Tim Shoppa wrote:

In 1930's QST's it's not too uncommon to see neophytes warned that
crystals will often oscillate on something other than their marked
frequency. They didn't call this overtone operation, though.

They /might/ be suggesting that frequency can change with loading. I find
that some of the reference crystals I use are quite some way off their marked
frequency when given capacitive loading that differs from that recommended by
the manufacturers!

BC-604's (WWII era) start with a ridiculously low crystal (400ish kHz)
frequency and multiply up but I think the reason for this is more to
do with FM deviation than anything else. ("Armstrong method"?) For
many decades, broadcast FM stations similarly started with low crystal
frequencies and multiplied up.

Some of the broadcast transmitters I worked on 25 years ago used this method
for FM, and were /really/ difficult to line up! They also included complex
circuitry for the required "pre-distortion" of the audio to compensate for
the non-linear deviation you got out of a crystal oscillators. Some
manufacturers tried to overcome the distortion issue by using phase
modulation and the "right" audio curves, but these required even more stages
of multiplication!

One of my earliest jobs as a broadcast transmitter engineer was to develop a
PLL to replace the horrible multiplier chains in some of these transmitters.
I used (normally) either half or quarter frequency generation, and used the
last one or two multiplier stages. The CMOS PLL circuitry could be prone to
bizarre effects with high field strengths, so they were built in sealed
diecast boxes, and the lower frequency generation meant that the high power
output stages were unlikely to couple back into the oscillator!

Bob

On Nov 22, 8:43*pm, Stray Dog wrote:
Despite what at least one other person responding to this said, I can rest
assure you that if you run a doubler/multiplier stage even in a linear
mode, AND if you tune the output of that stage to the multiple harmonic,
you will definitely get output at that harmonic frequency which is
stronger than the input drive voltage.

Huh? No way... you MUST have non-linearities to make a doubler.

On Sun, 14 Dec 2008, Telstar Electronics wrote:

Date: Sun, 14 Dec 2008 08:20:56 -0800 (PST)
From: Telstar Electronics
Newsgroups: rec.radio.amateur.homebrew
Subject: Doubling

On Nov 22, 8:43*pm, Stray Dog wrote:
Despite what at least one other person responding to this said, I can rest
assure you that if you run a doubler/multiplier stage even in a linear
mode, AND if you tune the output of that stage to the multiple harmonic,
you will definitely get output at that harmonic frequency which is
stronger than the input drive voltage.

Huh? No way... you MUST have non-linearities to make a doubler.

All tubes (and transistors, etc) have non-linearities (if the transfer
characteristics are non-straight lines) if that is what you are talking
about.

However, I have observed output on a scope of second harmonics (and, yes,
the time base was set right and auto-self triggering) and the
amplifier was running no higher than Class B. You should actually try this
yourself and see for yourself. Tune the output to the second harmonic and
you will see grow out of the vally new "peaks" corresponding to that
second harmonic.

I don't know what the solid state gear is doing, but from many schematics
of the vintage tube gear I'm familiar with show, and measure, biasing for
linear operation, even in stages meant to multiply frequency.

"Telstar Electronics" wrote in message ...
On Nov 22, 8:43 pm, Stray Dog wrote:
? Despite what at least one other person responding to this said, I can rest
assure you that if you run a doubler/multiplier stage even in a linear
mode, AND if you tune the output of that stage to the multiple harmonic,
you will definitely get output at that harmonic frequency which is
stronger than the input drive voltage.

Huh? No way... you MUST have non-linearities to make a doubler.

Actually you do not need any nonlinearity to make a doubler (quadrupler, etc.).

Assume you have two Class B (or AB) stages that are driven in push-pull. The outputs are connected in parallel. And to make things even more linear, let each stage have a resistive load. Each stage will produce a linearly amplified (but inverted) version of the input signal FOR THE POSITIVE HALF of the driving waveform only. Being driven 180 degrees out of phase with the input signal, the second stage will produce a linearly amplified but (again inverted) version of the input signal FOR THE NEGATIVE HALF of the driving waveform. Both outputs will have a DC offset of the plate (collector, drain) voltage.

The resultant waveform with the outputs in parallel will look like much like a full wave rectified version of the input signal subtracted from the plate voltage. To express this mathematically, let the input signal be expressed as:

Vin = A sin(wt)

Now let the voltage gain of each stage be "-k" and the plate voltage be "B". The resultant waveform of the two stages connected in parallel will be:

Vout = B - abs[A*k sin(wt)] where "abs" is the absolute value

Vout = B - A*k sin(wt) for 0 wt Pi and
= B + A*k sin(wt) for Pi wt 2Pi or alternately for -Pi wt 0

We can then calculate the Fourier series of this waveform to determine its spectrum. I will not present the calculations here as it is too difficult to show the integration over defined integrals using only plain text (and I doubt many readers will have math fonts anyway). If you wish to see the math for the Fourier series for a number of functions, read:
http://www.maths.qmul.ac.uk/~agp/calc3/notes2.pdf or
http://www.physics.hku.hk/~phys2325/notes/chap7.doc.

Vout = B - 2*A*K/Pi * [1 - SUMMATION {2*cos(nwt)/(n*n - 1)] for n=2, 4, 6, 8...

Note that the original frequency has been eliminated and that only even order harmonics are present, and that the amplitudes drop off quite rapidly. For example, the fourth harmonic will be one fifth of the second harmonic.

For those that need a simplified explanation of Fourier series, Don Lancaster wrote a good article that can be found at:
http://www.tinaja.com/glib/muse90.pdf. I always thought Don had a ham license but I could not find one.

In a real implementation of this multiplier, a tuned circuit would be used as the plate load. The Q of this tuned circuit will assure that only the second harmonic is present in the output. The two stages would need to be well balanced if cancellation of odd harmonics and the fundamental is required.

73, Dr. Barry L. Ornitz WA4VZQ


POSTSCRIPT:

Now let me describe how it is possible to produce ONLY the second harmonic. Instead of using two Class B or AB stages, it is possible to use triodes operating where their plate current is proportional to the square of the grid voltage. Driving the two such stages in push-pull with the outputs in parallel with a resistive load, the output waveform will be:

Vout = B - A*A*k sin(wt)*sin(wt)

Using a trigonometric identity {see:
http://en.wikipedia.org/wiki/List_of_trigonometric_identities},

sin(x)*sin(x) = sin(x)^2 = 0.5[1-cos(2x)]

thus Vout = B - A*A*K/2 + A*A*k/2 cos(2wt)

This shows that only the second harmonic is found at the output.

NoSPAM wrote:
"Telstar Electronics"
wrote in message
...
On Nov 22, 8:43 pm, Stray Dog
wrote:
? Despite what at least one other person responding to this said, I
can rest
assure you that if you run a doubler/multiplier stage even in a linear
mode, AND if you tune the output of that stage to the multiple
harmonic,
you will definitely get output at that harmonic frequency which is
stronger than the input drive voltage.

Huh? No way... you MUST have non-linearities to make a doubler.

Actually you do not need any nonlinearity to make a doubler
(quadrupler, etc.).

Assume you have two Class B (or AB) stages that are driven in
push-pull. The outputs are connected in parallel. And to make things
even more linear, let each stage have a resistive load. Each stage
will produce a linearly amplified (but inverted) version of the input
signal FOR THE POSITIVE HALF of the driving waveform only. Being
driven 180 degrees out of phase with the input signal, the second
stage will produce a linearly amplified but (again inverted) version
of the input signal FOR THE NEGATIVE HALF of the driving waveform.
Both outputs will have a DC offset of the plate (collector, drain)
voltage.
Class B or even Class AB in the circuit you described are non-linear.
Try that circuit
with Class A biasing.

Bill K7NOM


The resultant waveform with the outputs in parallel will look like
much like a full wave rectified version of the input signal subtracted
from the plate voltage. To express this mathematically, let the input
signal be expressed as:

Vin = A sin(wt)

Now let the voltage gain of each stage be "-k" and the plate voltage
be "B". The resultant waveform of the two stages connected in
parallel will be:

Vout = B - abs[A*k sin(wt)] where "abs" is the absolute value

Vout = B - A*k sin(wt) for 0 wt Pi and
= B + A*k sin(wt) for Pi wt 2Pi or
alternately for -Pi wt 0

We can then calculate the Fourier series of this waveform to determine
its spectrum. I will not present the calculations here as it is too
difficult to show the integration over defined integrals using only
plain text (and I doubt many readers will have math fonts anyway). If
you wish to see the math for the Fourier series for a number of
functions, read:
http://www.maths.qmul.ac.uk/~agp/calc3/notes2.pdf
http://www.maths.qmul.ac.uk/%7Eagp/calc3/notes2.pdfhttp://www.physics.hku.hk/%7Ephys2325/notes/chap7.doc or
_http://www.physics.hku.hk/~phys2325/notes/chap7.doc
http://www.physics.hku.hk/%7Ephys2325/notes/chap7.doc._
Vout = B - 2*A*K/Pi * [1 - SUMMATION {2*cos(nwt)/(n*n - 1)] for n=2,
4, 6, 8...

Note that the original frequency has been eliminated and that only
even order harmonics are present, and that the amplitudes drop off
quite rapidly. For example, the fourth harmonic will be one fifth of
the second harmonic.

For those that need a simplified explanation of Fourier series, Don
Lancaster wrote a good article that can be found at:
http://www.tinaja.com/glib/muse90.pdf. I always thought Don had a ham
license but I could not find one.

In a real implementation of this multiplier, a tuned circuit would be
used as the plate load. The Q of this tuned circuit will assure that
only the second harmonic is present in the output. The two stages
would need to be well balanced if cancellation of odd harmonics and
the fundamental is required.

73, Dr. Barry L. Ornitz WA4VZQ


POSTSCRIPT:

Now let me describe how it is possible to produce ONLY the second
harmonic. Instead of using two Class B or AB stages, it is possible
to use triodes operating where their plate current is proportional to
the square of the grid voltage. Driving the two such stages in
push-pull with the outputs in parallel with a resistive load, the
output waveform will be:

Vout = B - A*A*k sin(wt)*sin(wt)

Using a trigonometric identity {see:
http://en.wikipedia.org/wiki/List_of_trigonometric_identities},

sin(x)*sin(x) = sin(x)^2 = 0.5[1-cos(2x)]

thus Vout = B - A*A*K/2 + A*A*k/2 cos(2wt)

This shows that only the second harmonic is found at the output.

"Bill Janssen" wrote in message
...
NoSPAM wrote:
"Telstar Electronics"
wrote in message
...
On Nov 22, 8:43 pm, Stray Dog
wrote:
? Despite what at least one other person responding to this said, I can
rest
assure you that if you run a doubler/multiplier stage even in a
linear
mode, AND if you tune the output of that stage to the multiple
harmonic,
you will definitely get output at that harmonic frequency which is
stronger than the input drive voltage.

Huh? No way... you MUST have non-linearities to make a doubler.
Actually you do not need any nonlinearity to make a doubler
(quadrupler, etc.).
Assume you have two Class B (or AB) stages that are driven in
push-pull. The outputs are connected in parallel. And to make things
even more linear, let each stage have a resistive load. Each stage will
produce a linearly amplified (but inverted) version of the input signal
FOR THE POSITIVE HALF of the driving waveform only. Being driven 180
degrees out of phase with the input signal, the second stage will
produce a linearly amplified but (again inverted) version of the input
signal FOR THE NEGATIVE HALF of the driving waveform. Both outputs will
have a DC offset of the plate (collector, drain) voltage.
Class B or even Class AB in the circuit you described are non-linear. Try
that circuit
with Class A biasing.

Bill K7NOM


All that is really required is that the active devices have a different
gain with positive input signals than with negative input signals. This is
easily achieved with Class B and Class AB stages. As long as both stages
are identical the fundamental and odd order harmonics will cancel. You are
correct that with two Class A stages where the gain is identical for either
polarity of input, the output signal will perfectly cancel. To make the
method work here, you could synchronously switch the input signal between
two perfectly linear stages. My point was that a full-wave rectified
signal contains only even order harmonics.

In the real world, as Stray Dog pointed out, ALL amplifier stages are
nonlinear to some degree. The reason that Class AB and B amplifiers are
considered linear RF amplifiers is that the tuned circuit on the output
supplies supplies the "missing half" of the waveform. Without the tuned
circuit, harmonics of the 2nd, 4th, 6th, etc. order as well as the
fundamental are present. Odd order harmonics are only found if the gain is
nonlinear for positive input signals. The tuned output stage passes the
fundamental and suppresses the harmonics.

Thanks for pointing this out, Bill.

73, Barry WA4VZQ

On Dec 14, 10:27*pm, "NoSPAM" wrote:
*Actually you do not need any nonlinearity to make a doubler
(quadrupler, etc.).

You mean to tell me that you take a clean sine wave... pass it
through... say a single-ended class A amp... and you can put a tank on
the output of that amplifier... and tune for a harmonic? You will get
nothing.

On Sun, 14 Dec 2008, NoSPAM wrote:

Date: Sun, 14 Dec 2008 23:27:11 -0500
From: NoSPAM
Newsgroups: rec.radio.amateur.homebrew
Followup-To: rec.radio.amateur.homebrew
Subject: Doubling

"Bill Janssen" wrote in message
...
NoSPAM wrote:
"Telstar Electronics"
wrote in message
...
On Nov 22, 8:43 pm, Stray Dog
wrote:
? Despite what at least one other person responding to this said, I can
rest
assure you that if you run a doubler/multiplier stage even in a
linear
mode, AND if you tune the output of that stage to the multiple
harmonic,
you will definitely get output at that harmonic frequency which is
stronger than the input drive voltage.

Huh? No way... you MUST have non-linearities to make a doubler.
Actually you do not need any nonlinearity to make a doubler (quadrupler,
etc.).
Assume you have two Class B (or AB) stages that are driven in push-pull.
The outputs are connected in parallel. And to make things even more
linear, let each stage have a resistive load. Each stage will produce a
linearly amplified (but inverted) version of the input signal FOR THE
POSITIVE HALF of the driving waveform only. Being driven 180 degrees out
of phase with the input signal, the second stage will produce a linearly
amplified but (again inverted) version of the input signal FOR THE
NEGATIVE HALF of the driving waveform. Both outputs will have a DC offset
of the plate (collector, drain) voltage.
Class B or even Class AB in the circuit you described are non-linear. Try
that circuit
with Class A biasing.

Bill K7NOM


All that is really required is that the active devices have a different gain
with positive input signals than with negative input signals. This is easily
achieved with Class B and Class AB stages. As long as both stages are
identical the fundamental and odd order harmonics will cancel. You are
correct that with two Class A stages where the gain is identical for either
polarity of input, the output signal will perfectly cancel. To make the
method work here, you could synchronously switch the input signal between two
perfectly linear stages. My point was that a full-wave rectified signal
contains only even order harmonics.

In the real world, as Stray Dog pointed out, ALL amplifier stages are
nonlinear to some degree. The reason that Class AB and B amplifiers are
considered linear RF amplifiers is that the tuned circuit on the output
supplies supplies the "missing half" of the waveform. Without the tuned
circuit, harmonics of the 2nd, 4th, 6th, etc. order as well as the
fundamental are present. Odd order harmonics are only found if the gain is
nonlinear for positive input signals. The tuned output stage passes the
fundamental and suppresses the harmonics.

Thanks for pointing this out, Bill.

73, Barry WA4VZQ


I'll just add a footnote. When I actually built a few "buffer" amplifiers
(tube jobs, 12BY7s, 6AG7s, etc), and for the hell of it, hooked up my
scope (an old Tektronix solid state scope with one microsecond/div
timebase, max) and actually looked at the sine wave (it looked 'nice' by
the way) and then tuned the air variable through both the fundamental or
the second harmonic (and I'm talking about 2-3 mHz signal source), I was
amazed to be able to easily see the extra "peaks" come out of the
"valleys" of the fundamental and I'm running these tubes at zero bias, low
plate voltage, too. Look in the tube manuals for any class C tube and they
talk about -50 to -70 v, grid negative wrt cathode. Class B and below talk
about negative bias much lower but still pretty negative.

Like I said, I was surprised. This _should_ be discussed in the ARRL
handbooks (maybe it is, but I couldn't find it [maybe I didn't look hard
enough?]) and it would be worth 1-2 pages to show everyone what these
signals have in them.

Here is another goodie (true story). R-390 local oscillator (runs 2.4 to
3.4 mHz, single 6BA6 tube). Had it set to about 3 mHz and looking at that
"nice" (I have no harmonic meter to measure distortion) sine wave on the
scope, and I "loaded down" the oscillator output lead with a tuned circuit
and tuned that circuit to about 6 mHz. Guess what? Got double the number
of peaks on the scope, just as with the linear amplifier. All calculate
out on peaks vs time base divisions. So? Does anyone want to suggest that
having the output LC circuit of an LC free-running oscillator tuned to
double the frequency of the LC circuit is making it "oscillate" on its
second overtone? ;-)

Yeah, I checked resonant frequencies with a GDO on all this stuff, too.
I'm not making any of this up.

For the record, I also have an old Knight Kit RF oscillator (100Kc to 400
mHz on 3rd harmonic) and put that into my scope and the waveform looks
like crap (but you can pick up the signal on a SW receiver set to where
the scale matches the frequency of the oscillator). And, the
shape of the crap changes from one end of the band to
the other. Also have an old HP audio oscillator (high quality stuff) and
it puts out a _very_ 'nice' sine wave no matter where in the range you set
the dial (one Hz to 200 kHz).

73 all,

"Telstar Electronics" wrote in message
...
You mean to tell me that you take a clean sine wave... pass it
through... say a single-ended class A amp... and you can put a tank on
the output of that amplifier... and tune for a harmonic? You will get
nothing.

Class A means that plate current is flowing throughout the entire cycle of
the input wave with the tube operated between cutoff and saturation. It
says nothing about the linearity of the tube's transconductance (plate
current as a function of grid voltage). With real devices, the
transconductance curve is ALWAYS nonlinear to some degree, producing
distortion (and harmonics). As you decrease the drive to a single-ended
Class A amplifier, you are working on a smaller and smaller portion portion
of the transconductance curve which decreases distortion. In the limit
where only an infinitesimal part of the transconductance curve is used, you
will get no distortion and no harmonics. Of course, in this situation the
tube produces NO output.while drawing current from the power supply.

The scheme that I was talking about, known as a push-push doubler,
generally uses the tubes operated in Class B although AB operation will
work too, but it produces less harmonics. The real advantage of a
push-push doubler is that odd order harmonics and the fundamental cancel
out, making the resultant waveform easier to filter.

73, Barry WA4VZQ

On Mon, 15 Dec 2008, Telstar Electronics wrote:

Date: Mon, 15 Dec 2008 06:16:29 -0800 (PST)
From: Telstar Electronics
Newsgroups: rec.radio.amateur.homebrew
Subject: Doubling

On Dec 14, 10:27*pm, "NoSPAM" wrote:
*Actually you do not need any nonlinearity to make a doubler
(quadrupler, etc.).

You mean to tell me that you take a clean sine wave...

You might want to consider qualifying your thinking on this by setting a
specification for harmonic distortion (in other words, you might need to
consider how much of that "clean sine wave" signal has other components
in it, including non-harmonic componentes)

pass it
through... say a single-ended class A amp...

You might also want to consider, here, too, how much harmonic distortion
THAT class A amplifier also causes which makes a contribution to the
output.

and you can put a tank on
the output of that amplifier... and tune for a harmonic? You will get
nothing.

You might even more also want to consider that any tuned circuit will pass
energy not at the resonance of that tuned circuit.

You would probably contribute to your own enlightenment if you actually
did some real experiments on this. It does not take long to do.

Back when I was an undergraduate student with major in physics (BS, 1966),
I worked in a Mossbauer Effect spectrometer lab and we built most of our
equipment (dual delay line pulse amplifiers, regulated DC power supplies,
repairing survey meters, etc) my boss had me build a waveform converter
that used a network of resistors and diodss to convert a sawtooth waveform
to sine wave and he was doing this because the book he got the circuit
from said that there would be less than 1% harmonic distortion and he was
interested in that specification for the spectrometer drives and all of
our commercial high quality signal generators were worse in that
specification, particulary at the very low frequencies we ran the drives
at (less than one cycle per second).

So, you have to define what you mean by "clean sine wave." But, I'll also
say that, no, you will not get nothing if you tune to the second harmonic
and have a linear amplifier (unless, maybe, you have a _perfect_ sine wave
and a _perfect_ linear amplifier [the rest of you guys might want to comment
on this yeah, I know about Fourier analysis, too]).