On Fri, 12 Mar 2004 17:57:24 +0000, Paul Burridge
wrote:


Great. So without a spectrum analyser there's no way to tell? If I
examine the output of the multiplier, it's very messy. There's a
dominant 3rd harmonic alright (my frequency counter resolves it
without difficulty) but the scope trace reveals a number of 'ghost
traces' of different frequencies and amplitudes co-incident with the
dominant trace. All rather confusing. I suppose the only answer is to
build Reg's band pass filter and stick it between the inverter output
and the multiplier input? shrug

---
You may want to try something like this:


COUNTER SCOPE COUNTER
| | |
| | |
FIN--[50R]-+-[1N4148]---+----+-------+---FOUT
| |
[L] [C]
| |
GND----------------------+----+

The 50 ohm resistor is the internal impedance of a function generator,
and when I set it to output a square wave at 1.5VPP, I got 10.8kHz for
the fundamental of the tank. Then I tuned the function generator down
until I got a peak out of the tank, and here's what I found:

Fin Fout Vout fout/fin
kHz kHz VPP
-----|-----|------|---------
10.8 10.8 0.9 1.0
3.58 10.8 0.25 3.02 ~ 3
2.14 10.8 0.2 5.05 ~ 5

So with a square wave in there were no even harmonics and it was easy
to trap the 3rd and 5th harmonics with a tank.


Next, I tried it with a 3VPP sine wave in and got:

Fin Fout Vout fout/fin
kHz kHz VPP
-----|-----|------|---------
10.8 10.8 1.3 1.0
5.39 10.8 0.9 ~ 2.0
2.14 10.8 0.3 5.05 ~ 5

So it looks like the second and the fifth harmonics were there. There
were also some other responses farther down, but I just wanted to see
primarily whether the fifth had enough amplitude to work with, and
apparently it does, so I let the rest of it slide.

So, it looks like if you square up your oscillator's output to 50% duty
cycle you could get the 5th harmonic without too much of a problem. If
you can't, then clip the oscillator's output with a diode or make its
duty cycle less than or greater than 50%, and you ought to be able to
get the 5th that way.

--
John Fields

(Mike Andrews) wrote in message ...
In (rec.radio.amateur.homebrew), Paul Burridge wrote:
Hi all,

Is there some black magic required to get higher order harmonics out
of an oscillator?
I'm only trying to get 17.2Mhz out of a 3.44Mhz source and am thus far
failing spectacularly. I've tried everything I can think of so far to
no avail. All I can get apart from the fundamental is a strong third
harmonic on 10.32Mhz, regardless of what I tune for. I've tried
passing the osc output through two successive inverter gates to
sharpen it up, but still nothing beyond the third appears after tuned
amplification for the fifth. I no longer have a spectrum analyser so
can't check for the presence of a decent comb of harmonics at the
input to the multiplier stage but can only assume the fifth is well
down in the mush for some reason. I could change the inverters for
schmitt triggers and gain a couple of nS but can't see that making
enough difference. What about sticking a varactor in there somewhere?
Would its non-linearity assist or are they only any good for even
order harmonics?
Any suggestions, please. I'm stumped!

There must be something killing the fifth harmonic, which should be
present at (1/5) of the amplitude of the fundamental in a square
wave. That's a pretty strong component.

If you can amplify the output of the source and then square it up
sharply, the fifth harmonic ought to be pretty easy to extract. The
larger the amplitude of that square wave, the larger the amplitude of
the fifth harmonic, of course, so amplification is your friend here --
but you may want to shield very well indeed to keep other components
out of places where they don't belong and may cause trouble.

Have a look at
http://hyperphysics.phy-astr.gsu.edu/hbase/audio/geowv.html
for a lot of stuff that you probably already know.

Best of luck, and please keep us posted.

Hey Mike,

Thanks for that great link. What an awesome site! I am going to be a
regular visitor.

All the best,

Jack

(Mike Andrews) wrote in message ...
In (rec.radio.amateur.homebrew), Paul Burridge wrote:
Hi all,

Is there some black magic required to get higher order harmonics out
of an oscillator?
I'm only trying to get 17.2Mhz out of a 3.44Mhz source and am thus far
failing spectacularly. I've tried everything I can think of so far to
no avail. All I can get apart from the fundamental is a strong third
harmonic on 10.32Mhz, regardless of what I tune for. I've tried
passing the osc output through two successive inverter gates to
sharpen it up, but still nothing beyond the third appears after tuned
amplification for the fifth. I no longer have a spectrum analyser so
can't check for the presence of a decent comb of harmonics at the
input to the multiplier stage but can only assume the fifth is well
down in the mush for some reason. I could change the inverters for
schmitt triggers and gain a couple of nS but can't see that making
enough difference. What about sticking a varactor in there somewhere?
Would its non-linearity assist or are they only any good for even
order harmonics?
Any suggestions, please. I'm stumped!

There must be something killing the fifth harmonic, which should be
present at (1/5) of the amplitude of the fundamental in a square
wave. That's a pretty strong component.

If you can amplify the output of the source and then square it up
sharply, the fifth harmonic ought to be pretty easy to extract. The
larger the amplitude of that square wave, the larger the amplitude of
the fifth harmonic, of course, so amplification is your friend here --
but you may want to shield very well indeed to keep other components
out of places where they don't belong and may cause trouble.

Have a look at
http://hyperphysics.phy-astr.gsu.edu/hbase/audio/geowv.html
for a lot of stuff that you probably already know.

Best of luck, and please keep us posted.

Hey Mike,

Thanks for that great link. What an awesome site! I am going to be a
regular visitor.

All the best,

Jack

On Fri, 12 Mar 2004 16:31:19 -0600, John Fields
wrote:

On Fri, 12 Mar 2004 17:57:24 +0000, Paul Burridge
wrote:


Great. So without a spectrum analyser there's no way to tell? If I
examine the output of the multiplier, it's very messy. There's a
dominant 3rd harmonic alright (my frequency counter resolves it
without difficulty) but the scope trace reveals a number of 'ghost
traces' of different frequencies and amplitudes co-incident with the
dominant trace. All rather confusing. I suppose the only answer is to
build Reg's band pass filter and stick it between the inverter output
and the multiplier input? shrug

---
You may want to try something like this:


COUNTER SCOPE COUNTER
| | |
| | |
FIN--[50R]-+-[1N4148]---+----+-------+---FOUT
| |
[L] [C]
| |
GND----------------------+----+

The 50 ohm resistor is the internal impedance of a function generator,
and when I set it to output a square wave at 1.5VPP, I got 10.8kHz for
the fundamental of the tank. Then I tuned the function generator down
until I got a peak out of the tank, and here's what I found:

Fin Fout Vout fout/fin
kHz kHz VPP
-----|-----|------|---------
10.8 10.8 0.9 1.0
3.58 10.8 0.25 3.02 ~ 3
2.14 10.8 0.2 5.05 ~ 5

So with a square wave in there were no even harmonics and it was easy
to trap the 3rd and 5th harmonics with a tank.


Next, I tried it with a 3VPP sine wave in and got:

Fin Fout Vout fout/fin
kHz kHz VPP
-----|-----|------|---------
10.8 10.8 1.3 1.0
5.39 10.8 0.9 ~ 2.0
2.14 10.8 0.3 5.05 ~ 5

So it looks like the second and the fifth harmonics were there. There
were also some other responses farther down, but I just wanted to see
primarily whether the fifth had enough amplitude to work with, and
apparently it does, so I let the rest of it slide.

So, it looks like if you square up your oscillator's output to 50% duty
cycle you could get the 5th harmonic without too much of a problem. If
you can't, then clip the oscillator's output with a diode or make its
duty cycle less than or greater than 50%, and you ought to be able to
get the 5th that way.

Historical note: about 1960, a guy at HP was doing exactly this with
some new diodes, and he got way more higher harmonics than theory
predicts. To figure it out, they hooked up the just-invented HP185
sampling scope (which then used avalanche transistors to make its
sampling pulses) and discovered the diode reverse-recovery snap
phenom. Soon the scope itself was using this effect. They were
originally called Boff diodes, after the discoverer Frank Boff, but
the name didn't stick (wonder why?) and they became "snap diodes" and
later "step-recovery diodes". I think I may have the HP Journal
article around somewhere.

See page 31:

http://cp.literature.agilent.com/lit...5980-2090E.pdf


John

On Fri, 12 Mar 2004 16:31:19 -0600, John Fields
wrote:

On Fri, 12 Mar 2004 17:57:24 +0000, Paul Burridge
wrote:


Great. So without a spectrum analyser there's no way to tell? If I
examine the output of the multiplier, it's very messy. There's a
dominant 3rd harmonic alright (my frequency counter resolves it
without difficulty) but the scope trace reveals a number of 'ghost
traces' of different frequencies and amplitudes co-incident with the
dominant trace. All rather confusing. I suppose the only answer is to
build Reg's band pass filter and stick it between the inverter output
and the multiplier input? shrug

---
You may want to try something like this:


COUNTER SCOPE COUNTER
| | |
| | |
FIN--[50R]-+-[1N4148]---+----+-------+---FOUT
| |
[L] [C]
| |
GND----------------------+----+

The 50 ohm resistor is the internal impedance of a function generator,
and when I set it to output a square wave at 1.5VPP, I got 10.8kHz for
the fundamental of the tank. Then I tuned the function generator down
until I got a peak out of the tank, and here's what I found:

Fin Fout Vout fout/fin
kHz kHz VPP
-----|-----|------|---------
10.8 10.8 0.9 1.0
3.58 10.8 0.25 3.02 ~ 3
2.14 10.8 0.2 5.05 ~ 5

So with a square wave in there were no even harmonics and it was easy
to trap the 3rd and 5th harmonics with a tank.


Next, I tried it with a 3VPP sine wave in and got:

Fin Fout Vout fout/fin
kHz kHz VPP
-----|-----|------|---------
10.8 10.8 1.3 1.0
5.39 10.8 0.9 ~ 2.0
2.14 10.8 0.3 5.05 ~ 5

So it looks like the second and the fifth harmonics were there. There
were also some other responses farther down, but I just wanted to see
primarily whether the fifth had enough amplitude to work with, and
apparently it does, so I let the rest of it slide.

So, it looks like if you square up your oscillator's output to 50% duty
cycle you could get the 5th harmonic without too much of a problem. If
you can't, then clip the oscillator's output with a diode or make its
duty cycle less than or greater than 50%, and you ought to be able to
get the 5th that way.

Historical note: about 1960, a guy at HP was doing exactly this with
some new diodes, and he got way more higher harmonics than theory
predicts. To figure it out, they hooked up the just-invented HP185
sampling scope (which then used avalanche transistors to make its
sampling pulses) and discovered the diode reverse-recovery snap
phenom. Soon the scope itself was using this effect. They were
originally called Boff diodes, after the discoverer Frank Boff, but
the name didn't stick (wonder why?) and they became "snap diodes" and
later "step-recovery diodes". I think I may have the HP Journal
article around somewhere.

See page 31:

http://cp.literature.agilent.com/lit...5980-2090E.pdf


John

Assuming you have edges quite a bit shorter than the period, it's easy
to see what pulse widths you want to avoid to maximize the 5th: don't
let 5*pi*width/period be an integer multiple of pi. So avoid
width/period = 1/5, 2/5, 3/5 or 4/5. 2/5 and 3/5 (40% and 60%) are
not all that far from 50%. There are lots of ways to get 50% (or
close to it). One is to slow the edges a bit, and put the result into
a Schmitt trigger with adjustable DC level; the DC level will then
adjust the period. You can servo the DC level with an integrator tied
to the output and referenced to (v(high)+v(low))/2, for high accuracy.
Maybe that's too complicated, though, if you want things small. Note
that by not causing dissipation of the fundamental or other harmonics,
a multiplier can be considerably more efficient than indicated by the
percentage available power in the selected harmonic. In other words,
don't put a filter on a logic output that shorts out the fundamental,
but rather one that looks like an open circuit to the fundamental,
etc.

Cheers,
Tom


Paul Burridge wrote in message . ..
On Fri, 12 Mar 2004 16:08:15 +0000, John Woodgate
wrote:

I read in sci.electronics.design that Reg Edwards
wrote (in
et.com) about 'Extracting the 5th Harmonic', on Fri, 12 Mar 2004:
According to Fourier, at some mark-space ratios of a square wave certain
harmonics may be missing from the spectrum.


For a waveform like this (use Courier font):
_____
/ \ /
_____/ \____________/

with rise-time f, dwell time d, fall time r and period T, the harmonic
magnitudes are given by:

Cn = 2Aav{sinc(n[pi]f/T)}{sinc(n[pi][f+d]/T)}{sinc(n[pi][r-f]/T)},

where sinc(x)= {sin(x)}/x

There seems to be a number of opportunities for a harmonic to 'hide' in
a zero of that function.

Great. So without a spectrum analyser there's no way to tell? If I
examine the output of the multiplier, it's very messy. There's a
dominant 3rd harmonic alright (my frequency counter resolves it
without difficulty) but the scope trace reveals a number of 'ghost
traces' of different frequencies and amplitudes co-incident with the
dominant trace. All rather confusing. I suppose the only answer is to
build Reg's band pass filter and stick it between the inverter output
and the multiplier input? shrug

Assuming you have edges quite a bit shorter than the period, it's easy
to see what pulse widths you want to avoid to maximize the 5th: don't
let 5*pi*width/period be an integer multiple of pi. So avoid
width/period = 1/5, 2/5, 3/5 or 4/5. 2/5 and 3/5 (40% and 60%) are
not all that far from 50%. There are lots of ways to get 50% (or
close to it). One is to slow the edges a bit, and put the result into
a Schmitt trigger with adjustable DC level; the DC level will then
adjust the period. You can servo the DC level with an integrator tied
to the output and referenced to (v(high)+v(low))/2, for high accuracy.
Maybe that's too complicated, though, if you want things small. Note
that by not causing dissipation of the fundamental or other harmonics,
a multiplier can be considerably more efficient than indicated by the
percentage available power in the selected harmonic. In other words,
don't put a filter on a logic output that shorts out the fundamental,
but rather one that looks like an open circuit to the fundamental,
etc.

Cheers,
Tom


Paul Burridge wrote in message . ..
On Fri, 12 Mar 2004 16:08:15 +0000, John Woodgate
wrote:

I read in sci.electronics.design that Reg Edwards
wrote (in
et.com) about 'Extracting the 5th Harmonic', on Fri, 12 Mar 2004:
According to Fourier, at some mark-space ratios of a square wave certain
harmonics may be missing from the spectrum.


For a waveform like this (use Courier font):
_____
/ \ /
_____/ \____________/

with rise-time f, dwell time d, fall time r and period T, the harmonic
magnitudes are given by:

Cn = 2Aav{sinc(n[pi]f/T)}{sinc(n[pi][f+d]/T)}{sinc(n[pi][r-f]/T)},

where sinc(x)= {sin(x)}/x

There seems to be a number of opportunities for a harmonic to 'hide' in
a zero of that function.

Great. So without a spectrum analyser there's no way to tell? If I
examine the output of the multiplier, it's very messy. There's a
dominant 3rd harmonic alright (my frequency counter resolves it
without difficulty) but the scope trace reveals a number of 'ghost
traces' of different frequencies and amplitudes co-incident with the
dominant trace. All rather confusing. I suppose the only answer is to
build Reg's band pass filter and stick it between the inverter output
and the multiplier input? shrug

The 5th harmonic should be only 14dB below the fundamental, although it will
drop fairly quickly as the sides of the input square wave deviate from vertical.

Does the 3.44MHz have a 50% duty cycle?

Are you filtering before amplifying (eg a high impedance 3 pole
bandpass/highpass L-C filter with a gain of about 5 at 17.2MHz).

Does the inverter supply a decent square wave under the load of the filter?

If all else fails, could you reverse the process - generate 17.2MHz and divide
it down to 3.44MHz?

(Many) years ago I made a functional TV modulator for an Apple ][ PC by pulling
out the 3rd harmonic of the 14.318MHz system clock. I know it was only 3rd
harmonic, but it was at ~43MHz, so I would expect similar or better logic should
be able to produce 17.2MHz for you.

On Fri, 12 Mar 2004 13:56:10 +0000, Paul Burridge
wrote:

Hi all,

Is there some black magic required to get higher order harmonics out
of an oscillator?
I'm only trying to get 17.2Mhz out of a 3.44Mhz source and am thus far
failing spectacularly. I've tried everything I can think of so far to
no avail. All I can get apart from the fundamental is a strong third
harmonic on 10.32Mhz, regardless of what I tune for. I've tried
passing the osc output through two successive inverter gates to
sharpen it up, but still nothing beyond the third appears after tuned
amplification for the fifth. I no longer have a spectrum analyser so
can't check for the presence of a decent comb of harmonics at the
input to the multiplier stage but can only assume the fifth is well
down in the mush for some reason. I could change the inverters for
schmitt triggers and gain a couple of nS but can't see that making
enough difference. What about sticking a varactor in there somewhere?
Would its non-linearity assist or are they only any good for even
order harmonics?
Any suggestions, please. I'm stumped!

Tony (remove the "_" to reply by email)

The 5th harmonic should be only 14dB below the fundamental, although it will
drop fairly quickly as the sides of the input square wave deviate from vertical.

Does the 3.44MHz have a 50% duty cycle?

Are you filtering before amplifying (eg a high impedance 3 pole
bandpass/highpass L-C filter with a gain of about 5 at 17.2MHz).

Does the inverter supply a decent square wave under the load of the filter?

If all else fails, could you reverse the process - generate 17.2MHz and divide
it down to 3.44MHz?

(Many) years ago I made a functional TV modulator for an Apple ][ PC by pulling
out the 3rd harmonic of the 14.318MHz system clock. I know it was only 3rd
harmonic, but it was at ~43MHz, so I would expect similar or better logic should
be able to produce 17.2MHz for you.

On Fri, 12 Mar 2004 13:56:10 +0000, Paul Burridge
wrote:

Hi all,

Is there some black magic required to get higher order harmonics out
of an oscillator?
I'm only trying to get 17.2Mhz out of a 3.44Mhz source and am thus far
failing spectacularly. I've tried everything I can think of so far to
no avail. All I can get apart from the fundamental is a strong third
harmonic on 10.32Mhz, regardless of what I tune for. I've tried
passing the osc output through two successive inverter gates to
sharpen it up, but still nothing beyond the third appears after tuned
amplification for the fifth. I no longer have a spectrum analyser so
can't check for the presence of a decent comb of harmonics at the
input to the multiplier stage but can only assume the fifth is well
down in the mush for some reason. I could change the inverters for
schmitt triggers and gain a couple of nS but can't see that making
enough difference. What about sticking a varactor in there somewhere?
Would its non-linearity assist or are they only any good for even
order harmonics?
Any suggestions, please. I'm stumped!

Tony (remove the "_" to reply by email)

On Fri, 12 Mar 2004 13:56:10 +0000, Paul Burridge
posted this:

Hi all,

Is there some black magic required to get higher order harmonics out
of an oscillator?
I'm only trying to get 17.2Mhz out of a 3.44Mhz source and am thus far
failing spectacularly. I've tried everything I can think of so far to
no avail.

Is this a simulated circuit or a "real" one built with "real"
components?

I have at least one suggestion, but I need to know whether to send an
LTspice netlist or a gif.

Jim