Frequency Halver

[Robert Baer]

John Larkin wrote:

On 18 Mar 2005 03:24:39 -0800, stephen_cochrane@hotmail.com
(stevieboy01) wrote:


I may be very stupid for asking this, but is there a simple analogue
circuit in which I can input a frequency (currently 20kHz) and output
half the frequency?

Steve



Injection-locked oscillator, maybe, but not all that simple.

John



A "starved" sub-harmonic oscillator is rather simple; see an earlier

response by me for more details.

 

[Fred Bloggs]

Tony Williams wrote:

In article <1111153053.673722.110540@g14g2000cwa.googlegroups.com>,
Bill Sloman <bill.sloman@ieee.org> wrote:


For what it is worth, I'm pretty sure that there is no analog
technique that will halve the frequency of a sine wave.


There is an analogue sum available Bill, that may
(or may not) be persuaded to cooperate.

2
Cos(2A) = 2.Cos(A) - 1.


2R 2R
Cos(2A)---/\/\---+------/\/\---+-------->Cos(A)
| |\ |
+---|->-------+----+
| |/ |
| +----+ |
| | -X|-<--+
1 ---/\/\----+--/\/\--|XY | |
2R R | Y|-<--+
+----+

Bitter experience of trying to realise a similar
sum says that the 'Cos(A)' produced will probably
be the full wave rectified version of Cos(A). It
is because squaring Cos(A) inherently loses the
polarity information.

What is needed is some sort of polarity enforcer,
that switches over at every full cycle of Cos(2A).

But I never devised one in the similar circuit
that I tried. Any suggestions?

2 2
Note: I was trying to use Sin + Cos = 1 to get
a 2-phase Sin/Cos from just Sine. Same
loss of polarity through the squaring.
ie. Sin/

Tony,

Try Sin(2A)=-2*Sin(A)*Sin(A-pi/2), this is an inverting summer with
phase shifter and multiplier in feedback path summed with Sin(2A). If
input is Apk*Sin(2A) then output should be sqrt(Apk)*Sin(A).

 

[John Woodgate]

I read in sci.electronics.design that Tony Williams
<tonyw@ledelec.demon.co.uk> wrote (in <4d4e042a86tonyw@ledelec.demon.co.
uk&gt about 'Frequency Halver', on Sat, 19 Mar 2005:

What is needed is some sort of polarity enforcer,
that switches over at every full cycle of Cos(2A).

You mean a half-wave rectified cos2A feeding via a D-type FF that clever
op-amp circuit that can be switched between +1 and -1 gain?
--
Regards, John Woodgate, OOO - Own Opinions Only.
There are two sides to every question, except
'What is a Moebius strip?'
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk

 

[John Fields]

On 18 Mar 2005 03:24:39 -0800, stephen_cochrane@hotmail.com
(stevieboy01) wrote:

I may be very stupid for asking this, but is there a simple analogue
circuit in which I can input a frequency (currently 20kHz) and output
half the frequency?

---
If you can do it digitally, the easiest way would be to use a
comparator to square up the incoming signal, then use the comparator's
output signal as the clock of a "D" type flip-flop wired as a
divide-by-two, and then filter the output square wave either passively
or actively. If you use a dual op-amp you can use one section for the
comparator and the other for the filter.

--
John Fields

 

[Tony Williams]

In article <423BFF14.5060704@nospam.com>,
Fred Bloggs <nospam@nospam.com> wrote:

Tony,

Try Sin(2A)=-2*Sin(A)*Sin(A-pi/2), this is an inverting summer
with phase shifter and multiplier in feedback path summed with
Sin(2A). If input is Apk*Sin(2A) then output should be
sqrt(Apk)*Sin(A).

I'd forgotten that actual voltages are Vpk*Sin(), etc.
Thanks for the subtle reminder.

Yes Fred. You've picked the only frequency-doubler sum
that does not require squaring, and it is the use of Cos
that keeps the output polarity honest. But generating Cos
from Sin can itself be a problem.... easy at fixed freq,
somewhat troublesome otherwise. Note that the relative
phase shift has to be kept constant, whereas the amplitude
has to be kept equal to Vin.

--
Tony Williams.

 

[Tony Williams]

In article <uSS+SfCgPAPCFwuu@jmwa.demon.co.uk>,
John Woodgate <jmw@jmwa.demon.contraspam.yuk> wrote:

What is needed is some sort of polarity enforcer,
that switches over at every full cycle of Cos(2A).

You mean a half-wave rectified cos2A feeding via a D-type FF that
clever op-amp circuit that can be switched between +1 and -1 gain?

Something like that but possibly cruder.

I suspect that the Vout polarity remains positive
(or negative) because of zero offsets in the cct.

A possible solution is to divide 2F by 2 and simply
capacitively couple one output of the flipflop into
the virtual earth of the summing amplifier. The
small charge injections (at each zero crossing of
Vout) should be large enough to overcome the offset,
and alternately kick Vout into the opposing polarity.

--
Tony Williams.

 

Robert Baer wrote:

bill.sloman@ieee.org wrote:

Sorry John, but I think you have just described a frequency
doubler,
rather than a frequency halver.

For what it is worth, I'm pretty sure that there is no analog
technique
that will halve the frequency of a sine wave. It is easy enough to
use
a largely digital circuit to produce a sine wave which follows half
the
average frequency of of an analogue sine wave, and if you got
really
cute, you could track the phase of the input sine wave and produce
an
output whose phase varied at half the rate - though since the
maxima
and minima of a sine wave don't tell you much about the
instantaneous
phase, this isn't going to be perfect either.

---------
Bill Sloman, Nijmegen

Incorrect; over 40 years ago we did that at Sylvania with a
tetrode.
See a previous response by me earlier in this thread.

You didn't halve the frequency of a sine wave, you used the input
frequency to excite a tuned circuit that was resonant at roughly half
the frequency of the input circuit, a much less direct relationship.

----------
Bill Sloman, Nijmegen

 

[Robert Baer]

Fred Bloggs wrote:

Tony Williams wrote:

In article <1111153053.673722.110540@g14g2000cwa.googlegroups.com>,
Bill Sloman <bill.sloman@ieee.org> wrote:


For what it is worth, I'm pretty sure that there is no analog
technique that will halve the frequency of a sine wave.



There is an analogue sum available Bill, that may
(or may not) be persuaded to cooperate.

2
Cos(2A) = 2.Cos(A) - 1.


2R 2R
Cos(2A)---/\/\---+------/\/\---+-------->Cos(A)
| |\ |
+---|->-------+----+
| |/ |
| +----+ |
| | -X|-<--+
1 ---/\/\----+--/\/\--|XY | |
2R R | Y|-<--+
+----+

Bitter experience of trying to realise a similar
sum says that the 'Cos(A)' produced will probably
be the full wave rectified version of Cos(A). It
is because squaring Cos(A) inherently loses the
polarity information.

What is needed is some sort of polarity enforcer,
that switches over at every full cycle of Cos(2A).

But I never devised one in the similar circuit
that I tried. Any suggestions?
2 2
Note: I was trying to use Sin + Cos = 1 to get a 2-phase
Sin/Cos from just Sine. Same
loss of polarity through the squaring.
ie. Sin/


Tony,

Try Sin(2A)=-2*Sin(A)*Sin(A-pi/2), this is an inverting summer with
phase shifter and multiplier in feedback path summed with Sin(2A). If
input is Apk*Sin(2A) then output should be sqrt(Apk)*Sin(A).

Too complicated.

All one needs a non-linear device to feed a sub-harmonic oscillator
that is set below the threshold of oscillation.
Energy from the NLD fed to that "almost" oscillator will get it going.
Like sitting in a swing that is still; the self-resonant frequency of
the system can be excited by hand-pumping at twice the SRF, given
sufficent energy; the hand-pumping is nonlinear.

 

[Robert Baer]

bill.sloman@ieee.org wrote:

Robert Baer wrote:

bill.sloman@ieee.org wrote:


Sorry John, but I think you have just described a frequency

doubler,

rather than a frequency halver.

For what it is worth, I'm pretty sure that there is no analog

technique

that will halve the frequency of a sine wave. It is easy enough to

use

a largely digital circuit to produce a sine wave which follows half

the

average frequency of of an analogue sine wave, and if you got

really

cute, you could track the phase of the input sine wave and produce

an

output whose phase varied at half the rate - though since the

maxima

and minima of a sine wave don't tell you much about the

instantaneous

phase, this isn't going to be perfect either.

---------
Bill Sloman, Nijmegen


Incorrect; over 40 years ago we did that at Sylvania with a

tetrode.

See a previous response by me earlier in this thread.


You didn't halve the frequency of a sine wave, you used the input
frequency to excite a tuned circuit that was resonant at roughly half
the frequency of the input circuit, a much less direct relationship.

----------
Bill Sloman, Nijmegen

Correct, but the result is essentially the same.

And it will track frequency changes, apparently up to 10% and perhaps
allows AM to pass thru as well (this last part i do not remember; been
too long).

 

[John Larkin]

On Sat, 19 Mar 2005 09:36:16 +0000 (GMT), Tony Williams
<tonyw@ledelec.demon.co.uk> wrote:

In article <1111153053.673722.110540@g14g2000cwa.googlegroups.com>,
Bill Sloman <bill.sloman@ieee.org> wrote:

For what it is worth, I'm pretty sure that there is no analog
technique that will halve the frequency of a sine wave.

There is an analogue sum available Bill, that may
(or may not) be persuaded to cooperate.

2
Cos(2A) = 2.Cos(A) - 1.


2R 2R
Cos(2A)---/\/\---+------/\/\---+-------->Cos(A)
| |\ |
+---|->-------+----+
| |/ |
| +----+ |
| | -X|-<--+
1 ---/\/\----+--/\/\--|XY | |
2R R | Y|-<--+
+----+

No circuit like this can halve the frequency of a sinewave. Any box
that halves frequency has input values for which the output must have
*two* possible values; for example, an input of +1 sometimes makes a
positive output, and sometimes makes negative. So any halver must have
delay or storage of some sort, and circuits like this, which have
predictable and single-valued instantaneous response, don't.

Another way to look at is that single-valued linear+nonlinear
functions make even and odd harmonics but don't make fractional
harmonics.

Bitter experience of trying to realise a similar
sum says that the 'Cos(A)' produced will probably
be the full wave rectified version of Cos(A). It
is because squaring Cos(A) inherently loses the
polarity information.

What is needed is some sort of polarity enforcer,
that switches over at every full cycle of Cos(2A).

That would be a divide-by-two flipflop!


John

 

[John Larkin]

On Mon, 21 Mar 2005 06:25:25 GMT, Robert Baer
<robertbaer@earthlink.net> wrote:

bill.sloman@ieee.org wrote:

Robert Baer wrote:

bill.sloman@ieee.org wrote:


Sorry John, but I think you have just described a frequency

doubler,

rather than a frequency halver.

For what it is worth, I'm pretty sure that there is no analog

technique

that will halve the frequency of a sine wave. It is easy enough to

use

a largely digital circuit to produce a sine wave which follows half

the

average frequency of of an analogue sine wave, and if you got

really

cute, you could track the phase of the input sine wave and produce

an

output whose phase varied at half the rate - though since the

maxima

and minima of a sine wave don't tell you much about the

instantaneous

phase, this isn't going to be perfect either.

---------
Bill Sloman, Nijmegen


Incorrect; over 40 years ago we did that at Sylvania with a

tetrode.

See a previous response by me earlier in this thread.


You didn't halve the frequency of a sine wave, you used the input
frequency to excite a tuned circuit that was resonant at roughly half
the frequency of the input circuit, a much less direct relationship.

----------
Bill Sloman, Nijmegen

Correct, but the result is essentially the same.
And it will track frequency changes, apparently up to 10% and perhaps
allows AM to pass thru as well (this last part i do not remember; been
too long).

It must have been a synchronized oscillator. No tetrode [1] will have
an f/2 component of plate current when f is applied to a grid.

John

[1] except a thyratron, maybe.

 

[Rob Gaddi]

stevieboy01 wrote:

I may be very stupid for asking this, but is there a simple analogue
circuit in which I can input a frequency (currently 20kHz) and output
half the frequency?

Steve

20 kHz IN
.-----.
| G | ___
|_-_-_|-->|--|___|---o----.
| | | |
'-----' | | .-------------.
--- '- |VCC #OE|
--- | 10 kHz |
| | OSC | 10 kHz OUT
o-------'GND OUT'-----------
| '-------------'
|
===
GND
(created by AACircuit v1.28.5 beta 02/06/05 www.tech-chat.de)

Now then Stevie boy, our magical disappearing original poster, since at
this point you've failed to respond to assumptions ranging from the idea
that you plan to use this 20 kHz to transmit secured data to using said
20 kHz to toast bread, how about a little more information on why it is
that you would like to turn a perfectly good, potentially snappy little
20 kHz signal into a 10 kHz saunter? Is it a sine? Is it a square? Is
it a tiny leprechaun, dancing a tiny jig? Is it big? Small? Small,
but getting bigger, like current theories about the universe? Do you
know its duty cycle? Do you care about its duty cycle?

The usefulness of this thread will most likely continue to decline until
more data is provided.

-- Rob

 

[Robert Baer]

John Larkin wrote:

On Mon, 21 Mar 2005 06:25:25 GMT, Robert Baer
robertbaer@earthlink.net> wrote:


bill.sloman@ieee.org wrote:


Robert Baer wrote:


bill.sloman@ieee.org wrote:



Sorry John, but I think you have just described a frequency

doubler,


rather than a frequency halver.

For what it is worth, I'm pretty sure that there is no analog

technique


that will halve the frequency of a sine wave. It is easy enough to

use


a largely digital circuit to produce a sine wave which follows half

the


average frequency of of an analogue sine wave, and if you got

really


cute, you could track the phase of the input sine wave and produce

an


output whose phase varied at half the rate - though since the

maxima


and minima of a sine wave don't tell you much about the

instantaneous


phase, this isn't going to be perfect either.

---------
Bill Sloman, Nijmegen


Incorrect; over 40 years ago we did that at Sylvania with a

tetrode.


See a previous response by me earlier in this thread.


You didn't halve the frequency of a sine wave, you used the input
frequency to excite a tuned circuit that was resonant at roughly half
the frequency of the input circuit, a much less direct relationship.

----------
Bill Sloman, Nijmegen


Correct, but the result is essentially the same.
And it will track frequency changes, apparently up to 10% and perhaps
allows AM to pass thru as well (this last part i do not remember; been
too long).



It must have been a synchronized oscillator. No tetrode [1] will have
an f/2 component of plate current when f is applied to a grid.

John

[1] except a thyratron, maybe.


I did not describe that.

I said that the plate was at ground, and that the input signal was
applied to the plate.
I also said that the power was extracted at negative gain from the
grid, and that the second grid was at about 30V.
The cathode, grid #1 are set up as a hartley (or colpitts)
oscillator; grid #2 acts as the plate and is powered so the oscillator
section is a bit under oscillation - ersonant frequency is one-half (ie:
subharmonic of input).
Please read what i originally described.

 

[Rob Gaddi]

Robert Baer wrote:

Rob Gaddi wrote:

20 kHz IN
.-----.
| G | ___
|_-_-_|-->|--|___|---o----.
| | | |
'-----' | | .-------------.
--- '- |VCC #OE|
--- | 10 kHz |
| | OSC | 10 kHz OUT
o-------'GND OUT'-----------
| '-------------'
|
===
GND

The usefulness of this thread will most likely continue to decline
until more data is provided.

-- Rob

I like your non-converter!

It's actually a hell of a circuit. In addition to providing near exact
frequency halving of a 20 kHz input signal, it's highly immune to phase
noise and jitter on the input. In fact, if you're a little bit off on
the frequency of your input signal, it even corrects for it and still
gives you the same output. For that matter, even if you're fairly far
off on that 20 kHz the results remain much the same.

 

No, elderly homo netherlandalis is equally unemployable - if anything,
fluency in English is an advantage.

The ideal Dutch employee is a cheap, biddable 17-year-old with forty
years of experience, but they aren't all that serious about the
experience.

----------
Bill Sloman, Nijmegen

 

[Jamie]

bill.sloman@ieee.org wrote:

No, elderly homo netherlandalis is equally unemployable - if anything,
fluency in English is an advantage.

The ideal Dutch employee is a cheap, biddable 17-year-old with forty
years of experience, but they aren't all that serious about the
experience.

----------
Bill Sloman, Nijmegen

hmm,lets see, 17 year olds with forty years of experience, did i get

that correct?
i know i am not very good at math, but this one is throwing me off.

or has the Dutch got some form of medical science of transferring
brands from oldies into teen bodies.

 

[Rich Grise]

On Fri, 18 Mar 2005 14:33:57 -0800, Winfield Hill wrote:

bill.sloman@ieee.org wrote...

The problem with the Dutch employment market is that they don't like
giving jobs to people over the age of about 45.

Of the 17,000 people over 57.5 who were drawing unemployment benefit
last year, about 250 succeeded in finding work - about 1.5%. We've all
got to apply for a job every week to hang onto our unemployment benefit,
which means that the employment agencies throw away 17,000 job
applications every week. Those of us who actually want to find a job
suspect that the agencies just scan the CVs for dates earlier than 1950,
and throw anything including an earlier date.

They don't admit this - it would be against the (unenforced) law - so
they look for very specific experience, or invent specious reservations
if you bother going after them.

That's a universal problem these days, where it's likely the person
making the hiring decisions is much younger and nervous or predudiced
about hiring someone his father's age.

I've said it here before, the answer is to start your own company (and
only hire older folks, starting with yourself, of course). That'll solve
the problem, and you might even have a good time.

I got that part down pat - the stumbling block for me seems to be getting
actual customers. ;-)

Thanks,
Rich

 

[Robert Baer]

Rob Gaddi wrote:

stevieboy01 wrote:

I may be very stupid for asking this, but is there a simple analogue
circuit in which I can input a frequency (currently 20kHz) and output
half the frequency?

Steve


20 kHz IN
.-----.
| G | ___
|_-_-_|-->|--|___|---o----.
| | | |
'-----' | | .-------------.
--- '- |VCC #OE|
--- | 10 kHz |
| | OSC | 10 kHz OUT
o-------'GND OUT'-----------
| '-------------'
|
===
GND
(created by AACircuit v1.28.5 beta 02/06/05 www.tech-chat.de)

Now then Stevie boy, our magical disappearing original poster, since at
this point you've failed to respond to assumptions ranging from the idea
that you plan to use this 20 kHz to transmit secured data to using said
20 kHz to toast bread, how about a little more information on why it is
that you would like to turn a perfectly good, potentially snappy little
20 kHz signal into a 10 kHz saunter? Is it a sine? Is it a square? Is
it a tiny leprechaun, dancing a tiny jig? Is it big? Small? Small,
but getting bigger, like current theories about the universe? Do you
know its duty cycle? Do you care about its duty cycle?

The usefulness of this thread will most likely continue to decline until
more data is provided.

-- Rob
I like your non-converter!

 

[Robert Baer]

Rob Gaddi wrote:

Robert Baer wrote:

Rob Gaddi wrote:


20 kHz IN
.-----.
| G | ___
|_-_-_|-->|--|___|---o----.
| | | |
'-----' | | .-------------.
--- '- |VCC #OE|
--- | 10 kHz |
| | OSC | 10 kHz OUT
o-------'GND OUT'-----------
| '-------------'
|
===
GND


The usefulness of this thread will most likely continue to decline
until more data is provided.

-- Rob


I like your non-converter!


It's actually a hell of a circuit. In addition to providing near exact
frequency halving of a 20 kHz input signal, it's highly immune to phase
noise and jitter on the input. In fact, if you're a little bit off on
the frequency of your input signal, it even corrects for it and still
gives you the same output. For that matter, even if you're fairly far
off on that 20 kHz the results remain much the same.
Too bad you forgot to patent it; with the right marketing one could

sell it for a few million or so...

 

[John Woodgate]

I read in sci.electronics.design that Jamie
<jamie_5_not_valid_after_5_Please@charter.net> wrote (in
<Ze_%d.6671$Ol6.1781@fe06.lga&gt about 'Frequency Halver', on Tue, 22 Mar
2005:

hmm,lets see, 17 year olds with forty years of experience, did i get
that correct?
i know i am not very good at math, but this one is throwing me off.

or has the Dutch got some form of medical science of transferring
brands from oldies into teen bodies.

It's only a slight exaggeration. I recall a couple of years ago, someone

reporting a want ad for someone with 5 years of experience with Windows
XP.

The HR people and headhunters who write these ads are definitely from
the planet Zog.
--
Regards, John Woodgate, OOO - Own Opinions Only.
There are two sides to every question, except
'What is a Moebius strip?'
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk