Extracting the 5th Harmonic
 

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! :(
--

The BBC: Licensed at public expense to spread lies.

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.

--
Mike Andrews

Tired old sysadmin

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.

--
Mike Andrews

Tired old sysadmin

According to Fourier, at some mark-space ratios of a square wave certain
harmonics may be missing from the spectrum.

Just generate a a train of very short sharp pulses from the oscillator and
you will find all the harmonics are present allbeit with reducing
amplitudes. A single transistor should do the job.

According to Fourier, at some mark-space ratios of a square wave certain
harmonics may be missing from the spectrum.

Just generate a a train of very short sharp pulses from the oscillator and
you will find all the harmonics are present allbeit with reducing
amplitudes. A single transistor should do the job.

Is there some black magic required to get higher order harmonics out
of an oscillator?

No black magic, you just need to filter for the fifth harmonic. I'm
extracting the 16th harmonic of 64 MHz out of a MMIC, and retuning the
filter, can actually extract a little more 15th than 16th. You can generate
a comb generator to do the job of generating large quantities of all
harmonics, but for this simple of a job, it'd be overkill big time. Either
make a better filter, amplify your fundamental more before filtering, (the 5
volt digital squarer ought to put out +17 dBm) or check the HP app note
AN983 and take advantage of "filter gain".

W4ZCB

Is there some black magic required to get higher order harmonics out
of an oscillator?

No black magic, you just need to filter for the fifth harmonic. I'm
extracting the 16th harmonic of 64 MHz out of a MMIC, and retuning the
filter, can actually extract a little more 15th than 16th. You can generate
a comb generator to do the job of generating large quantities of all
harmonics, but for this simple of a job, it'd be overkill big time. Either
make a better filter, amplify your fundamental more before filtering, (the 5
volt digital squarer ought to put out +17 dBm) or check the HP app note
AN983 and take advantage of "filter gain".

W4ZCB

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.

In RF circles, the 'normal' way to do this would be a simple Class C
amplifier with a collector load tuned to the fifth harmonic. In calls C,
conduction only occurs for a small fraction of a cycle which produces a
correspondingly higher proportion of higher harmonics than a square wave.

Ian

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.

In RF circles, the 'normal' way to do this would be a simple Class C
amplifier with a collector load tuned to the fifth harmonic. In calls C,
conduction only occurs for a small fraction of a cycle which produces a
correspondingly higher proportion of higher harmonics than a square wave.

Ian

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.
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk

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.
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk

On Fri, 12 Mar 2004 16:08:15 +0000, John Woodgate wrote:

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

I've never seen this terminology before. Is this standard math parlance or
is it something of your own?

Don't flame, I'm genuinely curious.

Bob

On Fri, 12 Mar 2004 16:08:15 +0000, John Woodgate wrote:

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

I've never seen this terminology before. Is this standard math parlance or
is it something of your own?

Don't flame, I'm genuinely curious.

Bob

In rec.radio.amateur.homebrew,sci.electronics.design, Bob Stephens
wrote:

On Fri, 12 Mar 2004 16:08:15 +0000, John Woodgate wrote:

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

I've never seen this terminology before. Is this standard math parlance or
is it something of your own?

You can google for it (Usenet or Web) and find it, I've seen it
used a good bit in signal processing and such.

Don't flame, I'm genuinely curious.

Bob

-----
http://mindspring.com/~benbradley

In rec.radio.amateur.homebrew,sci.electronics.design, Bob Stephens
wrote:

On Fri, 12 Mar 2004 16:08:15 +0000, John Woodgate wrote:

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

I've never seen this terminology before. Is this standard math parlance or
is it something of your own?

You can google for it (Usenet or Web) and find it, I've seen it
used a good bit in signal processing and such.

Don't flame, I'm genuinely curious.

Bob

-----
http://mindspring.com/~benbradley

In (rec.radio.amateur.homebrew), Ben Bradley wrote:
In rec.radio.amateur.homebrew,sci.electronics.design, Bob Stephens
wrote:

On Fri, 12 Mar 2004 16:08:15 +0000, John Woodgate wrote:

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

I've never seen this terminology before. Is this standard math parlance or
is it something of your own?

You can google for it (Usenet or Web) and find it, I've seen it
used a good bit in signal processing and such.

And it shows up in some math classes as well, though its main use is
in electronics. I suspect it showed up because the instructor wanted
to show a real-life example, which just happened to be -- electronics.

--
End-to-end connectivity is the "coin of the realm" for internet
operations. Use it wisely. You only control your end of it.

In (rec.radio.amateur.homebrew), Ben Bradley wrote:
In rec.radio.amateur.homebrew,sci.electronics.design, Bob Stephens
wrote:

On Fri, 12 Mar 2004 16:08:15 +0000, John Woodgate wrote:

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

I've never seen this terminology before. Is this standard math parlance or
is it something of your own?

You can google for it (Usenet or Web) and find it, I've seen it
used a good bit in signal processing and such.

And it shows up in some math classes as well, though its main use is
in electronics. I suspect it showed up because the instructor wanted
to show a real-life example, which just happened to be -- electronics.

--
End-to-end connectivity is the "coin of the realm" for internet
operations. Use it wisely. You only control your end of it.

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 BBC: Licensed at public expense to spread lies.

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 BBC: Licensed at public expense to spread lies.

On Fri, 12 Mar 2004 17:25:59 +0000 (UTC), Mike Andrews wrote:

In (rec.radio.amateur.homebrew), Ben Bradley wrote:
In rec.radio.amateur.homebrew,sci.electronics.design, Bob Stephens
wrote:

On Fri, 12 Mar 2004 16:08:15 +0000, John Woodgate wrote:

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

I've never seen this terminology before. Is this standard math parlance or
is it something of your own?

You can google for it (Usenet or Web) and find it, I've seen it
used a good bit in signal processing and such.

And it shows up in some math classes as well, though its main use is
in electronics. I suspect it showed up because the instructor wanted
to show a real-life example, which just happened to be -- electronics.

I've always seen it as 1/x sin(x) "one over ex sine ex". the hyperbolic
sine function sinh is usually pronounced "Cinch"
So how do you pronounce sinc? "Sink ?"

On Fri, 12 Mar 2004 17:25:59 +0000 (UTC), Mike Andrews wrote:

In (rec.radio.amateur.homebrew), Ben Bradley wrote:
In rec.radio.amateur.homebrew,sci.electronics.design, Bob Stephens
wrote:

On Fri, 12 Mar 2004 16:08:15 +0000, John Woodgate wrote:

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

I've never seen this terminology before. Is this standard math parlance or
is it something of your own?

You can google for it (Usenet or Web) and find it, I've seen it
used a good bit in signal processing and such.

And it shows up in some math classes as well, though its main use is
in electronics. I suspect it showed up because the instructor wanted
to show a real-life example, which just happened to be -- electronics.

I've always seen it as 1/x sin(x) "one over ex sine ex". the hyperbolic
sine function sinh is usually pronounced "Cinch"
So how do you pronounce sinc? "Sink ?"

I read in sci.electronics.design that Bob Stephens stephensyomamadigita
wrote (in
) about 'Extracting the 5th Harmonic', on Fri, 12 Mar 2004:
So how do you pronounce
sinc? "Sink ?"

If you wish.
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk

I read in sci.electronics.design that Bob Stephens stephensyomamadigita
wrote (in
) about 'Extracting the 5th Harmonic', on Fri, 12 Mar 2004:
So how do you pronounce
sinc? "Sink ?"

If you wish.
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk

"Bob Stephens" wrote in message
.. .
On Fri, 12 Mar 2004 17:25:59 +0000 (UTC), Mike Andrews wrote:

In
(rec.radio.amateur.homebrew), Ben Bradley wrote:
In rec.radio.amateur.homebrew,sci.electronics.design, Bob Stephens
wrote:

On Fri, 12 Mar 2004 16:08:15 +0000, John Woodgate wrote:

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

I've never seen this terminology before. Is this standard math parlance
or
is it something of your own?

You can google for it (Usenet or Web) and find it, I've seen it
used a good bit in signal processing and such.

And it shows up in some math classes as well, though its main use is
in electronics. I suspect it showed up because the instructor wanted
to show a real-life example, which just happened to be -- electronics.

I've always seen it as 1/x sin(x) "one over ex sine ex". the hyperbolic
sine function sinh is usually pronounced "Cinch"
So how do you pronounce sinc? "Sink ?"

Yes, it's pronounced "sink", and it's quite common in signal processing.
You define it as being the _limit_ of sin(x)/x as x - 0 because otherwise
it's undefined at zero, and all the mathematicians in the crowd will curse
at you for being yet another engineer who's treating math so casually.

"Bob Stephens" wrote in message
.. .
On Fri, 12 Mar 2004 17:25:59 +0000 (UTC), Mike Andrews wrote:

In
(rec.radio.amateur.homebrew), Ben Bradley wrote:
In rec.radio.amateur.homebrew,sci.electronics.design, Bob Stephens
wrote:

On Fri, 12 Mar 2004 16:08:15 +0000, John Woodgate wrote:

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

I've never seen this terminology before. Is this standard math parlance
or
is it something of your own?

You can google for it (Usenet or Web) and find it, I've seen it
used a good bit in signal processing and such.

And it shows up in some math classes as well, though its main use is
in electronics. I suspect it showed up because the instructor wanted
to show a real-life example, which just happened to be -- electronics.

I've always seen it as 1/x sin(x) "one over ex sine ex". the hyperbolic
sine function sinh is usually pronounced "Cinch"
So how do you pronounce sinc? "Sink ?"

Yes, it's pronounced "sink", and it's quite common in signal processing.
You define it as being the _limit_ of sin(x)/x as x - 0 because otherwise
it's undefined at zero, and all the mathematicians in the crowd will curse
at you for being yet another engineer who's treating math so casually.

In (rec.radio.amateur.homebrew), Tim Wescott wrote:

Yes, it's pronounced "sink", and it's quite common in signal processing.
You define it as being the _limit_ of sin(x)/x as x - 0 because otherwise
it's undefined at zero, and all the mathematicians in the crowd will curse
at you for being yet another engineer who's treating math so casually.

That's not precisely true.

Some fraction of us mathematicians wander away, shaking our heads and
muttering "Engineers!" under our breaths.

--
The official state religion of France is Bureaucracy. They've replaced
the Trinity with the Triplicate.
-- David Richerby, in a place not to be named.

In (rec.radio.amateur.homebrew), Tim Wescott wrote:

Yes, it's pronounced "sink", and it's quite common in signal processing.
You define it as being the _limit_ of sin(x)/x as x - 0 because otherwise
it's undefined at zero, and all the mathematicians in the crowd will curse
at you for being yet another engineer who's treating math so casually.

That's not precisely true.

Some fraction of us mathematicians wander away, shaking our heads and
muttering "Engineers!" under our breaths.

--
The official state religion of France is Bureaucracy. They've replaced
the Trinity with the Triplicate.
-- David Richerby, in a place not to be named.

In article , Paul Burridge
writes:

Is there some black magic required to get higher order harmonics out
of an oscillator?

[did you miss a class at Hogwarts? :-) ]

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.

As others have suggested, the duty cycle may be off such that
the 5th harmonic is not as strong as it should be (it would be only
about 10% of the fundamental frequency with the 'best' duty cycle).

Part of the problem can be in trying to L-C tune logic gate outputs,
presuming a great deal that such is what you are doing. If you must
use logic gate inverters, use an open collector kind and put a 5th
harmonic parallel-tuned circuit there and couple it to a relatively high
impedance buffer amplifier input. Or, use a transistor stage and tune
the collector (or drain if FET) to the 5th harmonic.

With TTL gates the output characteristics are non-linear in that a
conducting-to-logic-0 state is a rather low impedance source while
output conducting to a logic-1 state is a medium impedance source.
The resulting loading is not good for trying to filter out a 5th or higher
harmonic. An open-collector output allows the average output Z to
be higher with less upset of a tuned circuit.

The above also applies to a series-tuned L-C circuit for the 5th but
that may be an advantage with the curious impedance of TTL gate
inputs. Using CMOS logic gates over all might prove to be an
advantage since their input impedances are quite high and most
output characteristics don't differ as much between logic 0 and 1.

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?

Varactors don't create harmonics all by themselves. Those need to be
"tuned" either through resonant circuits or harmonics selected via
L-C filters. What you want to do can be done with stock parts but in
different arrangements.

Len Anderson
retired (from regular hours) electronic engineer person.

In article , Paul Burridge
writes:

Is there some black magic required to get higher order harmonics out
of an oscillator?

[did you miss a class at Hogwarts? :-) ]

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.

As others have suggested, the duty cycle may be off such that
the 5th harmonic is not as strong as it should be (it would be only
about 10% of the fundamental frequency with the 'best' duty cycle).

Part of the problem can be in trying to L-C tune logic gate outputs,
presuming a great deal that such is what you are doing. If you must
use logic gate inverters, use an open collector kind and put a 5th
harmonic parallel-tuned circuit there and couple it to a relatively high
impedance buffer amplifier input. Or, use a transistor stage and tune
the collector (or drain if FET) to the 5th harmonic.

With TTL gates the output characteristics are non-linear in that a
conducting-to-logic-0 state is a rather low impedance source while
output conducting to a logic-1 state is a medium impedance source.
The resulting loading is not good for trying to filter out a 5th or higher
harmonic. An open-collector output allows the average output Z to
be higher with less upset of a tuned circuit.

The above also applies to a series-tuned L-C circuit for the 5th but
that may be an advantage with the curious impedance of TTL gate
inputs. Using CMOS logic gates over all might prove to be an
advantage since their input impedances are quite high and most
output characteristics don't differ as much between logic 0 and 1.

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?

Varactors don't create harmonics all by themselves. Those need to be
"tuned" either through resonant circuits or harmonics selected via
L-C filters. What you want to do can be done with stock parts but in
different arrangements.

Len Anderson
retired (from regular hours) electronic engineer person.

Mike Andrews wrote:

In (rec.radio.amateur.homebrew), Tim
Wescott wrote:

Yes, it's pronounced "sink", and it's quite common in signal processing.
You define it as being the _limit_ of sin(x)/x as x - 0 because
otherwise it's undefined at zero, and all the mathematicians in the crowd
will curse at you for being yet another engineer who's treating math so
casually.

That's not precisely true.

Some fraction of us mathematicians wander away, shaking our heads and
muttering "Engineers!" under our breaths.


Reminds me of the old joke about the mathemetician, the physicist and the
engineer. They were each shown into a room in the centre of which was £50
note / $100 bill (depending on which side of the pond you live).

They were told they could walk half the distance to the money and stop.
Then they could walk half the remaining ditance and so on until they got
the money.

The mathemetician worked out you would never reach the money so he didn't
even try. The physicist, working to five decimal places was still there a
week later. The engineer did three iterations, said 'That's close enough'
and picked up the money.

The moral is of course, horses for courses.

Ian

Mike Andrews wrote:

In (rec.radio.amateur.homebrew), Tim
Wescott wrote:

Yes, it's pronounced "sink", and it's quite common in signal processing.
You define it as being the _limit_ of sin(x)/x as x - 0 because
otherwise it's undefined at zero, and all the mathematicians in the crowd
will curse at you for being yet another engineer who's treating math so
casually.

That's not precisely true.

Some fraction of us mathematicians wander away, shaking our heads and
muttering "Engineers!" under our breaths.


Reminds me of the old joke about the mathemetician, the physicist and the
engineer. They were each shown into a room in the centre of which was £50
note / $100 bill (depending on which side of the pond you live).

They were told they could walk half the distance to the money and stop.
Then they could walk half the remaining ditance and so on until they got
the money.

The mathemetician worked out you would never reach the money so he didn't
even try. The physicist, working to five decimal places was still there a
week later. The engineer did three iterations, said 'That's close enough'
and picked up the money.

The moral is of course, horses for courses.

Ian

The Hyperbolic Cosine is pronounced Cosh.
The Hyperbolic Sine is pronounced Shine.
The Hyperbolic Tangent is pronounced Than with a soft Th.

At least that's the way I've been doing it for the last 55 years.

They don't seem to come up very often in conversation although they are just
as fundamental in mathematics as are the trigonometrical functions. They
crop up all over the place especially in transmission lines where they
appear in complex form such as Tanh(A+jB).

The Hyperbolic Cosine is pronounced Cosh.
The Hyperbolic Sine is pronounced Shine.
The Hyperbolic Tangent is pronounced Than with a soft Th.

At least that's the way I've been doing it for the last 55 years.

They don't seem to come up very often in conversation although they are just
as fundamental in mathematics as are the trigonometrical functions. They
crop up all over the place especially in transmission lines where they
appear in complex form such as Tanh(A+jB).

In article , "Tim Wescott"
writes:

I've always seen it as 1/x sin(x) "one over ex sine ex". the hyperbolic
sine function sinh is usually pronounced "Cinch"
So how do you pronounce sinc? "Sink ?"

Yes, it's pronounced "sink", and it's quite common in signal processing.
You define it as being the _limit_ of sin(x)/x as x - 0 because otherwise
it's undefined at zero, and all the mathematicians in the crowd will curse
at you for being yet another engineer who's treating math so casually.

Heh heh heh...rememberances of my instructor throughout all math
classes except analytical geometry...same one, who also had
a HOBBY of advanced math. :-)

Instructor always warned everyone NOT to pronounce the apparent
word meaning hyperbolic sine...just say "hyperbolic" before "sine"
but write it "SinC." Someone in the class would object and then
he would write the word for hyperbolic tangent on the board and
challenge him to pronounce "TanH." :-)

Basic algebra texts explain what they are and their identities, but
some want to emulate Professor Higgins in "My Fair Lady"...i.e.,
"...they don't care what they DO, only that they pronounce it
correctly!" :-) :-) :-)

Len Anderson
retired (from regular hours) electronic engineer person

In article , "Tim Wescott"
writes:

I've always seen it as 1/x sin(x) "one over ex sine ex". the hyperbolic
sine function sinh is usually pronounced "Cinch"
So how do you pronounce sinc? "Sink ?"

Yes, it's pronounced "sink", and it's quite common in signal processing.
You define it as being the _limit_ of sin(x)/x as x - 0 because otherwise
it's undefined at zero, and all the mathematicians in the crowd will curse
at you for being yet another engineer who's treating math so casually.

Heh heh heh...rememberances of my instructor throughout all math
classes except analytical geometry...same one, who also had
a HOBBY of advanced math. :-)

Instructor always warned everyone NOT to pronounce the apparent
word meaning hyperbolic sine...just say "hyperbolic" before "sine"
but write it "SinC." Someone in the class would object and then
he would write the word for hyperbolic tangent on the board and
challenge him to pronounce "TanH." :-)

Basic algebra texts explain what they are and their identities, but
some want to emulate Professor Higgins in "My Fair Lady"...i.e.,
"...they don't care what they DO, only that they pronounce it
correctly!" :-) :-) :-)

Len Anderson
retired (from regular hours) electronic engineer person

"Reg Edwards" wrote in message ...
According to Fourier, at some mark-space ratios of a square wave certain
harmonics may be missing from the spectrum.

Just generate a a train of very short sharp pulses from the oscillator and
you will find all the harmonics are present allbeit with reducing
amplitudes. A single transistor should do the job.

The inverse of the duty cycle. For a square wave 1:1 M/S = 1/2 duty
and all harmonics divisble by 2 are absent. For duty 1/5, fifth
harmonic (and multiples)are absent.

"Reg Edwards" wrote in message ...
According to Fourier, at some mark-space ratios of a square wave certain
harmonics may be missing from the spectrum.

Just generate a a train of very short sharp pulses from the oscillator and
you will find all the harmonics are present allbeit with reducing
amplitudes. A single transistor should do the job.

The inverse of the duty cycle. For a square wave 1:1 M/S = 1/2 duty
and all harmonics divisble by 2 are absent. For duty 1/5, fifth
harmonic (and multiples)are absent.

Mike Andrews wrote:
In (rec.radio.amateur.homebrew), Ben Bradley wrote:

In rec.radio.amateur.homebrew,sci.electronics.design, Bob Stephens
wrote:


On Fri, 12 Mar 2004 16:08:15 +0000, John Woodgate wrote:


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

I've never seen this terminology before. Is this standard math parlance or
is it something of your own?


You can google for it (Usenet or Web) and find it, I've seen it
used a good bit in signal processing and such.


And it shows up in some math classes as well, though its main use is
in electronics. I suspect it showed up because the instructor wanted
to show a real-life example, which just happened to be -- electronics.

And if you want to see the graph of it, look at the Broadcomm logo! 8-)
--
Charlie
--
Edmondson Engineering
Unique Solutions to Unusual Problems

Mike Andrews wrote:
In (rec.radio.amateur.homebrew), Ben Bradley wrote:

In rec.radio.amateur.homebrew,sci.electronics.design, Bob Stephens
wrote:


On Fri, 12 Mar 2004 16:08:15 +0000, John Woodgate wrote:


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

I've never seen this terminology before. Is this standard math parlance or
is it something of your own?


You can google for it (Usenet or Web) and find it, I've seen it
used a good bit in signal processing and such.


And it shows up in some math classes as well, though its main use is
in electronics. I suspect it showed up because the instructor wanted
to show a real-life example, which just happened to be -- electronics.

And if you want to see the graph of it, look at the Broadcomm logo! 8-)
--
Charlie
--
Edmondson Engineering
Unique Solutions to Unusual Problems

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