I'm trying to settle a debate with a friend, and my knowledge of
mixers is pretty rusty.

Say you have a receiver whose IF is 455 kHz, and it's tuned to a
station at 1500 kHz. If all's working OK, at the output of the mixer
you should have four frequencies:

1500 (original signal)
1955 (oscillator signal - osc. working above the signal freq.)
3455 (sum)
455 (difference)

My question is by what process does the mixer produce the 3455 and 455
frequencies. I say it's an add and subtract process, my friend says
(via mathematics) it's a multiplication process. Who's right?

thanks,

Joe W9TXU

Your friend is right.

If you simply add or subtract two waveforms, no new frequencies are
created. You end up with only the frequencies you started with and no
more. (Theoretically, you could make one or more disappear if one of the
added waveforms contained a precise negative of one or more frequency
components of the other -- but you can never get any new frequencies.)
That's because addition is a linear process, with linear having a
precise definition that's appeared here a number of times before.
(Subtraction is just addition, with one waveform inverted before
adding.) Multiplication, though, is a nonlinear process by the precise
definition used in circuit analysis, and it does create additional
frequencies. Multiplying the two original signals of 1500 and 1955
generates the two new frequencies of 455 and 3455, for a total of four
frequencies after multiplication. Adding them wouldn't do it.

Most good mixers are actually more like switches than multipliers, but
they're still nonlinear -- very much so -- and don't do anything
remotely like adding the two signals. A doubly balanced mixer produces
the sum and difference frequencies while not letting the original two
frequencies get through to the output.

The generation of the new frequencies by multiplication of the two
originals is easily shown mathematically, as your friend says, with a
short derivation by means of a trig identity. I'll be glad to post the
derivation if you or other readers are interested, although it's widely
available elsewhere.

Roy Lewallen, W7EL

Joer wrote:
I'm trying to settle a debate with a friend, and my knowledge of
mixers is pretty rusty.

Say you have a receiver whose IF is 455 kHz, and it's tuned to a
station at 1500 kHz. If all's working OK, at the output of the mixer
you should have four frequencies:

1500 (original signal)
1955 (oscillator signal - osc. working above the signal freq.)
3455 (sum)
455 (difference)

My question is by what process does the mixer produce the 3455 and 455
frequencies. I say it's an add and subtract process, my friend says
(via mathematics) it's a multiplication process. Who's right?

thanks,

Joe W9TXU

Roy Lewallen wrote:
Multiplying the two original signals of 1500 and 1955 generates the two
new frequencies of 455 and 3455, for a total of four frequencies after
multiplication. Adding them wouldn't do it.

Part of the confusion is that audio engineers talk about "mixing" where
they actually mean adding. Mixing - as RF engineers use the term - is
precisely what they don't want!


--
73 from Ian G3SEK 'In Practice' columnist for RadCom (RSGB)
Editor, 'The VHF/UHF DX Book'
http://www.ifwtech.co.uk/g3sek

"Ian White, G3SEK" a écrit dans le message news:
...
Roy Lewallen wrote:
Multiplying the two original signals of 1500 and 1955 generates the two
new frequencies of 455 and 3455, for a total of four frequencies after
multiplication. Adding them wouldn't do it.

Part of the confusion is that audio engineers talk about "mixing" where
they actually mean adding. Mixing - as RF engineers use the term - is
precisely what they don't want!



Well, ear is also somewhat non linear. So they are also doing mixing.

Fred.

Fred,
You're exactly correct! That's why a piano tuner person can strike a tuning
fork and a piano key at the same time and hear the frequency difference as a
low beat note.

As to Ian's comment...I don't think "adding" is the correct term either.
"Multiplying" or "sampling" are more precise terms. A perfect balanced
unity-gain mixer actually uses one of the input signals to sample the other.
On the positive half cycle of the LO, one phase of the RF signal is sampled,
and on the other half cycle of the LO the opposite phase of the RF is
sampled. Mathematically, this is equivalent to multiplying the RF signal by
+1 or -1 on alternating half cycles of the LO.

Joe
W3JDR

"Fred Bartoli"
r_AndThisToo wrote in
message ...

"Ian White, G3SEK" a écrit dans le message news:
...
Roy Lewallen wrote:
Multiplying the two original signals of 1500 and 1955 generates the two
new frequencies of 455 and 3455, for a total of four frequencies after
multiplication. Adding them wouldn't do it.

Part of the confusion is that audio engineers talk about "mixing" where
they actually mean adding. Mixing - as RF engineers use the term - is
precisely what they don't want!



Well, ear is also somewhat non linear. So they are also doing mixing.

Fred.

"W3JDR" a écrit dans le message news:
...
Fred,
You're exactly correct! That's why a piano tuner person can strike a
tuning
fork and a piano key at the same time and hear the frequency difference as
a
low beat note.


Sure. Just try to suppress ear non linear effects and see how miserable
composers will feel without it and how poor the music will sound to our
"marvellous new ears".


As to Ian's comment...I don't think "adding" is the correct term either.
"Multiplying" or "sampling" are more precise terms. A perfect balanced
unity-gain mixer actually uses one of the input signals to sample the
other.
On the positive half cycle of the LO, one phase of the RF signal is
sampled,
and on the other half cycle of the LO the opposite phase of the RF is
sampled. Mathematically, this is equivalent to multiplying the RF signal
by
+1 or -1 on alternating half cycles of the LO.


Or, convolving, if the frequency domain, which tells all the story.

Fred.

W3JDR wrote:
Fred,
You're exactly correct! That's why a piano tuner person can strike a tuning
fork and a piano key at the same time and hear the frequency difference as a
low beat note.

Hearing beats does not require non-linear or multiplicative mixing -
please see my separate reply to Fred.


As to Ian's comment...I don't think "adding" is the correct term either.

I was referring to what *audio* engineers call "mixing", which is
nothing else but simple adding or linear combining.

I agree with everything you say below...

"Multiplying" or "sampling" are more precise terms. A perfect balanced
unity-gain mixer actually uses one of the input signals to sample the other.
On the positive half cycle of the LO, one phase of the RF signal is sampled,
and on the other half cycle of the LO the opposite phase of the RF is
sampled. Mathematically, this is equivalent to multiplying the RF signal by
+1 or -1 on alternating half cycles of the LO.

...but the processes you describe are not what a straightforward audio
"mixing" desk does.

The device you describe above, an audio engineer would know as a
"modulator" or a "ring modulator". For example, the LO could be at a low
frequency, to get some kind of throbbing effect. Both RF and audio
engineers would agree, that is true modulation.

The difference is that RF engineers would also call that process
"mixing"... but audio engineers would not because, to in their
professional world, "mixing" means adding or linear combining.


--
73 from Ian G3SEK 'In Practice' columnist for RadCom (RSGB)
Editor, 'The VHF/UHF DX Book'
http://www.ifwtech.co.uk/g3sek

"W3JDR" a écrit dans le message news:
...
Fred,
You're exactly correct! That's why a piano tuner person can strike a
tuning
fork and a piano key at the same time and hear the frequency difference as
a
low beat note.


Sure. Just try to suppress ear non linear effects and see how miserable
composers will feel without it and how poor the music will sound to our
"marvellous new ears".


As to Ian's comment...I don't think "adding" is the correct term either.
"Multiplying" or "sampling" are more precise terms. A perfect balanced
unity-gain mixer actually uses one of the input signals to sample the
other.
On the positive half cycle of the LO, one phase of the RF signal is
sampled,
and on the other half cycle of the LO the opposite phase of the RF is
sampled. Mathematically, this is equivalent to multiplying the RF signal
by
+1 or -1 on alternating half cycles of the LO.


Or, convolving, if the frequency domain, which tells all the story.

Fred.

W3JDR wrote:
Fred,
You're exactly correct! That's why a piano tuner person can strike a tuning
fork and a piano key at the same time and hear the frequency difference as a
low beat note.

Hearing beats does not require non-linear or multiplicative mixing -
please see my separate reply to Fred.


As to Ian's comment...I don't think "adding" is the correct term either.

I was referring to what *audio* engineers call "mixing", which is
nothing else but simple adding or linear combining.

I agree with everything you say below...

"Multiplying" or "sampling" are more precise terms. A perfect balanced
unity-gain mixer actually uses one of the input signals to sample the other.
On the positive half cycle of the LO, one phase of the RF signal is sampled,
and on the other half cycle of the LO the opposite phase of the RF is
sampled. Mathematically, this is equivalent to multiplying the RF signal by
+1 or -1 on alternating half cycles of the LO.

...but the processes you describe are not what a straightforward audio
"mixing" desk does.

The device you describe above, an audio engineer would know as a
"modulator" or a "ring modulator". For example, the LO could be at a low
frequency, to get some kind of throbbing effect. Both RF and audio
engineers would agree, that is true modulation.

The difference is that RF engineers would also call that process
"mixing"... but audio engineers would not because, to in their
professional world, "mixing" means adding or linear combining.


--
73 from Ian G3SEK 'In Practice' columnist for RadCom (RSGB)
Editor, 'The VHF/UHF DX Book'
http://www.ifwtech.co.uk/g3sek

Fred Bartoli wrote:

"Ian White, G3SEK" a écrit dans le message news:
...
Roy Lewallen wrote:
Multiplying the two original signals of 1500 and 1955 generates the two
new frequencies of 455 and 3455, for a total of four frequencies after
multiplication. Adding them wouldn't do it.

Part of the confusion is that audio engineers talk about "mixing" where
they actually mean adding. Mixing - as RF engineers use the term - is
precisely what they don't want!



Well, ear is also somewhat non linear. So they are also doing mixing.

What the audio engineers do at the "mixing desk" involves only adding.
What our ears do, is something else.

But in fact, our ears are very close to linear. There is a belief that
because we can hear "beat" frequencies, there must be some non-linear
mixing in our ears... but that is actually a fallacy. The way we hear
beat frequencies - the difference frequency between two separate audio
tones - is due to simple linear addition and subtraction of two sound
pressure waves. Non-linear mixing is not required.

(If non-linear mixing were involved, we'd hear the sum frequency as well
as the difference frequency... but in fact we don't, unless there is
some other source of non-linearity outside of our ears.)


--
73 from Ian G3SEK 'In Practice' columnist for RadCom (RSGB)
Editor, 'The VHF/UHF DX Book'
http://www.ifwtech.co.uk/g3sek