Ian:

[snip]
"Ian White, G3SEK" wrote in message
...
Roy Lewallen wrote::
:
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)
[snip]

Mixer, modulator, multiplier, demodulator, detector, switcher, balanced
modulator, adder, subtractor, heh, heh....

The term mixer is overused, or... "overloaded" as the computer scientists
like to say.

Yes indeed, too bad for beginners, but it's part of the mystique of our
trade as well, that there are plenty of examples of misuse,
misappropriation, and the outright abuse of terms and their meanings in our
trade! Keeps gurus in business and nosey outsiders out, as well. :-) Heh,
heh...

Even within the English speaking community, there is often no consistency of
terminology use, for example "tube" versus "valve", etc...

British and American use of the term "mixer" in the television production
equipment business has further confusing examples of overuse and overlapping
meanings. In television production technology the term "mixer" is also used
to describe switching and sepcial effects equipment and the terms are
applied differently on each side of the Atlantic. What you Brits call a
television "mixer" is called a television "switcher" in America, and what's
more... the same names are used for the operators of the said
mixing/switching equipment. [Grass Valley, Ross, Central Dynamics, etc...
are manufacturers of such.] You can often see the equipment operator's names
listed opposite the titles Mixer or Switcher on the TV screen when they roll
the credits at the end of television shows. And to make things worse, the
"function" of an audio "mixer" is again entirely different than a video
"mixer", whilst television video mixers often contain integrated audio
mixers. Impossible for beginners to figure out what experts are talking
about, go figure!

--
Peter K1PO
Indialantic By-the-Sea, FL

Bill Turner wrote:

Correct of course, but as I understand it, the only complication is
that there are harmonics present. It is still a case of add and
subtract, isn't it?

The original question only mentioned the *four* frequencies present in
the output, ignoring the harmonics.

Unless you can show me otherwise, I stand by my original observation.


The math does show otherwise.

When we talk about "square-law" and "third-order", we're actually buying
into a whole package deal of math-based concepts. Logically, the deal is
that we can't use those words *meaningfully* unless we also accept what
the math tells us, namely:

1. Each order of distortion is independent of all the other orders. It
generates its own individual package of output frequencies.

2. Frequencies that are in the same-order package *must* all be
generated together (you can't have one of them without having all the
others too).

3. Frequencies that are in different-order packages are totally separate
and unconnected.


2f1 and 2f2 are part of the package of 2nd-order products, along with
(f1 + f1) and (f1 - f2)... there are four 2nd-order output frequencies,
no more and no less.

3f1, 3f2, (2f1 + f2), (2f1 - f2), (f1 + 2f1) and (f2 - 2f1) are all part
of the 3rd-order package... there are six 3rd-order output frequencies,
no more and no less.

A perfect square-law mixer produces only 2nd-order products. 2f1 and 2f2
are present at the output, but they do not "go round again" and mix with
the input signals to produce (2f1 + f2) etc. Those 3rd-order products
arise *entirely and exclusively* from 3rd-order distortion.

That conclusion follows by strict, non-negotiable mathematical logic
from the fundamental definition of what "order of distortion" means.



As others have said, from the practical engineering point of view, the
way you envision mixing products being produced is "purely academic".
But that "purely academic" debate is exactly what we're involved in
here... so here, it makes all the difference in the world.




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

Bill Turner wrote:

Correct of course, but as I understand it, the only complication is
that there are harmonics present. It is still a case of add and
subtract, isn't it?

The original question only mentioned the *four* frequencies present in
the output, ignoring the harmonics.

Unless you can show me otherwise, I stand by my original observation.


The math does show otherwise.

When we talk about "square-law" and "third-order", we're actually buying
into a whole package deal of math-based concepts. Logically, the deal is
that we can't use those words *meaningfully* unless we also accept what
the math tells us, namely:

1. Each order of distortion is independent of all the other orders. It
generates its own individual package of output frequencies.

2. Frequencies that are in the same-order package *must* all be
generated together (you can't have one of them without having all the
others too).

3. Frequencies that are in different-order packages are totally separate
and unconnected.


2f1 and 2f2 are part of the package of 2nd-order products, along with
(f1 + f1) and (f1 - f2)... there are four 2nd-order output frequencies,
no more and no less.

3f1, 3f2, (2f1 + f2), (2f1 - f2), (f1 + 2f1) and (f2 - 2f1) are all part
of the 3rd-order package... there are six 3rd-order output frequencies,
no more and no less.

A perfect square-law mixer produces only 2nd-order products. 2f1 and 2f2
are present at the output, but they do not "go round again" and mix with
the input signals to produce (2f1 + f2) etc. Those 3rd-order products
arise *entirely and exclusively* from 3rd-order distortion.

That conclusion follows by strict, non-negotiable mathematical logic
from the fundamental definition of what "order of distortion" means.



As others have said, from the practical engineering point of view, the
way you envision mixing products being produced is "purely academic".
But that "purely academic" debate is exactly what we're involved in
here... so here, it makes all the difference in the world.




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

How'm I doin' Roy & Reg?

=========================

Steve, you're doing fine.

Absolutely no reference to Terman, Kraus, or those 3 gentlemen of
118-radials fame who forgot to measure ground conductivity before going
home. ;o)
----
Reg

How'm I doin' Roy & Reg?

=========================

Steve, you're doing fine.

Absolutely no reference to Terman, Kraus, or those 3 gentlemen of
118-radials fame who forgot to measure ground conductivity before going
home. ;o)
----
Reg

In article ,
(Joer) writes:

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?

Neither and both! :-)

It depends on the definitions of "linearity," "mixing," and "adding."

In a perfect linear circuit, two or more signals can exist as separate
entities, none affecting any other. You can "mix" them (inject them)
with the group of signals. Since the circuit is perfectly linear, no new
frequencies are added which are attributed to a sum or difference of
existing frequency signal components.

In sound recording "mixing" and "adding" always refers to operation
with nearly-perfect linear circuits to a recording medium.

"Mixers" in radios are highly non-linear. Some are outright switches
(Tayloe Mixer), some are very nearly on-off switches (diode rings),
and some use gross distortion of normally-linear characteristics
(tubes, particularly pentagrids...and Gilbert Cell double-differential
transistor structures). NON-LINEARITY creates new frequencies.

Mixing (in a mixer circuit) an incoming signal with a local oscillator
creates a mathematical sum and difference of the signal and the
LO frequencies...in addition to the existing signal and LO
frequencies passing through the mixer circuit (balanced mixers will
suppress the LO and double-balanced mixers can suppress the
signal frequency as well).

In this process of mixer circuit mixing, the new frequency products
(using "products" in a very general sense, not just multiplication)
still retain the amplitudes of the original. The signal's amplitude
containing AM sidebands is repeated at the new sum and difference
frequencies. Relative phase is also preserved. If the signal has
modulation components due to FM or PM, those appear on the new
sum and difference frequencies. If the much-stronger LO contains
any AM, FM, or PM, that is repeated on the new sum and difference
frequency components as AM, FM, or PM.

It gets worse. :-) The LO is seldom a pure sinewave so it has
harmonic content. New sum and difference frequencies will exist
as a result of LO harmonics! [most of those are simply filtered
out, dissipated, rejected] Scoping an LO injection waveform on
a wideband oscilloscope might come as a shock... :-)

The "process" is all due to NON-LINEARITY. The mixer output
contains the original signals plus components at frequencies
which are the sum and difference of the original...plus a few more.

Mathematics is used as a way of explaining the non-linear mixing
process. That isn't the full explaination but it is close enough.
Don't get caught up in plus and minus signs on equations and
too much argument over that...nor of the mathematical purists
who play games with term re-arrangements and "hidden meanings."

Non-linearity of all amplifiers will cause heterodyne creations. A
low-level example is the intermodulation distortion values such as
"IP3.".

Len Anderson
retired (from regular hours) electronic engineer person

In article ,
(Joer) writes:

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?

Neither and both! :-)

It depends on the definitions of "linearity," "mixing," and "adding."

In a perfect linear circuit, two or more signals can exist as separate
entities, none affecting any other. You can "mix" them (inject them)
with the group of signals. Since the circuit is perfectly linear, no new
frequencies are added which are attributed to a sum or difference of
existing frequency signal components.

In sound recording "mixing" and "adding" always refers to operation
with nearly-perfect linear circuits to a recording medium.

"Mixers" in radios are highly non-linear. Some are outright switches
(Tayloe Mixer), some are very nearly on-off switches (diode rings),
and some use gross distortion of normally-linear characteristics
(tubes, particularly pentagrids...and Gilbert Cell double-differential
transistor structures). NON-LINEARITY creates new frequencies.

Mixing (in a mixer circuit) an incoming signal with a local oscillator
creates a mathematical sum and difference of the signal and the
LO frequencies...in addition to the existing signal and LO
frequencies passing through the mixer circuit (balanced mixers will
suppress the LO and double-balanced mixers can suppress the
signal frequency as well).

In this process of mixer circuit mixing, the new frequency products
(using "products" in a very general sense, not just multiplication)
still retain the amplitudes of the original. The signal's amplitude
containing AM sidebands is repeated at the new sum and difference
frequencies. Relative phase is also preserved. If the signal has
modulation components due to FM or PM, those appear on the new
sum and difference frequencies. If the much-stronger LO contains
any AM, FM, or PM, that is repeated on the new sum and difference
frequency components as AM, FM, or PM.

It gets worse. :-) The LO is seldom a pure sinewave so it has
harmonic content. New sum and difference frequencies will exist
as a result of LO harmonics! [most of those are simply filtered
out, dissipated, rejected] Scoping an LO injection waveform on
a wideband oscilloscope might come as a shock... :-)

The "process" is all due to NON-LINEARITY. The mixer output
contains the original signals plus components at frequencies
which are the sum and difference of the original...plus a few more.

Mathematics is used as a way of explaining the non-linear mixing
process. That isn't the full explaination but it is close enough.
Don't get caught up in plus and minus signs on equations and
too much argument over that...nor of the mathematical purists
who play games with term re-arrangements and "hidden meanings."

Non-linearity of all amplifiers will cause heterodyne creations. A
low-level example is the intermodulation distortion values such as
"IP3.".

Len Anderson
retired (from regular hours) electronic engineer person