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Frequency multiplication

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Jim Thompson

Jan 1, 1970
0
What's the maximum multiplication factor it's practical and sensible
to attempt to achieve in one single stage of multiplication? (Say from
a 7Mhz square wave source with 5nS rise/fall times.)

You ought to be able to answer that yourself... what's the spectral
roll-off of a square wave ??

...Jim Thompson
 
P

Paul Burridge

Jan 1, 1970
0
What's the maximum multiplication factor it's practical and sensible
to attempt to achieve in one single stage of multiplication? (Say from
a 7Mhz square wave source with 5nS rise/fall times.)
 
W

W3JDR

Jan 1, 1970
0
I think it boils down to something very practical:

If you want good spectral purity, then you need to bandpass filter the
output of the multiplier. It becomes a matter of how close and how large the
undesired spectral components are compared to the desired spectral
components. After that, you can consult your filter design charts to
determine how complex a filter will be required and whether it's physically
realizable.

As an example, a x4 multiplier stage will have a desired output at Fin x 4,
and close-in undesired products at Fin x 3 and Fin x 5. This means the
output bandpass filter has to be able to attenuate signals at +/-25% of the
center frequency sufficiently to meet the desired spectral purity. In
practice with simple single-ended multiplier designs, a x4 multiplier is
approaching the threshold of realizability for high purity applications
(40-60 dB purity). It is possible to make push-pull and push-push
multipliers that have better output purity, but these techniques are seldom
used.

Joe
W3JDR
 
J

Jim Thompson

Jan 1, 1970
0
I think it boils down to something very practical:

If you want good spectral purity, then you need to bandpass filter the
output of the multiplier. It becomes a matter of how close and how large the
undesired spectral components are compared to the desired spectral
components. After that, you can consult your filter design charts to
determine how complex a filter will be required and whether it's physically
realizable.

As an example, a x4 multiplier stage will have a desired output at Fin x 4,
and close-in undesired products at Fin x 3 and Fin x 5. This means the
output bandpass filter has to be able to attenuate signals at +/-25% of the
center frequency sufficiently to meet the desired spectral purity. In
practice with simple single-ended multiplier designs, a x4 multiplier is
approaching the threshold of realizability for high purity applications
(40-60 dB purity). It is possible to make push-pull and push-push
multipliers that have better output purity, but these techniques are seldom
used.

Joe
W3JDR
[snip]

I would think a "W3JDR" would know that even harmonics are *much*
harder to obtain in nonlinear multipliers.

...Jim Thompson
 
P

Paul Keinanen

Jan 1, 1970
0
What's the maximum multiplication factor it's practical and sensible
to attempt to achieve in one single stage of multiplication? (Say from
a 7Mhz square wave source with 5nS rise/fall times.)

While you might be able to generate odd harmonics of a 1 kHz square
wave up to several hundred megahertz, there are two practical
problems.

First you would need some method to separate the wanted harmonic from
the unwanted.

For low multiplication factors in HF/VHF a series of bandpass LC
filters would be needed to attenuate the unwanted harmonics. For
higher frequencies some helical or cavity resonators may be needed.

One old method to separate nearby harmonics is to use a wave analyser.
The wanted harmonics is mixed down with a VFO to some fixed
intermediate frequency in which a fixed crystal filter is inserted
(bandwidth 0,5-50 kHz depending on application). The filtered and
amplified signal is then mixed back to the original frequency by the
same VFO. The absolute stability of the VFO does not matter very much,
since any drift is cancelled in the up-conversion. However, the
stability must be sufficient to keep the desired harmonics within the
IF filter bandwidth. This kind of tricks was once used to multiply
some high precision frequency standard to some odd (say 61th
harmonic).

The other problem with high multiplication factors is that the
amplitude of the higher harmonics is quite low, thus needing quite a
lot of amplification after filtering. However, the level of the
original harmonics was low compared also to the wide band thermal
(white) noise, thus, after amplification, the wide band thermal noise
level is also high, reducing the final signal to noise ratio and in
reception, cause reciprocal mixing programs.

Thus, it is better to use several multiplier stages with low
multiplication factors, since it easier to filter out the desired
harmonics after each multiplier. The gain distribution is also better,
thus the noise floor does not become uncomfortably close to the wanted
signal.

However, if some strange multiplication factor (such as the 17th) is
needed (in which case a series of multipliers can not be used), these
days it would be easier to use a PLL with a fixed digital divider.
Keep the VCO tuning range as small as possible, thus reducing the
MHz/V sensitivity and noise through the tuning line and use a large
loop bandwidth to clean the areas around the generated signal.

Paul OH3LWR
 
P

Paul Burridge

Jan 1, 1970
0
You ought to be able to answer that yourself... what's the spectral
roll-off of a square wave ??

I suppose it boils down to how much signal is left in the mush as the
harmonics get higher and higher. Knew I shoulda held on to that
spectrum analyser I used to have. :-(
I suppose that's the proper answer though: get the rise/fall times as
small and possible, measure the specral output and pick a suitable
harmonic with enough energy in it to set it 'comfortably' above the
noise floor?
 
U

Uncle Peter

Jan 1, 1970
0
Jim Thompson said:
I would think a "W3JDR" would know that even harmonics are *much*
harder to obtain in nonlinear multipliers.

...Jim Thompson


One would think a "PE" could give the man a civil answer.

Pete
 
W

W3JDR

Jan 1, 1970
0
I would think a "W3JDR" would know that even harmonics are *much*
I guessed I missed Jim's comment in the earlier post, or I would have replied earlier.
Jim, I'm not not sure what you're trying to say, but there seems to be a sarcastic undertone to the way you said it.

Anyway, it turns out that non-linear single-ended elements are great generators of even-order harmonics. That's why the classical HF/VHF multiplier circuit is typically a single ended transistor amplifier with output and input tuned to different frequencies. If you bias the device so it is non-linear, then it becomes a natural harmonic generator. You can enhance even-order generation and supress the odd-order generation by using a non-linear 'push-push' stage, just as you can suppress even order harmonics with a 'push-pull' stage.

In either case, the important thing to remember is that symmetrical clipping or limiting generates mostly odd-order distortion and unsymmetrical clipping or limiting generates mostly even order distortion. The quantification of this is left to those more mathematically inclined.

Joe
W3JDR
 
J

Jim Thompson

Jan 1, 1970
0
I guessed I missed Jim's comment in the earlier post, or I would have replied earlier.
Jim, I'm not not sure what you're trying to say, but there seems to be a sarcastic undertone to the way you said it.

Only mildly so, just "funning" you ;-)
Anyway, it turns out that non-linear single-ended elements are great generators of even-order harmonics. That's why the classical HF/VHF multiplier circuit is typically a single ended transistor amplifier with output and input tuned to different frequencies. If you bias the device so it is non-linear, then it becomes a natural harmonic generator. You can enhance even-order generation and supress the odd-order generation by using a non-linear 'push-push' stage, just as you can suppress even order harmonics with a 'push-pull' stage.

In either case, the important thing to remember is that symmetrical clipping or limiting generates mostly odd-order distortion and unsymmetrical clipping or limiting generates mostly even order distortion. The quantification of this is left to those more mathematically inclined.

Joe
W3JDR

It depends on what your are starting from. If it's a sine wave, yes
even harmonics can be made from diode non-linearities.

The OP has a inverter-style XTAL oscillator, output very nearly
square.

A square wave is rich in odd harmonics, a perfect square wave has NO
even harmonics.

...Jim Thompson
 
W

W3JDR

Jan 1, 1970
0
It depends on what your are starting from. If it's a sine wave, yes
even harmonics can be made from diode non-linearities.

The OP has a inverter-style XTAL oscillator, output very nearly
square.

A square wave is rich in odd harmonics, a perfect square wave has NO
even harmonics.


Oh! I see what you're talking about...
I presumed that he was starting with a single spectral component (sine wave) and wanted to end up with another single spectral component.


Joe
W3JDR
 
S

Steve Nosko

Jan 1, 1970
0
Not really, Jim...unless you mean something special by "nonlinear
multipliers" like diodes/varactors which I suspect fall under your comment.
In the two-way radios of the 60's & early 80's before synthesizers, I
designed many a single stage multiplier of 2x or 3x, which were preferred
and sometimes 4x. They worked very well...using cap input coupling, to keep
the base Z low at the harmonics and keeping the conduction angle optimized
for output level. Also, the adjacent harmonics are easier to filter than
higher orders of multiplication (when that is a factor. Only a single
resonant circuit was required between stages.
The bottom line depends upon the spurious requirements. Then there are
always preferences for what we may have used in the past - and what the
application actually is.
Starting with a spectral comb(like a square wave or other pulse-type
waveform) and picking off the desired harmonic can also be very effective,
but again, it depends upon the specific application.
I did a synthesizer mixer with no tuned circuits to get from 40 MHz
crystal oscillator to 220MHz to mix down a VCO to an IF for the programmable
divider. Was really sweet! Did the same for what I believe was the very
first synthesized 2M hand held in 1973. A Motorola HT220. Even had the
Transmit VCO _ON_ yes _ON_ the TX frequency. Total current drain was 7ma.
Tx spurious (-70dBc) better than the original (-35-40dB) Still have it.

--
Steve N, K,9;d, c. i My email has no u's.

Jim Thompson said:
I think it boils down to something very practical:
...It becomes a matter of how close and how large the
undesired spectral components are compared to the desired spectral
components. ...
As an example, a x4 multiplier stage will have a desired output at Fin x 4,
and close-in undesired products at Fin x 3 and Fin x 5. ...
Joe, W3JDR
[snip]

I would think a "W3JDR" would know that even harmonics are *much*
harder to obtain in nonlinear multipliers.

...Jim Thompson
 
J

John Fields

Jan 1, 1970
0
It depends on what your are starting from. If it's a sine wave, yes
even harmonics can be made from diode non-linearities.

The OP has a inverter-style XTAL oscillator, output very nearly
square.

A square wave is rich in odd harmonics, a perfect square wave has NO
even harmonics.

---
Starting with a perfect square wave at f1, bang the hell out of a diode
with it, and then bandpass it and the 3rd harmonic (f2) separately, then
mix them to get f1, f2, f1+f2, and f1-f2. Using a doubly balanced mixer
will get rid of f1 and f2, then notching out f1+f2 will leave f1-f2,
which will be 2f1, that non-existent second harmonic.
 
S

Steve Nosko

Jan 1, 1970
0
See my previous post. What is your application? That would help get better
advise.
 
W

W3JDR

Jan 1, 1970
0
"> Starting with a perfect square wave at f1, bang the hell out of a diode
with it, and then bandpass it and the 3rd harmonic (f2) separately, then
mix them to get f1, f2, f1+f2, and f1-f2. Using a doubly balanced mixer
will get rid of f1 and f2, then notching out f1+f2 will leave f1-f2,
which will be 2f1, that non-existent second harmonic."
Oh yuchh...that sounds painful!
Why not just distort the symmetry of the square digitally (like drive it into an exclusive-or with a small delay on one input) to make a short impulse, then bandpass filter the output? Or staying in the purely digital domain, use same said exclusive-or and delay one of the two inputs by t/4 (t=period of input sq wave) and get a 2*F square wave out.

Joe
W3JDR
 
J

James Meyer

Jan 1, 1970
0
Starting with a perfect square wave at f1, bang the hell out of a diode
with it, and then bandpass it and the 3rd harmonic (f2) separately, then
mix them to get f1, f2, f1+f2, and f1-f2. Using a doubly balanced mixer
will get rid of f1 and f2, then notching out f1+f2 will leave f1-f2,
which will be 2f1, that non-existent second harmonic.

What purpose does the diode serve? You're already starting with a
"perfect" square wave.

OTOH, if you have had some bad experiences with diodes in the past, I
can easily understand your tendency to abuse them as often as you can.

Jim
 
J

John Woodgate

Jan 1, 1970
0
I read in sci.electronics.design that John Fields <jfields@austininstrum
Starting with a perfect square wave at f1, bang the hell out of a diode
with it, and then bandpass it and the 3rd harmonic (f2) separately, then
mix them to get f1, f2, f1+f2, and f1-f2. Using a doubly balanced mixer
will get rid of f1 and f2, then notching out f1+f2 will leave f1-f2,
which will be 2f1, that non-existent second harmonic.

No need to abuse any diodes. The third harmonic is already there, just
10 dB down. You only need a bit of gain after the peaky filter.
 
S

Stephen Quigg

Jan 1, 1970
0
What's the maximum multiplication factor it's practical and sensible
to attempt to achieve in one single stage of multiplication? (Say from
a 7Mhz square wave source with 5nS rise/fall times.)

Not radio, but interesting nevertheless. The older Hewlett-Packard cesium
clocks, ie 5060/61/62 vintage multiplied a crystal oscillator up to 90 MHz in
several stages. This fed into a step-recovery diode that sits in a cavity, and
has 12.631... MHz applied to the SRD bias. The cavity selects the ***102nd***
harmonic ie 9180 MHz, and there are also sidebands at +/- 12.631.. MHz This is
then fed into a hi-Q cavity tuned to the upper sideband ie 9192.631... MHz
which is the desired cesium transition frequency.

Adjusting the whole thing was a bit fiddly, and there were also some
factory-set adjustments that you NEVER TOUCHED unless you had plenty of time
and a squillion dollars worth of test gear. This was all a 1960's design and
was a bit of a stretch. The newer (5071) clocks do things QUITE differently.

Steve Quigg
 
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