Doubling
 

This is a really dumb question but it dawned on me that I did not know
the correct answer.

In terms of old transmitters from the 20s/30s...In a crystal oscillator
I understand the concept of setting the oscillator output tank to
favor the harmonic from the crystal. (Stop me if I'm wrong already...)

But in a doubling amplifier stage am I counting on having enough
harmonic content at the input or am I creating the harmonic with the
non-linearity of the amplifier?

TIA
-Bill WX4A

Doubling
 

"exray" wrote in message
...
In terms of old transmitters from the 20s/30s...In a crystal oscillator I
understand the concept of setting the oscillator output tank to favor the
harmonic from the crystal. (Stop me if I'm wrong already...)

But in a doubling amplifier stage am I counting on having enough harmonic
content at the input or am I creating the harmonic with the non-linearity
of the amplifier?

TIA
-Bill WX4A

Hi Bill.

Remember that single ended frequency multiplier stages are usually operated
in Class-C where the nonlinear operation of the stage produces the
harmonics. In a Class-C stage, the grid (of the tube since we are talking
about vintage transmitters) is biased such that the plate current only flows
in short pulses. The narrower the pulse width, the greater the harmonic
generation of the stage. If you look in the old RCA Transmitting Tube
Manual, there is a design procedure where the "conduction angle" of the tube
is chosen for proper harmonic generation.

Frequency doubling is unique in that two Class-B stages may be used in a
push-push arrangement. Here the grids are driven in push-pull while the
plates are connected together in parallel. The resulting waveform will
essentially be the equivalent of full-wave rectification of the input
signal. Without going into Fourier series, the resultant waveform only
contains even harmonics of the input signal while the fundamental driving
frequency is cancelled out.

Fortunately I was already a ham operator when my high school math class
taught Fourier series *. I immediately saw the practical value of this
mathematical concept and it made good sense to me. Your question is a good
one and reading some of the tutorials on Fourier series (do a Google search)
will be very useful to your understanding of harmonic generation and
intermodulation distortion. I hope that my simple explanation will start
you in your own exploration.

73, Barry L. Ornitz WA4VZQ

* More years ago that I care to admit! :-)

Doubling
 

NoSPAM wrote:


Remember that single ended frequency multiplier stages are usually operated
in Class-C where the nonlinear operation of the stage produces the
harmonics. In a Class-C stage, the grid (of the tube since we are talking
about vintage transmitters) is biased such that the plate current only flows
in short pulses.

Thanks Barry, I get it. I was becoming distracted by some of the old
1930s articles touting the tritet osc for its ability to create more
harmonic output (true) for directly driving following stages.

I suppose thats just another way of reaching the same goal.

(btw, haven't heard from you in years - I recall your great input over
on r.a.r. +p. No, it hasn't changed )

-Bill

Doubling
 

On Fri, 21 Nov 2008 22:30:24 -0400, exray
wrote:

This is a really dumb question but it dawned on me that I did not know
the correct answer.

In terms of old transmitters from the 20s/30s...In a crystal oscillator
I understand the concept of setting the oscillator output tank to
favor the harmonic from the crystal. (Stop me if I'm wrong already...)

In an overtone oscillator, the resonator actually forces the crystal
to mechanically resonate at 1/3, 1/5, 1/7, 1/9 etc. of the crystal
width. Due to the end effects, the frequency is *not* _exactly_ 3, 5,
7, 9 etc. times the fundamental frequency, but quite close. In
principle, the oscillator is producing a single frequency, the
(harmonic) mechanical resonance frequency of the crystal.

But in a doubling amplifier stage am I counting on having enough
harmonic content at the input or am I creating the harmonic with the
non-linearity of the amplifier?

The non-linearity of the stage will produce the harmonics, which are
_exact_ integer multipliers of the input frequency. Symmetrically
clipping stages generate strong odd harmonics, while asymmetric
stages create strong even harmonics. The following stages need to
filter out the desired harmonics.

So if you need exactly 30.000... MHz, you either have to use a
10.000... MHz fundamental crystal oscillator followed by a tripler
(and filtering stage) or order an _overtone_ crystal for exactly
30.000... MHz.

Running a nominally 10.000... MHz fundamental mode crystal in an
overtone oscillator tuned at 30 MHz will not produce exactly 30.000...
MHz but something quite closely, due to the end effect.

Paul OH3LWR

Doubling
 

On Fri, 21 Nov 2008, exray wrote:

Date: Fri, 21 Nov 2008 22:30:24 -0400
From: exray
Newsgroups: rec.radio.amateur.homebrew
Subject: Doubling

This is a really dumb question but it dawned on me that I did not know the
correct answer.

In terms of old transmitters from the 20s/30s...In a crystal oscillator I
understand the concept of setting the oscillator output tank to favor the
harmonic from the crystal. (Stop me if I'm wrong already...)

I think this is correct, but the books say that tuning the output of the
oscillator can "pull" the frequency of the oscillating crystal. I have
sometimes seen this.

But in a doubling amplifier stage am I counting on having enough harmonic
content at the input or am I creating the harmonic with the non-linearity of
the amplifier?

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. In the last few years I have built
many tube stages and observed the harmonic voltage output on a wideband
oscilloscope. As a matter of fact if you ever get a wideband scope and
look at the locked output waveform as you tune through the both the
fundamental and the harmonic frequency you will be very surprised at what
you will see. All of the descriptions in all of the handbooks I have read
(a few) explain this from a theoretical perspective but don't bother to
actually show, with photographs of actual scope traces, how this works.
It would just take an extra page or two and would make people think about
what they are doing.

All amplifiers have some non-linearity, the question is what effect this
has on you meeting "purity" of emissions requirements. The more important
question is whether you are getting the gain/drive that you want from a
given stage of amplification. Reducing unwanted spurious emissions might
require more tuned circuits or measurement using a receive with an S-meter
and operated many wavelengths from your antenna. Most "appliance
operators" just buy a commercial rig and don't worry about anything;
homebrewers might not worry either if their signals go through a tuned
circuit, an antenna tuner, and an antenna for a narrow frequency range.

If you really want to blow your mind, then hook an oscilloscope to the
output of a mixer with two low harmonic content input sine waves to be
mixed. The raw output will look like hell on a scope. The only way to see
the mixed (say, difference) frequency will be to go through at least a
couple of tuned circuits that are tuned for the wanted sine wave
frequency.

I've done this stuff. There are a couple of other minor matters that are
not quite correct in our ham handbooks, too.


TIA
-Bill WX4A

Doubling
 

On Nov 21, 8:24*pm, "NoSPAM" wrote:
"exray" wrote in message

...

*In terms of old transmitters from the 20s/30s...In a crystal oscillator I
understand the concept of setting the oscillator output tank to favor the
harmonic from the crystal. *(Stop me if I'm wrong already...)

*But in a doubling amplifier stage am I counting on having enough harmonic
content at the input or am I creating the harmonic with the non-linearity
of the amplifier?

*TIA
*-Bill *WX4A

Hi Bill.

Remember that single ended frequency multiplier stages are usually operated
in Class-C where the nonlinear operation of the stage produces the
harmonics. *In a Class-C stage, the grid (of the tube since we are talking
about vintage transmitters) is biased such that the plate current only flows
in short pulses. *The narrower the pulse width, the greater the harmonic
generation of the stage. *If you look in the old RCA Transmitting Tube
Manual, there is a design procedure where the "conduction angle" of the tube
is chosen for proper harmonic generation.

Frequency doubling is unique in that two Class-B stages may be used in a
push-push arrangement. *Here the grids are driven in push-pull while the
plates are connected together in parallel. *The resulting waveform will
essentially be the equivalent of full-wave rectification of the input
signal. *Without going into Fourier series, the resultant waveform only
contains even harmonics of the input signal while the fundamental driving
frequency is cancelled out.

Fortunately I was already a ham operator when my high school math class
taught Fourier series *. *I immediately saw the practical value of this
mathematical concept and it made good sense to me. *Your question is a good
one and reading some of the tutorials on Fourier series (do a Google search)
will be very useful to your understanding of harmonic generation and
intermodulation distortion. *I hope that my simple explanation will start
you in your own exploration.

* * 73, *Barry L. Ornitz * WA4VZQ

* More years ago that I care to admit! *:-)

Wow, there's a name I haven't seen for a while. I must be frequenting
the wrong groups. I was just thinking about you a couple days ago.
Hi Barry!

More about what Barry wrote: in the limit as the conduction angle
goes to zero and you generate a very narrow pulse of current, the
harmonics end up all the same amplitude. That's for an impulse of
zero width. Unfortunately, given limited amplitude of the current in
that very narrow pulse, the total energy becomes small. As you widen
the pulse, you'll see that the "comb" of harmonics no longer has
constant amplitude, but the amplitudes as you go up the "comb" (higher
in frequency)drop, and there will be a frequency at which they go to
zero, and then increase again (and go to zero again, and increase
again). The magnitudes follow a sin(x)/x shape, for perfectly
rectangular pulses. This becomes interesting for a the design of
frequency multiplier stages: if for example you want to get x4 out of
a stage you better NOT run it at a conduction angle that results in
nulling of the fourth harmonic! I think I was bit by this a time or
two in my youth when I didn't understand this. (I'm working on
something right now where I want that comb of harmonics to be all very
nearly equal amplitude up to about 100MHz, and that tells me how
narrow the pulse must be.)

Cheers,
Tom

Doubling
 

On Nov 21, 9:30*pm, exray wrote:
This is a really dumb question but it dawned on me that I did not know
the correct answer.

In terms of old transmitters from the 20s/30s...In a crystal oscillator
* I understand the concept of setting the oscillator output tank to
favor the harmonic from the crystal. *(Stop me if I'm wrong already...)

You're right on the trail. Most oscillator circuits are operating deep
in class C. The exceptions are called "marginal, doesn't always start"
oscillators :-).

Some oscillators make the crystal operate on an overtone. An overtone
is often very very close to a harmonic. In this case the LC tank
chooses the overtone where gain is going to be greater than one.
Overtones close to odd harmonics are usually much more active in the
crystal.

Other oscillators make the crystal operate on the fundamental, and the
output picks off the harmonic. This is where the electron coupled
oscillator shines.

It's possible to have the crystal operate on the overtone, and then
electron-couple to pick a harmonic of the overtone. You see this in
some 40's/50's/60's era VHF projects.

But in a doubling amplifier stage am I counting on having enough
harmonic content at the input or am I creating the harmonic with the
non-linearity of the amplifier?

Mostly creating. It doesn't hurt if there's some harmonic content at
the input. Again, for efficiency most of the power stages will be in
class C already, and if they need to multiply in a non-power stage
they'll set it up to make a lot of harmonics.

Individual stages are sometimes configured in push-pull to favor odd
harmonics over even ones, or are biased to be favorable for the
desired harmonic.

Tim.

Doubling
 

On Fri, 21 Nov 2008 22:30:24 -0400, exray wrote:

This is a really dumb question but it dawned on me that I did not know
the correct answer.

In terms of old transmitters from the 20s/30s...In a crystal oscillator
I understand the concept of setting the oscillator output tank to
favor the harmonic from the crystal. (Stop me if I'm wrong already...)

You're wrong already, kinda.

Most of the schematics that I've seen from back then have the crystal
oscillating at it's fundamental. If the energy extracted from the
oscillator is at twice the crystal frequency it's because of harmonics
generated in the tube.

I don't have a lot of reference material to look at, but I don't think
that using a crystal's overtones to generate RF really picked up until
the 50's (it was probably done during WW-II, but I only see it put forth
as a common method starting with my '50's ARRL handbooks).

But in a doubling amplifier stage am I counting on having enough
harmonic content at the input or am I creating the harmonic with the
non-linearity of the amplifier?

You're creating the harmonic with the nonlinearity of the amplifier. A
class C stage (which is pretty much assumed for CW transmitters) is very
rich in harmonics, and the harder you drive it the higher the harmonics
go. So it's pretty easy to get one to generate considerable energy at a
harmonic frequency, which you then pick out with your tank circuit.

--
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html

Doubling
 

Tim Wescott wrote:
On Fri, 21 Nov 2008 22:30:24 -0400, exray wrote:

This is a really dumb question but it dawned on me that I did not know
the correct answer.

In terms of old transmitters from the 20s/30s...In a crystal oscillator
I understand the concept of setting the oscillator output tank to
favor the harmonic from the crystal. (Stop me if I'm wrong already...)

You're wrong already, kinda.

Most of the schematics that I've seen from back then have the crystal
oscillating at it's fundamental. If the energy extracted from the
oscillator is at twice the crystal frequency it's because of harmonics
generated in the tube.

Ok, I'll buy that. One description I read of the tritet osc described
it as being an oscillator with inherent class c amplification, hence the
plate circuit being tuned to the desired 'harmonic' and the crystal is
indeed operating at its fundamental freq.

-Bill

Doubling
 

On Nov 27, 1:30*am, Tim Wescott wrote:
I don't have a lot of reference material to look at, but I don't think
that using a crystal's overtones to generate RF really picked up until
the 50's (it was probably done during WW-II, but I only see it put forth
as a common method starting with my '50's ARRL handbooks).

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.

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.

Tim.

Doubling
 

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

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.

Doubling
 

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.

Doubling
 

"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.

Doubling
 

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.

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

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... 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.

Doubling
 

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,

Doubling
 

"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

Doubling
 

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]).

Doubling
 

"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.

Of course you will. No active device is perfect.

I decided to illustrate the fact that a single ended triode operated in
Class A can produce harmonics. For a tube, I used a 6C4 (1/2 of a 12AU7)
operated with 300 volts on the plate, a grid bias voltage of -7 volts,
driven with a pure sine wave of 14 volts peak-to-peak. The high driving
voltage was chosen to illustrate my earlier points, but the stage _IS_
operated Class A with the plate current between cutoff and saturation.

Since the "rec"groups are not supposed to have binaries in them, I placed
the graphics as PDF attachments to a post entitled "Harmonics generated by
a Class A stage" in the "alt.binaries.ham-radio" newsgroup. If anyone
wishes to see these curves and their newsgroup provider does not provide
this group, I apologize. I believe Google Groups may not provide binaries,
so I suggest getting a real newsreader and a good newsfeed.

The first graph is entitled "Transconductance.pdf" and it shows the plate
current as a function of the grid voltage. This data was obtained directly
from the General Electric datasheet, ET-T1604 dated March, 1960. Since
Excel stinks when plotting and doing calculations with data that is not
best expressed in a bar chart, I used an evaluation copy of PSIPlot from
Poly Software International (http://www.polysoftware,com) to generate the
plots. {Real scientists and engineers never use a bar chart except when
making presentations to brain challenged management!} :-)

The driving waveform and the resultant plate current waveform are shown in
the graph entitled "Waveforms.pdf". The obvious flattening is due to
cutoff being approached at the crest of the driving waveform. After all,
the transconductance curve is not perfectly a straight line.

Finally, the spectrum of current waveform is plotted in the graph called
"Spectrum.pdf". The spectrum has been normalized with respect to the DC
output. The scale of the X-axis is slightly off but it was not worth my
time correcting it. The fundamental is about 60 to 70 percent of the DC
output, and the second harmonic is about 40 percent of the DC output. All
higher harmonic are less than one percent of the DC output except the
fifth. Higher harmonics are still greater than one tenth of a percent of
the DC up to the _13th_ harmonic. Harmonics beyond the 14th are still
readily measured.

In conclusion, even single ended Class A amplifiers generate harmonics.
If a lower driving voltage were used, the amplitudes of the harmonics would
be reduced, but the fundamental would also be reduced. Please follow-up to
the "rec.radio.amateur.homebrew" newsgroup. Golden-eared audiophools will
be ignored.

73, Dr. Barry L. Ornitz WA4VZQ

Doubling
 

On Mon, 15 Dec 2008 23:29:35 -0500, "NoSPAM"
wrote:

"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.

Of course you will. No active device is perfect.

I decided to illustrate the fact that a single ended triode operated in
Class A can produce harmonics. For a tube, I used a 6C4 (1/2 of a 12AU7)
operated with 300 volts on the plate, a grid bias voltage of -7 volts,
driven with a pure sine wave of 14 volts peak-to-peak. The high driving
voltage was chosen to illustrate my earlier points, but the stage _IS_
operated Class A with the plate current between cutoff and saturation.

Did you bypass the cathode resistor or not ?

All active elements are more or less nonlinear, so if you need more or
less linear amplification, you need to use feedback/feedforward.

A non-bypassed cathode/emitter resistor will greatly improve the
linearity of a single stage.

Paul OH3LWR

Doubling
 

On Dec 14, 8:22*pm, "NoSPAM" wrote:
Actually you do not need any nonlinearity to make a doubler (quadrupler, etc.).

Nonsense... please read the definition section at
http://minicircuits.com/pages/pdfs/doub9-2.pdf

Doubling
 

On Tue, 16 Dec 2008, Paul Keinanen wrote:

Date: Tue, 16 Dec 2008 09:47:22 +0200
From: Paul Keinanen
Newsgroups: rec.radio.amateur.homebrew
Subject: Doubling

On Mon, 15 Dec 2008 23:29:35 -0500, "NoSPAM"
wrote:

"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.

Of course you will. No active device is perfect.

I decided to illustrate the fact that a single ended triode operated in
Class A can produce harmonics. For a tube, I used a 6C4 (1/2 of a 12AU7)
operated with 300 volts on the plate, a grid bias voltage of -7 volts,
driven with a pure sine wave of 14 volts peak-to-peak. The high driving
voltage was chosen to illustrate my earlier points, but the stage _IS_
operated Class A with the plate current between cutoff and saturation.

Did you bypass the cathode resistor or not ?

I did the same experiment that he did (6C4) only ran the cathod at
chassis, and grid through an RF choke, and 100 vDC on plate, and drove at
about 1/2-1 volt and that is zero bias, no need for cathode cap bypass, and
I got gain and second harmonic.

All active elements are more or less nonlinear, so if you need more or
less linear amplification, you need to use feedback/feedforward.

A non-bypassed cathode/emitter resistor will greatly improve the
linearity of a single stage.

I'm still waiting for any "expert" comments from anyone who would care to
speculate on the contributions, from oscillator harmonic content vs
contribution from harmonic distortion in the amplifier.

Paul OH3LWR

Doubling
 

"Telstar Electronics" wrote in message
...
Nonsense... please read the definition section at
http://minicircuits.com/pages/pdfs/doub9-2.pdf

You are grasping at straws trying to defend your beliefs. Their definition
only applies to their products. You should have read the entire article.
If you consider the single discontinuity of an ideal diode at the origin as
nonlinear, then you are correct. In practice, two Class AB or B
amplifiers, operated over their most linear region (each individually
producing harmonics and intermodulation over 40 dB down from the
fundamental), can be used in a push-push configuration to produce even
order harmonics. I believe "Stray Dog" and I both have shown that single
ended Class A amplifiers DO produce harmonics.

The Mini Circuits "doubler" is, I believe, essentially a full wave
rectifier using Schottky diodes. If the diodes were ideal, i.e. had no
highly non-linear region at low voltages, there would be no fundamental
output or odd order harmonics. From my earlier discussion of full wave
rectification, perfect diodes would produce the fourth harmonic 14 dB lower
than the second harmonic, and the sixth harmonic slightly over 7 dB down
from the fourth. The Minicircuits device produces at its output the
fundamental and odd order harmonics in addition to the desired even order
harmonics. It also requires a drive level of between 0 and 20 dBm. Too
low a drive and the doubling action disappears; too high a drive and the
amplitude of the higher harmonics increases (until the device burns out).

Some further research into the push-push doubler reveals that two sharp
cutoff pentodes would do a better job than triodes for this application.
Also junction field effect transistors follow square law characteristics
over a fairly wide range making them ideal in frequency doubler operation
too. It is also possible to nearly achieve ideal diode behavior with the
use of very high gain amplifiers with feedback through the diode. See the
following Intersil ap-note for details:
http://www.intersil.com/data/an/an1114.pdf.

My post of the graphs has not appeared on the "alt.binaries.ham-radio"
Usenet newsgroup, even on my nntp server which still insists that the
newsgroup exists. I'll try again using "alt.binaries.radio.misc" this
time. My thanks go to "Stray Dog" for his efforts in also experimenting
with a single ended 6C4 triode.

73, Dr. Barry L. Ornitz WA4VZQ

Doubling
 

See minor point at end....

On Tue, 16 Dec 2008, NoSPAM wrote:

Date: Tue, 16 Dec 2008 19:33:53 -0500
From: NoSPAM
Newsgroups: rec.radio.amateur.homebrew
Followup-To: rec.radio.amateur.homebrew
Subject: Doubling

"Telstar Electronics" wrote in message
...
Nonsense... please read the definition section at
http://minicircuits.com/pages/pdfs/doub9-2.pdf

You are grasping at straws trying to defend your beliefs. Their definition
only applies to their products. You should have read the entire article. If
you consider the single discontinuity of an ideal diode at the origin as
nonlinear, then you are correct. In practice, two Class AB or B amplifiers,
operated over their most linear region (each individually producing harmonics
and intermodulation over 40 dB down from the fundamental), can be used in a
push-push configuration to produce even order harmonics. I believe "Stray
Dog" and I both have shown that single ended Class A amplifiers DO produce
harmonics.

The Mini Circuits "doubler" is, I believe, essentially a full wave rectifier
using Schottky diodes. If the diodes were ideal, i.e. had no highly
non-linear region at low voltages, there would be no fundamental output or
odd order harmonics. From my earlier discussion of full wave rectification,
perfect diodes would produce the fourth harmonic 14 dB lower than the second
harmonic, and the sixth harmonic slightly over 7 dB down from the fourth.
The Minicircuits device produces at its output the fundamental and odd order
harmonics in addition to the desired even order harmonics. It also requires
a drive level of between 0 and 20 dBm. Too low a drive and the doubling
action disappears; too high a drive and the amplitude of the higher harmonics
increases (until the device burns out).

Some further research into the push-push doubler reveals that two sharp
cutoff pentodes would do a better job than triodes for this application. Also
junction field effect transistors follow square law characteristics over a
fairly wide range making them ideal in frequency doubler operation too. It
is also possible to nearly achieve ideal diode behavior with the use of very
high gain amplifiers with feedback through the diode. See the following
Intersil ap-note for details: http://www.intersil.com/data/an/an1114.pdf.

My post of the graphs has not appeared on the "alt.binaries.ham-radio" Usenet
newsgroup, even on my nntp server which still insists that the newsgroup
exists. I'll try again using "alt.binaries.radio.misc" this time.

I learned many years ago that even non-binary newsgroups _can_ carry
attached files (in any format), but then later learned that ISPs can
configure their newsservers in ways that can prevent you from making a
post with an attached file. I discovered that when a post I tried to make
with a new ISP gave me an error message. It is possible that you have an
ISP that somehow prevents either/or the body and/or the attached file from
being posted either dependently or independently from each other. And,
tech support people don't understand this, and sometimes even the geeky
whips who are sysops don't understand it, either.

You might actually do better if you can set up a "personal" web page and
just load the jpeg or gif files with associated URLs.

My thanks
go to "Stray Dog" for his efforts in also experimenting with a single ended
6C4 triode.

Thank you for taking the time to read about my "discovery" and making an
acknowledgement. But, most of the tube transmitter schematics I ever
looked at for driver/buffer/multiplier stages sure looked like they
were running linear bias voltages on the control grids instead of
class C biases. And, it was quite an experience to see, on a quality
oscilloscope, that second harmonic come out of nothing as the air variable
capacitor was adjusted for the second harmonic frequency. And, the S-meter
on the receiver, tuned to the second harmonic frequency, also bumped up a
few S units, too, at the same time.


73, Dr. Barry L. Ornitz WA4VZQ

Doubling
 

On Dec 15, 11:29*pm, "NoSPAM" wrote:
"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.

Of course you will. *No active device is perfect.

Hey OM
The nature of the beast is:
single ended amps produce rich even harmonics
Push Pull amps produce rich odd harmonics

so you can gits odd harmonics from single ended but they are poor like
me.

73 OM
n8zu