>
>>> >Klaus Jensen
>>>
>>> If you mathematically multiply two sine waves (or use an analog
>>> multiplier) you get the sum and difference frequencies, as Sloman
>>> points out in his usual obnoxious way.
>>
>>What's obnoxious about spelling out the fundamental trignometrical
>>basis of what's going on?
>
> Calling a basic misunderstanding a "comic misapprehension."
>
>
> --

He blames his unemployment on age. I bet the HR people are just doing a
Usenet search and finding what an asshole he is.

[John Fields]

On Fri, 18 May 2012 17:15:31 +1000, Klaus Jensen

---
Since 30Hz * 60Hz is 1600Hz, I'm sure you meant 1.8kHz instead of
18kHz.

If that's what you really want, then in very general terms, what I'd
do would be to count the input frequencies, store the values to two
registers, say "x" and "y", then multiply the contents of the
registers and store the result in "z".

Next, I'd ramp up a VCO, count its output frequency, and compare that
to the contents of "z".

When they're equal I'd clamp the voltage driving the VCO's frequency,
and at that point the VCO's output frequency would be equal to the
product of the two AC input signals.

--
JF

[John Larkin]

On Fri, 18 May 2012 12:02:16 -0400, "tm" <No_on...@white-house.gov>
wrote:

I wouldn't hire him at half his age. I suspect not many others would,
either.

[Tim Wescott]

On Fri, 18 May 2012 17:15:31 +1000, Klaus Jensen wrote:

> Linear mixing of two generated frequencies is the electronic equivalent
> of mathematical "addition". This can be easily demonstrated in function
> generator software.

You are confused. I'm not even sure what you're basing that statement
on, but in RF design (which is I assume where you're pulling your terms),
a "frequency mixer" multiplies two signals together, at least one of
which is a sine wave or a distortion thereof, resulting in a signal that
has a spectrum with energy at the sum and difference frequencies of the
frequency content in the two original signals.

> What then is the software equivalent of "multiplying" two sinewave
> frequencies together?

Nonsense.

> For example, multiplying 30Hz by 60Hz to (presumeably) derive 18KHz. And
> what does the resulting signal look like?

Well, as John Fields pointed out, multiplying 30Hz by 60Hz results in
1800Hz, so you're arithmetic is wrong. The resulting signal looks like
whatever you want it to, because there isn't any widely-used useful
signal processing function that does this.

> I am aware of "multiplier" IC's, but want to do this in software as a
> purely mathematical function.

A "frequency multiplier" and a "multiplier" are two different things. A
"frequency multiplier" takes a sine-wave signal and runs it through some
nonlinearity to generate a repetitive wave at the sine-wave frequency,
then filters out one of the resulting harmonics -- so you can start with
frequency f, and get 2f, 3f, etc. A plain old "multiplier" just
multiplies two voltages: V_out = (V_1 * V_2)/(V_ref), where V_ref is some
reference voltage that's either explicit, or (more usually) inherent in
the design of the multiplier circuit.

Back up a few steps and tell us -- at a system level -- what you are
trying to _do_. Not "I want to multiply two frequencies together", but
tell us what you're building, what it needs to do, and why you need to do
this oddball thing to succeed.

--
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com

[John Larkin]

There is no mathematically pure way to do this. It depends on an
artifact, namely the second. If you measure the frequencies in KHz, or
MHz, or radians, you get a wildly different answer.

[Bill Sloman]

On May 18, 6:40 pm, John Larkin
<jjlar...@highNOTlandTHIStechnologyPART.com> wrote:
> On Fri, 18 May 2012 12:02:16 -0400, "tm" <No_one_h...@white-house.gov>
> wrote:
>
>
>
>
>
>
>
>
>
>
>
> >"John Larkin" <jjlar...@highNOTlandTHIStechnologyPART.com> wrote in message

Check out Parkinson's Law on injelititus.

It starts when some up-himself prick refuses to hire people who might
be smarter than he is ...

http://www.caprofession.com/parkinsons8.asp

--
Bill Sloman, Nijmegen

[Bill Sloman]

On May 18, 6:02 pm, "tm" <No_one_h...@white-house.gov> wrote:
> "John Larkin" <jjlar...@highNOTlandTHIStechnologyPART.com> wrote in message

Don't be silly. HR people aren't clever enough to do anything like
that.

--
Bill Sloman, Nijmegen

[Bill Sloman]

On May 18, 6:25 pm, John Fields <jfie...@austininstruments.com> wrote:
> On Fri, 18 May 2012 17:15:31 +1000, Klaus Jensen
>
>
>
>
>
>
>
>
>
> <klausjen...@promark.com> wrote:
>
> >Linear mixing of two generated frequencies  is the electronic
> >equivalent of mathematical  "addition". This can be easily
> >demonstrated in function generator software.
>
> >What then is the software equivalent of "multiplying" two sinewave
> >frequencies together?
>
> >For example, multiplying 30Hz by 60Hz to (presumeably) derive 18KHz.
> >And what does the resulting signal look like?
>
> >I am aware of "multiplier" IC's, but want to do this in software as a
> >purely mathematical function.
>
> >Klaus Jensen
>
> ---
> Since 30Hz * 60Hz is 1600Hz, I'm sure you meant 1.8kHz

Actually, 1.8kHz^2. Metre^2 is a meaningful unit. because we live in a
three dimensional universe. Einstein demonstrated that we actually
live in a four dimensional universe, where time is an imaginary
number. If it was five dimensional, with two mutually orthogonal
imaginary time axes, Hz^2 might be a meaningful unit, but my
imagination isn't up to envisaging how.

Isn't dimensional analysis fun.

--
Bill Sloman, Nijmegen

[Dave Platt]

In article <9tscr7pbk3fjs2r99...@4ax.com>,

John Fields <jfi...@austininstruments.com> wrote:

>Since 30Hz * 60Hz is 1600Hz, I'm sure you meant 1.8kHz instead of
>18kHz.

Well, it's actually 1800 (Hz^2), or 1800 / (sec ^ 2). It's an
acceleration, not a rate.

--
Dave Platt <dpl...@radagast.org> AE6EO
Friends of Jade Warrior home page: http://www.radagast.org/jade-warrior
I do _not_ wish to receive unsolicited commercial email, and I will
boycott any company which has the gall to send me such ads!

[John Larkin]

I want to, and do, hire people who are smarter than I am. But I don't
hire obnoxious fatheads.


--

John Larkin Highland Technology, Inc

jlarkin at highlandtechnology dot com

http://www.highlandtechnology.com

Precision electronic instrumentation
Picosecond-resolution Digital Delay and Pulse generators

Custom laser drivers and controllers

Photonics and fiberoptic TTL data links

VME thermocouple, LVDT, synchro acquisition and simulation

[Phil Hobbs]

On 05/18/2012 01:54 PM, Dave Platt wrote:
> In article<9tscr7pbk3fjs2r99...@4ax.com>,
> John Fields<jfi...@austininstruments.com> wrote:
>
>> Since 30Hz * 60Hz is 1600Hz, I'm sure you meant 1.8kHz instead of
>> 18kHz.
>
> Well, it's actually 1800 (Hz^2), or 1800 / (sec ^ 2). It's an
> acceleration, not a rate.
>

And it's an entirely sensible unit for measuring FM, or Doppler shift
from an accelerating body, or....

(I'm in the middle of an expert witness gig in which a lot is riding on
the distinction between power and power spectral density. Units matter!)

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510
845-480-2058

hobbs at electrooptical dot net
http://electrooptical.net

[John Larkin]

On Fri, 18 May 2012 14:50:10 -0400, Phil Hobbs
<pcdhSpamM...@electrooptical.net> wrote:

>On 05/18/2012 01:54 PM, Dave Platt wrote:
>> In article<9tscr7pbk3fjs2r99...@4ax.com>,
>> John Fields<jfi...@austininstruments.com> wrote:
>>
>>> Since 30Hz * 60Hz is 1600Hz, I'm sure you meant 1.8kHz instead of
>>> 18kHz.
>>
>> Well, it's actually 1800 (Hz^2), or 1800 / (sec ^ 2). It's an
>> acceleration, not a rate.
>>
>
>And it's an entirely sensible unit for measuring FM, or Doppler shift
>from an accelerating body, or....
>
>(I'm in the middle of an expert witness gig in which a lot is riding on
>the distinction between power and power spectral density. Units matter!)
>

Good luck. Maybe 1% of the population (and 0.1% of journalists) know
that a KW is different from a KWH.

[Artemus]

"Bill Sloman" <bill....@ieee.org> wrote in message
news:d69e2764-36df-46f7...@b1g2000vbb.googlegroups.com...

***************************

Wow! I learn something new here all the time.
The OP asked for A*B. (Regardless whether A*B makes any sense.)
Now I learn that A*B = sin(A)*sin(B)
Furthermore the cos(A)*cos(B) term can be ignored to make one's point.
Where do I sign up to be a AGW zealot? I understand the rules now.
Art

[Bill Sloman]

On May 18, 8:22 pm, John Larkin <jlar...@highlandtechnology.com>
wrote:
> On Fri, 18 May 2012 10:28:15 -0700 (PDT),BillSloman

On the other hand you haven't fired yourself, so your judgement is
clearly less than reliable.

--
Bill Sloman, Nijmegen

[Bill Sloman]

On May 18, 9:37 pm, John Larkin <jlar...@highlandtechnology.com>
wrote:

> On Fri, 18 May 2012 14:50:10 -0400, Phil Hobbs
>
>
>
>
>
>
>
>
>
> <pcdhSpamMeSensel...@electrooptical.net> wrote:
> >On 05/18/2012 01:54 PM, Dave Platt wrote:

> >> In article<9tscr7pbk3fjs2r99ku5u71sqmb6oo0...@4ax.com>,
> >> John Fields<jfie...@austininstruments.com>  wrote:

>
> >>> Since 30Hz * 60Hz is 1600Hz, I'm sure you meant 1.8kHz instead of
> >>> 18kHz.
>
> >> Well, it's actually 1800 (Hz^2), or 1800 / (sec ^ 2).  It's an
> >> acceleration, not a rate.
>
> >And it's an entirely sensible unit for measuring FM, or Doppler shift
> >from an accelerating body, or....
>
> >(I'm in the middle of an expert witness gig in which a lot is riding on
> >the distinction between power and power spectral density.  Units matter!)
>
> Good luck. Maybe 1% of the population (and 0.1% of journalists) know
> that a KW is different from a KWH.

You clearly spend time with the wrong 1% of the population. But
beggars can't be choosers.

--
Bill Sloman, Nijmegen

[Jamie]

Hmm...

I don't know if there is no mathematical way to do this in the analog
state how ever, using some FFT's (DFT) and (IDFT)'s One could then use
math at a software level to regenerate a signal based from two values.

Jamie

[Jamie]

Stay tuned, you don't understand, yet!

Slow-Man is here to save the planet! I have no idea what I'd
do with out his guidance!

Jamie

[Simon S Aysdie]

On May 18, 12:15 am, Klaus Jensen <klausjen...@promark.com> wrote:
> Linear mixing of two generated frequencies  is the electronic
> equivalent of mathematical  "addition". This can be easily
> demonstrated in function generator software.
>
> What then is the software equivalent of "multiplying" two sinewave
> frequencies together?
>
> For example, multiplying 30Hz by 60Hz to (presumeably) derive 18KHz.
> And what does the resulting signal look like?

No, it is not 18 kHz, as many have pointed out.

> I am aware of "multiplier" IC's, but want to do this in software as a
> purely mathematical function.

When it is said that it is a "multiplier," it means multiplication in
the time domain. (And thus convolution in the frequency domain.)

It is basic trig, and it has been given by others already. Pick the
form you want.

It is easy in software. Just do array multiplication, quite
literally. cos(w1*t)*cos(w2*t). You have to decide your w1, w2, and
t vector. Use python or whatever you want.

Or, you can use an identity form such as 0.5*cos((w1+w2)*t)
+0.5*cos((w1-w2)*t).

Actually, doing these types of multiplications in software is how I
have double checked some special trig identity formulations I
computed.

For "eternal sinusoids," the frequency domain convolution is easier if
you just want to know frequency and amplitude.

[John Fields]

On Fri, 18 May 2012 11:22:09 -0700, John Larkin
<jla...@highlandtechnology.com> wrote:

>On Fri, 18 May 2012 10:28:15 -0700 (PDT), Bill Sloman
><bill....@ieee.org> wrote:

>>Check out Parkinson's Law on injelititus.
>>
>>It starts when some up-himself prick refuses to hire people who might
>>be smarter than he is ...
>>
>>http://www.caprofession.com/parkinsons8.asp
>
>
>I want to, and do, hire people who are smarter than I am. But I don't
>hire obnoxious fatheads.

---
A wise choice, since two in a company would no doubt be
counter-productive.

--
JF

[Tim Williams]

"Phil Allison" <phi...@tpg.com.au> wrote in message
news:a1n85n...@mid.individual.net...

> A frequency multiplier is a non-linear device - such as a four
> quadrant multiplier - that exploits the trignometric relationships
> that I pointed out generate sum frequencies. The newb's 30Hz
> multiplied by 60Hz to get 90Hz is a trivial case.

Incorrect. A multiplier is a linear device, with respect to a single input.
For a function:
f(A, B) = A * B
it is true that (B != 0, and not a function of x or y):
f(c1*x + c2*y, B) = B*(c1*x + c2*y)
which is the definition of linearity.

Since the function has two inputs, it is more exactly bilinear, which is not
linear with two dependent inputs, but it is most certainly not non-linear in
general.

Tim

--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms

[John Fields]

---
Mathematically pure - whatever that's supposed to mean - or not, what
I described will work.
---

>It depends on an artifact, namely the second. If you measure the frequencies in KHz, or
>MHz, or radians, you get a wildly different answer.

---
In the first place, it's not radians, it's radians per second.

In the second place, if the slices of time used to measure the input
frequencies and generate the product frequency have a definite
mathematical relationship, then whether the "second" is an artifact or
not is of little consequence.

--
JF

[Phil Allison]

"Tim Williams"
> "Phil Allison"

>> A frequency multiplier is a non-linear device - such as a four
>> quadrant multiplier - that exploits the trignometric relationships
>> that I pointed out generate sum frequencies. The newb's 30Hz
>> multiplied by 60Hz to get 90Hz is a trivial case.
>
> Incorrect.

** I did not post the above.

Da Slow Man did.

Watch what you are doing

[Phil Allison]

"John Larkin"

>
> Calling a basic misunderstanding a "comic misapprehension."
>

** You gotta admit that some code scribbling wanker taking the term "
frequency multiplier " absolutely literally IS pretty damn funny.

Betcha the same fool thinks that a bottle of " steak sauce " contains steak.


.... Phil

[Klaus Jensen]

On Fri, 18 May 2012 17:15:31 +1000, Klaus Jensen
<klaus...@promark.com> wrote:

Thanks to everyone for the input to my naive OP. I can now see it is a
far more complex matter than I had first imagined.

I simply wanted to know if there is an equivalent dynamic function to
"summing" based upon multiplication instead of addition.

And what would be the result if viewed on a spectum analyzer.

If I generate 30Hz and 60Hz in the tone generator of an audio editing
application, and then "mix" them, a complex wave is obtained comprised
of the two frequencies.

If I mix them in hardware, a sum and difference (beat) frequency would
be added.

I am not aware what type of process would result in multiplication,
based upon either of these two approachs. Or what the multiplied
product would look like.

Of course I can generate a 1.8KHz sinewave directly, but that is not a
process of interaction.

Excuse me for still being dense, but I am in over my head and using a
straw.

Klaus Jensen

[Tim Wescott]

In the audio mixing case, you get a spectrum with both signals, and the
result is useful because people like to hear drums and vocals together.

In the radio mixing case (which is what you mean when you say "mix in
hardware"), you can use the signal at the sum or the difference frequency
to make a superheterodyne radio possible -- and you can implement a radio-
style mixer in a number of different and useful ways.

But that's as far as it goes. There really isn't any common, useful
process that gives you a "frequency A * frequency B" result -- if nothing
else, when you subject your question to dimensional analysis you find
that when you multiply 30Hz times 60Hz, you do _not_ get 1800Hz (even
though I fell into that trap). You get 1800(Hz)^2. Or maybe you get
71061 radians^2/sec^2. Whatever you get, unless you divide it by a
reference frequency you have an acceleration, not a rate.

[Phil Allison]

"Klaus Jensen"

>
> Thanks to everyone for the input to my naive OP. I can now see it is a
> far more complex matter than I had first imagined.
>
> I simply wanted to know if there is an equivalent dynamic function to
> "summing" based upon multiplication instead of addition.
>
> And what would be the result if viewed on a spectum analyzer.
>
> If I generate 30Hz and 60Hz in the tone generator of an audio editing
> application, and then "mix" them, a complex wave is obtained comprised
> of the two frequencies.
>
> If I mix them in hardware, a sum and difference (beat) frequency would
> be added.
>
> I am not aware what type of process would result in multiplication,
> based upon either of these two approachs. Or what the multiplied
> product would look like.

** This Wiki describes what a "frequency multiplier" is:

http://en.wikipedia.org/wiki/Frequency_multiplier

Your mad idea is undefined and therefore idiotic.

Piss off.


... Phil

[upsid...@downunder.com]

On Fri, 18 May 2012 17:15:31 +1000, Klaus Jensen
<klaus...@promark.com> wrote:

>For example, multiplying 30Hz by 60Hz to (presumeably) derive 18KHz.
>And what does the resulting signal look like?

If you want to generate 18000 Hz from 60 Hz, that is the 300th
harmonic.

The tradititional way is to use two x2 one x3 and two x5 multiplier
stages.

With such low (18 kHz) frequency, the simplest way would be using a
VCO phase locked to the 60 Hz reference with a divide by 300 counter.

[John Fields]

On Sat, 19 May 2012 13:06:29 +1000, Klaus Jensen

<klaus...@promark.com> wrote:

>On Fri, 18 May 2012 17:15:31 +1000, Klaus Jensen
><klaus...@promark.com> wrote:
>
>
>Thanks to everyone for the input to my naive OP. I can now see it is a
>far more complex matter than I had first imagined.
>
>I simply wanted to know if there is an equivalent dynamic function to
>"summing" based upon multiplication instead of addition.

---
There is heterodyning, where two sinusoidal sources are multiplied and
the resultant frequencies are the original frequencies plus their sum
and difference.
---

>And what would be the result if viewed on a spectum analyzer.

---
View using a fixed-pitch font:


. 10Hz 20Hz 30Hz 50Hz
. | | | |
. | | | |
.-------+------+------+--------------+--------
. f1-f2 f2 f1 f1+f2

>If I generate 30Hz and 60Hz in the tone generator of an audio editing
>application, and then "mix" them, a complex wave is obtained comprised
>of the two frequencies.

---
Yes.

The output would be the instantaneous algebraic sum of the amplitudes
of the signals, and the spectrum would look like this:

. 20Hz 30Hz
. | |
. | |
.-------+------+-----
. f2 f1

>If I mix them in hardware, a sum and difference (beat) frequency would
>be added.

---
"Heterodyne" is probably a better term, and if you heterodyne the two
signals, by whatever process, the result will contain the original
signals and their sum and difference signals.
---

>I am not aware what type of process would result in multiplication,
>based upon either of these two approachs.

---
Here's a pretty good link about RF mixing:

http://en.wikipedia.org/wiki/Frequency_mixer

>Or what the multiplied product would look like.

---
The spectrum would like what I posted above with the sidebands (the
sum and difference signals) and, ideally, they'd look like sine waves
with amplitudes varying in proportion to the amplitudes of f1 and f2
---

>Of course I can generate a 1.8KHz sinewave directly, but that is not a
>process of interaction.
>
>Excuse me for still being dense, but I am in over my head and using a
>straw.
>
>Klaus Jensen

---
Welcome to the group! :-)

--
JF

[John Larkin]

On Fri, 18 May 2012 18:59:45 -0500, John Fields

Not very well. The "count the input frequencies" part will have
ambiguity. If you use a 1-second timebase for the count operation,
each of the counted values will have a 1 count uncertainty from
measurement to measurement. The final output frequency will jump
around several per cent. If you freeze the VCO voltage, it stops
tracking the inputs and hangs at the last, ambiguous, frequency.

In other words, it's another asynchronous hairball.

The linear-multiplier operation, the one that makes the sum and
product frequencies, is mathematically perfect, so can be
electronically approximated very closely.

[John Fields]

---
As usual, you hypocritical oaf, you take a conceptual sketch and try
to denigrate its usefulness while stating that yours should be free
from criticism because they're only conceptual sketches.

Did it never occur to you that the input _periods_ could be measured
to whatever precision required, the multiplication done, and the
output synthesized while new periods were being measured?

Probably not, but then you're hardly one to own up to having egg on
your face.

--
JF

[John Larkin]

On Sat, 19 May 2012 09:34:33 -0500, John Fields

Of course I did. I do picosecond-resolution period measurements in
several of my products. But that's not what you said. And the whole
thing is silly.


--

John Larkin Highland Technology Inc
www.highlandtechnology.com jlarkin at highlandtechnology dot com

Precision electronic instrumentation
Picosecond-resolution Digital Delay and Pulse generators

Custom timing and laser controllers

Photonics and fiberoptic TTL data links

VME analog, thermocouple, LVDT, synchro, tachometer
Multichannel arbitrary waveform generators

[John Larkin]

On Sat, 19 May 2012 09:02:08 -0500, John Fields
<jfi...@austininstruments.com> wrote:

>On Sat, 19 May 2012 13:06:29 +1000, Klaus Jensen
><klaus...@promark.com> wrote:
>
>>On Fri, 18 May 2012 17:15:31 +1000, Klaus Jensen
>><klaus...@promark.com> wrote:
>>
>>
>>Thanks to everyone for the input to my naive OP. I can now see it is a
>>far more complex matter than I had first imagined.
>>
>>I simply wanted to know if there is an equivalent dynamic function to
>>"summing" based upon multiplication instead of addition.
>
>---
>There is heterodyning, where two sinusoidal sources are multiplied and
>the resultant frequencies are the original frequencies plus their sum
>and difference.

No. The output of a multiplier is the sum and difference of the input
sine waves. The two inputs don't make it through. It should be obvious
why.

A normal radio-type unbalanced mixer, or a simple diode mixer, will
propagate the inputs, because it's not a real multiplier.

[Nico Coesel]

I had this nice HP3314A which could output a frequency which was N* or
N/ by the input frequency. Basically it would lock its VCO using an
external reference frequency.

--
Failure does not prove something is impossible, failure simply
indicates you are not using the right tools...
nico@nctdevpuntnl (punt=.)
--------------------------------------------------------------

[Klaus Jensen]

On Fri, 18 May 2012 23:06:29 -0500, Tim Wescott <t...@seemywebsite.com>
wrote:

>But that's as far as it goes. There really isn't any common, useful
>process that gives you a "frequency A * frequency B" result

OK, I get the picture now. No real world process to "multiply" two
frequencies. Another nomenclature trap for the aspiring genius.

>-- if nothing
>else, when you subject your question to dimensional analysis you find
>that when you multiply 30Hz times 60Hz, you do _not_ get 1800Hz (even
>though I fell into that trap). You get 1800(Hz)^2.

So then, 3,240,000Hz (?) Seems strange, but no doubt true. Hard for me
to picture the implied dynamic though.

Thanks again to all for helping to sort out my thoughts.

Klaus Jensen

[Spehro Pefhany]

On Sun, 20 May 2012 13:04:04 +1000, the renowned Klaus Jensen
<klaus...@promark.com> wrote:

>On Fri, 18 May 2012 23:06:29 -0500, Tim Wescott <t...@seemywebsite.com>
>wrote:
>
>
>>But that's as far as it goes. There really isn't any common, useful
>>process that gives you a "frequency A * frequency B" result
>
>OK, I get the picture now. No real world process to "multiply" two
>frequencies. Another nomenclature trap for the aspiring genius.

Tim said nothing "common, useful". It's pretty straightforward to make
a circuit that would output 1800Hz when you input 30Hz and 60Hz- just
glomp together a few AD537s (two as F-V and one as V-F) and an AD633
(as a voltage multiplier) inbetween. It would be much cheaper in that
frequency range to do it in the digital domain, of course. Now, _why_
one would want to do it is the question, and because there's no good
answer for that, it follows that it's not a common requirement.

>>-- if nothing
>>else, when you subject your question to dimensional analysis you find
>>that when you multiply 30Hz times 60Hz, you do _not_ get 1800Hz (even
>>though I fell into that trap). You get 1800(Hz)^2.
>
>So then, 3,240,000Hz (?) Seems strange, but no doubt true. Hard for me
>to picture the implied dynamic though.

He's saying if you want 1800Hz from 60Hz and 30Hz, mathematically you
effectively have to have a constant of 1 second multiplied by the
product of the frequencies, since Hz * Hz * seconds = Hz.

>Thanks again to all for helping to sort out my thoughts.
>
>Klaus Jensen

Best regards,
Spehro Pefhany
--
"it's the network..." "The Journey is the reward"
sp...@interlog.com Info for manufacturers: http://www.trexon.com
Embedded software/hardware/analog Info for designers: http://www.speff.com

[John Fields]

On Sat, 19 May 2012 09:12:35 -0700, John Larkin
<jjla...@highNOTlandTHIStechnologyPART.com> wrote:

>On Sat, 19 May 2012 09:02:08 -0500, John Fields
><jfi...@austininstruments.com> wrote:
>
>>On Sat, 19 May 2012 13:06:29 +1000, Klaus Jensen
>><klaus...@promark.com> wrote:
>>
>>>On Fri, 18 May 2012 17:15:31 +1000, Klaus Jensen
>>><klaus...@promark.com> wrote:
>>>
>>>
>>>Thanks to everyone for the input to my naive OP. I can now see it is a
>>>far more complex matter than I had first imagined.
>>>
>>>I simply wanted to know if there is an equivalent dynamic function to
>>>"summing" based upon multiplication instead of addition.
>>
>>---
>>There is heterodyning, where two sinusoidal sources are multiplied and
>>the resultant frequencies are the original frequencies plus their sum
>>and difference.
>
>
>No. The output of a multiplier is the sum and difference of the input
>sine waves. The two inputs don't make it through. It should be obvious
>why.

---
I can't imagine why, since the multiplier will exhibit time-variable
gain resulting in amplitude modulation with the carrier, the local
oscillator, and both sidebands appearing at its output.
---

>A normal radio-type unbalanced mixer, or a simple diode mixer, will
>propagate the inputs, because it's not a real multiplier.

---
Sure it is.

It must be, otherwise it couldn't mix.

--
JF

[John Fields]

On Sat, 19 May 2012 09:03:09 -0700, John Larkin

---
Any neophyte without an axe to grind would have grasped the
equivalence without having to be led explicitly down that road.
---

>And the whole thing is silly.

---
Because you didn't come up with it?

Geez, I guess you've forgotten the old 7497.

--
JF

[amdx]

>>>>> Calling a basic misunderstanding a "comic misapprehension."
>>>

>>>>> --
>>>
>>>> He blames his unemployment on age. I bet the HR people are just doing a
>>>> Usenet search and finding what an asshole he is.
>>>

>>> I wouldn't hire him at half his age. I suspect not many others would,
>>> either.
>>

>> Check out Parkinson's Law on injelititus.
>>
>> It starts when some up-himself prick refuses to hire people who might
>> be smarter than he is ...
>>
>> http://www.caprofession.com/parkinsons8.asp
>
>
> I want to, and do, hire people who are smarter than I am. But I don't
> hire obnoxious fatheads.
>
>

Oh John, you just set yourself up as the straight man in a comedy team.
Mikek :-)

[John Larkin]

On Sun, 20 May 2012 02:25:10 -0500, John Fields

<jfi...@austininstruments.com> wrote:

>On Sat, 19 May 2012 09:12:35 -0700, John Larkin
><jjla...@highNOTlandTHIStechnologyPART.com> wrote:
>
>>On Sat, 19 May 2012 09:02:08 -0500, John Fields
>><jfi...@austininstruments.com> wrote:
>>
>>>On Sat, 19 May 2012 13:06:29 +1000, Klaus Jensen
>>><klaus...@promark.com> wrote:
>>>
>>>>On Fri, 18 May 2012 17:15:31 +1000, Klaus Jensen
>>>><klaus...@promark.com> wrote:
>>>>
>>>>
>>>>Thanks to everyone for the input to my naive OP. I can now see it is a
>>>>far more complex matter than I had first imagined.
>>>>
>>>>I simply wanted to know if there is an equivalent dynamic function to
>>>>"summing" based upon multiplication instead of addition.
>>>
>>>---
>>>There is heterodyning, where two sinusoidal sources are multiplied and
>>>the resultant frequencies are the original frequencies plus their sum
>>>and difference.
>>
>>
>>No. The output of a multiplier is the sum and difference of the input
>>sine waves. The two inputs don't make it through. It should be obvious
>>why.
>
>---
>I can't imagine why, since the multiplier will exhibit time-variable
>gain resulting in amplitude modulation with the carrier, the local
>oscillator, and both sidebands appearing at its output.

Bill posted the relevant trig identity. There are no fundamentals in
the output.

But you can just think about it. Input F2 periodically flips the phase
of F1, symmetrically. So F1 is present in the output in equal amounts
of straight-up and inverted. Those components cancel.

>---
>
>>A normal radio-type unbalanced mixer, or a simple diode mixer, will
>>propagate the inputs, because it's not a real multiplier.
>
>---
>Sure it is.
>
>It must be, otherwise it couldn't mix.

You're not an EE, and don't understand the theory, so why do you keep
asserting stuff that's wrong?

[Tim Wescott]

No. 60Hz is 60 cycles per second. 30Hz is 30 cycles per second. (60Hz)*
(30Hz) is 1800 cycles squared per second squared -- it's not a rate, it's
an acceleration. And it's meaningless, because what the heck is a
cycle^2?

Depending on the problem, (some number of radians per second) * (some
other number of radians per second) could possibly make dimensional sense
-- but only because a radian is a convenient name that we give to a
dimensionless ratio; in that case whatever the answer is would be in
seconds^(-2), it would be an angular acceleration (or a rate of frequency
ramping), and there had better be some physical process to resolve what
the "radians" were that got tossed out the window.

[josephkk]

But where does the additional seconds come from?

[josephkk]

On Sun, 20 May 2012 02:25:10 -0500, John Fields

<jfi...@austininstruments.com> wrote:

>On Sat, 19 May 2012 09:12:35 -0700, John Larkin
><jjla...@highNOTlandTHIStechnologyPART.com> wrote:
>
>>On Sat, 19 May 2012 09:02:08 -0500, John Fields
>><jfi...@austininstruments.com> wrote:
>>
>>>On Sat, 19 May 2012 13:06:29 +1000, Klaus Jensen
>>><klaus...@promark.com> wrote:
>>>
>>>>On Fri, 18 May 2012 17:15:31 +1000, Klaus Jensen
>>>><klaus...@promark.com> wrote:
>>>>
>>>>
>>>>Thanks to everyone for the input to my naive OP. I can now see it is a
>>>>far more complex matter than I had first imagined.
>>>>
>>>>I simply wanted to know if there is an equivalent dynamic function to
>>>>"summing" based upon multiplication instead of addition.
>>>
>>>---
>>>There is heterodyning, where two sinusoidal sources are multiplied and
>>>the resultant frequencies are the original frequencies plus their sum
>>>and difference.
>>
>>
>>No. The output of a multiplier is the sum and difference of the input
>>sine waves. The two inputs don't make it through. It should be obvious
>>why.
>
>---
>I can't imagine why, since the multiplier will exhibit time-variable
>gain resulting in amplitude modulation with the carrier, the local
>oscillator, and both sidebands appearing at its output.

Sorry, an analog multiplier (Gilbert cell) is double balanced, neither
input appears at the output (except in terms of unbalance or
nonlinearity).

?-(

>---
>
>>A normal radio-type unbalanced mixer, or a simple diode mixer, will
>>propagate the inputs, because it's not a real multiplier.
>
>---
>Sure it is.
>
>It must be, otherwise it couldn't mix.

Actually any non-linear device will do. Exponential devices like diodes
and transistors do pretty well at this, even square law devices like tubes
do a good job; and none are double balanced.

?-/

[John Fields]

Right.

Thanks.

---

>>>A normal radio-type unbalanced mixer, or a simple diode mixer, will
>>>propagate the inputs, because it's not a real multiplier.
>>
>>---
>>Sure it is.
>>
>>It must be, otherwise it couldn't mix.
>
>Actually any non-linear device will do. Exponential devices like diodes
>and transistors do pretty well at this, even square law devices like tubes
>do a good job; and none are double balanced.
>
>?-/

---
Right.

Thanks.
--
JF

[Spehro Pefhany]

It is defined into existence, becasue he wants to have Hz as the
output.

If you wanted to represent power with the output of a V-F converter
(maybe to transmit it across galvanic isolation), you'd need a
constant that has units of Hz/watt. If it was measuring displacement,
then you'd need a contant of Hz/femtometer or whatever.

In this case, the constant needs units of Hz/Hz^2 or seconds.

[Tim Wescott]

Good question, and ultimately what I was trying to get the OP to consider.

If it doesn't come from some physically meaningful aspect of the problem,
you're just pulling numbers out of your assumptions.

[josephkk]

You are welcome.

?-))

[John Larkin]

On Tue, 22 May 2012 12:01:20 -0700, Fred Abse
<excret...@invalid.invalid> wrote:

>On Sun, 20 May 2012 22:36:02 -0700, josephkk wrote:
>
>> Actually any non-linear device will do. Exponential devices like diodes
>> and transistors do pretty well at this, even square law devices like tubes
>> do a good job; and none are double balanced.
>

>Square law is good. It minimizes high order intermodulation products.

An ideal diode will mix, too, but the math is messy. It's easier to
pretend that a device is square-law and analyze that.


--

John Larkin Highland Technology, Inc

jlarkin at highlandtechnology dot com

http://www.highlandtechnology.com

Precision electronic instrumentation
Picosecond-resolution Digital Delay and Pulse generators

Custom laser drivers and controllers

Photonics and fiberoptic TTL data links

VME thermocouple, LVDT, synchro acquisition and simulation

[John Larkin]

On Tue, 22 May 2012 13:13:44 -0700, Fred Abse
<excret...@invalid.invalid> wrote:

>On Tue, 22 May 2012 12:11:48 -0700, John Larkin wrote:
>
>> On Tue, 22 May 2012 12:01:20 -0700, Fred Abse
>> <excret...@invalid.invalid> wrote:
>>
>>>On Sun, 20 May 2012 22:36:02 -0700, josephkk wrote:
>>>
>>>> Actually any non-linear device will do. Exponential devices like diodes
>>>> and transistors do pretty well at this, even square law devices like tubes
>>>> do a good job; and none are double balanced.
>>>
>>>Square law is good. It minimizes high order intermodulation products.
>>
>> An ideal diode will mix, too, but the math is messy. It's easier to
>> pretend that a device is square-law and analyze that.
>

>I once did an analysis using higher order terms. One interesting thing was
>the appearance of parametric amplification terms at the signal and LO
>frequencies.

Interesting... did you can get parametric gain from a regular diode or
an ideal diode?

You can get power gain from a diode, almost any kind, including PN,
varicap, pin, or ideal. You can also get power gain and shock-line
behavior from ceramic caps.

>
>I used to do things like that, for fun, when I was younger and sillier ;-)

Well, don't grow up too fast!

A little nonsense now and then
Is relished by the wisest men.

- Willy Wonka