Square + triangle = sine (almost)

On Mar 9, 9:38 pm, "JosephKK"<quiettechb...@yahoo.com> wrote:

Just to be off the wall, what is the integral of a triangle wave?
How about the second and third integrals?

To close the loop and make an oscillator, using a square wave
from a Schmitt trigger, one can use one stage of integration
(to a triangle wave) or three, but not two.  Two stages
gets to a double-parabola, three stages to a double-cubic.
The double-cubic has its small pointy defect at the crest
as does the triangle wave.

The three-stage thing is called a phase shift oscillator if you make
it without the Schmitt trigger part.

Alas, those all require multiple-gang variable resistors instead of a
single knob to adjust.  Have you ever priced a good three-gang
pot?   Or capacitor, for that matter?

MooseFET wrote:
On Mar 9, 8:36 pm, Bitrex <bit...@de.lete.earthlink.net> wrote:
Jim Thompson wrote:
On Tue, 09 Mar 2010 10:10:26 -0500, Phil Hobbs
pcdhSpamMeSensel...@electrooptical.net> wrote:
On 3/9/2010 9:59 AM, Jim Thompson wrote:
On Mon, 08 Mar 2010 21:42:22 -0800,
"JosephKK"<quiettechb...@yahoo.com>  wrote:
On Mon, 08 Mar 2010 09:25:15 -0700, Jim Thompson<To-Email-Use-The-Envelope-I...@My-Web-Site.com>  wrote:
On Mon, 08 Mar 2010 00:01:44 -0800, Muzaffer Kal<k...@dspia.com
wrote:
On Sun, 07 Mar 2010 23:11:20 -0800,
"JosephKK"<quiettechb...@yahoo.com>  wrote:
On Sat, 6 Mar 2010 20:21:10 -0800, D from BC<myrealaddr...@comic.com>  wrote:
In article<4b9324ee.4432...@news.tpg.com.au>, rontan...@esterbrook.com
says...
On Sun, 7 Mar 2010 14:31:48 +1100, "Phil Allison"<phi...@tpg.com.au
wrote:
"Harold Larsen"
If a squarewave contains all odd harmonics of the fundamental
frequency, and a triangle all even,
**  Sorry  -   that is  WRONG .
A triangle wave contains only odd harmonics too.
http://en.wikipedia.org/wiki/Triangle_wave
A "sawtooth" wave contains all integer harmonics.
OK thanks for the pull-up, but how about using a triangle-square wave
mix, in place of a filter, to simulate a sinewave .
I have not seen that method applied or described anywhere, but it
makes a fair approximation, at least to my eye.
Harold Larsen
This reminds of the XR2206 chip that makes square, triangle and sine
using analog technology.
Sure enough, as does the ICL8038.  Part of the question is how it is done.
The datasheet athttp://www.intersil.com/data/FN/FN2864.pdfhasa
pretty good schematic and explanation which  shows how it's done.
Yep.  "Piecewise-Linear", aka break-point analysis... taught in better
engineering schools
                                        ...Jim Thompson
I first saw it in a synchro to digital converter about 1973.  I had to think
hard for a while before i "got" it.
The only place I can remember using it in an actual product was for
linearizing a flat-face CRT sweep (RADAR)... and there it was
piecewise _curve_ fitting.
                                         ...Jim Thompson
Breakpoint amps are nearly always a crutch.  One poor guy I tried to
help (15 years back) ignored my advice and wound up with a multi-diode
breakpoint amp stuck inside a crystal oven to keep the breakpoints from
going all over the place with temperature.  Blech.  (It was in a fancy
measurement system, too.  Got all sorts of industry awards.)
The Widlar approach (National AN4, Figure uses BJT saturation to make
nice sharp breakpoints that don't drift much.  Of course you have to
wait for the transistor to come out of saturation.
About the only good use of breakpoint amps I've seen is inside
complicated FB loops, e.g. to approximately correct for the nonlinearity
of VCOs and heaters.  This reduces the variation of loop gain and so
makes frequency compensation easier.  Drift and inaccuracy are not a big
problem in those sorts of applications.
Cheers
Phil Hobbs
Ah, yes!  Thanks for the reminder!  I also linearized a frequency
hopping VCO for OmniSpectra _many_ years ago... for jumping close to
desired frequency, so the PLL lock was faster... a cavity beast
I would never use _just_ diodes, rather use them with OpAmps or
comparators, such as...
http://analog-innovations.com/SED/ClampForLarkin.pdf
(A Christmas gift, 2007. But he remains a cranky old git
http://analog-innovations.com/SED/LevelDetectAndFollow-LM339.pdf
http://analog-innovations.com/SED/LevelDetectAndFollow-TL431.pdf
http://analog-innovations.com/SED/PerfectDiodeForChargerIsolation.pdf
                                        ...Jim Thompson
The first schematic looks like the start of a decent guitar fuzzbox
pedal!  I think one could set more breakpoints with different slopes by
using more comparators with the breakpoint voltage on the non inverting
inputs and putting resistors in series with the diodes, right?

Back before guitar practice amps with DSP became commodity hardware,
Peavey had a patented technology called "TransTube" that purported to
make a solid state amp have a tone more like a tube amp.  I wonder if
they used a similar piecewise linear technique to make the amp have a
softer clipping characteristic.

At lowish frequencies, you can do this:

        ---------------------------------------/\/\---+----Out
       !                                              !
       +-----------------/\/\----+-/\/\---+---/\/\----+
       !                         !        !           !
       !                          --!-\   !           !
 In ---+--------!+\                 !  >--            !
                !  >---+--/\/\--+---!+/               !
              --!-/    !        !                     !
             !         !         ---/\/\--GND         !
  GND--/\/\--+--/\/\---+------------------------/\/\--

With rail to rail op-amps, you can get a total of 6 knees from Vee to
Vcc in the output
swing.

I'm having trouble following that circuit - it looks clever, but how
does it work?

On Mar 10, 1:50 am, Bitrex<bit...@de.lete.earthlink.net> wrote:
MooseFET wrote:
On Mar 9, 8:36 pm, Bitrex<bit...@de.lete.earthlink.net> wrote:
Jim Thompson wrote:
On Tue, 09 Mar 2010 10:10:26 -0500, Phil Hobbs
pcdhSpamMeSensel...@electrooptical.net> wrote:
On 3/9/2010 9:59 AM, Jim Thompson wrote:
On Mon, 08 Mar 2010 21:42:22 -0800,
"JosephKK"<quiettechb...@yahoo.com> wrote:
On Mon, 08 Mar 2010 09:25:15 -0700, Jim Thompson<To-Email-Use-The-Envelope-I...@My-Web-Site.com> wrote:
On Mon, 08 Mar 2010 00:01:44 -0800, Muzaffer Kal<k...@dspia.com
wrote:
On Sun, 07 Mar 2010 23:11:20 -0800,
"JosephKK"<quiettechb...@yahoo.com> wrote:
On Sat, 6 Mar 2010 20:21:10 -0800, D from BC<myrealaddr...@comic.com> wrote:
In article<4b9324ee.4432...@news.tpg.com.au>, rontan...@esterbrook.com
says...
On Sun, 7 Mar 2010 14:31:48 +1100, "Phil Allison"<phi...@tpg.com.au
wrote:
"Harold Larsen"
If a squarewave contains all odd harmonics of the fundamental
frequency, and a triangle all even,
** Sorry - that is WRONG .
A triangle wave contains only odd harmonics too.
http://en.wikipedia.org/wiki/Triangle_wave
A "sawtooth" wave contains all integer harmonics.
OK thanks for the pull-up, but how about using a triangle-square wave
mix, in place of a filter, to simulate a sinewave .
I have not seen that method applied or described anywhere, but it
makes a fair approximation, at least to my eye.
Harold Larsen
This reminds of the XR2206 chip that makes square, triangle and sine
using analog technology.
Sure enough, as does the ICL8038. Part of the question is how it is done.
The datasheet athttp://www.intersil.com/data/FN/FN2864.pdfhasa
pretty good schematic and explanation which shows how it's done.
Yep. "Piecewise-Linear", aka break-point analysis... taught in better
engineering schools
...Jim Thompson
I first saw it in a synchro to digital converter about 1973. I had to think
hard for a while before i "got" it.
The only place I can remember using it in an actual product was for
linearizing a flat-face CRT sweep (RADAR)... and there it was
piecewise _curve_ fitting.
...Jim Thompson
Breakpoint amps are nearly always a crutch. One poor guy I tried to
help (15 years back) ignored my advice and wound up with a multi-diode
breakpoint amp stuck inside a crystal oven to keep the breakpoints from
going all over the place with temperature. Blech. (It was in a fancy
measurement system, too. Got all sorts of industry awards.)
The Widlar approach (National AN4, Figure uses BJT saturation to make
nice sharp breakpoints that don't drift much. Of course you have to
wait for the transistor to come out of saturation.
About the only good use of breakpoint amps I've seen is inside
complicated FB loops, e.g. to approximately correct for the nonlinearity
of VCOs and heaters. This reduces the variation of loop gain and so
makes frequency compensation easier. Drift and inaccuracy are not a big
problem in those sorts of applications.
Cheers
Phil Hobbs
Ah, yes! Thanks for the reminder! I also linearized a frequency
hopping VCO for OmniSpectra _many_ years ago... for jumping close to
desired frequency, so the PLL lock was faster... a cavity beast
I would never use _just_ diodes, rather use them with OpAmps or
comparators, such as...
http://analog-innovations.com/SED/ClampForLarkin.pdf
(A Christmas gift, 2007. But he remains a cranky old git
http://analog-innovations.com/SED/LevelDetectAndFollow-LM339.pdf
http://analog-innovations.com/SED/LevelDetectAndFollow-TL431.pdf
http://analog-innovations.com/SED/PerfectDiodeForChargerIsolation.pdf
...Jim Thompson
The first schematic looks like the start of a decent guitar fuzzbox
pedal! I think one could set more breakpoints with different slopes by
using more comparators with the breakpoint voltage on the non inverting
inputs and putting resistors in series with the diodes, right?

Back before guitar practice amps with DSP became commodity hardware,
Peavey had a patented technology called "TransTube" that purported to
make a solid state amp have a tone more like a tube amp. I wonder if
they used a similar piecewise linear technique to make the amp have a
softer clipping characteristic.

At lowish frequencies, you can do this:

---------------------------------------/\/\---+----Out
! !
+-----------------/\/\----+-/\/\---+---/\/\----+
! ! ! !
! --!-\ ! !
In ---+--------!+\ !>-- !
!>---+--/\/\--+---!+/ !
--!-/ ! ! !
! ! ---/\/\--GND !
GND--/\/\--+--/\/\---+------------------------/\/\--

With rail to rail op-amps, you can get a total of 6 knees from Vee to
Vcc in the output
swing.

I'm having trouble following that circuit - it looks clever, but how
does it work?

Start with Vin = 0
Both op-amps are working normally.
A small change in Vin is given gain as it goes towards output

Increase Vin and at some point the 2nd op-amp hits the rail.
Now the gain is less.

Increase Vin and the 1st opamp hits the rail.
Now the gain is even lower.

Increase Vin and the (-) input of the 2nd opamp is going up
to where the 2nd opamp comes off the rail and swings downwards
The gain is further reduced.

The same works in the other direction.

At lowish frequencies, you can do this:

         ---------------------------------------/\/\---+----Out
        !                                              !
        +-----------------/\/\----+-/\/\---+---/\/\----+
        !                         !        !           !
        !                          --!-\   !           !
  In ---+--------!+\                 ! >--            !
                 ! >---+--/\/\--+---!+/               !
               --!-/    !        !                     !
              !         !         ---/\/\--GND         !
   GND--/\/\--+--/\/\---+------------------------/\/\--

With rail to rail op-amps, you can get a total of 6 knees from Vee to
Vcc in the output
swing.

Plessey used to sell packaged RF amps that worked a bit like that--they
were meant to be cascaded to form logarithmic IF strips.  They had a
gain of 10 dB for small signals, dropping to 0 dB when they saturated.
With a string of them in series, upping the signal input by 10 dB railed
another amplifier, and so reduced the overall gain by 10 dB.

That way, the differential gain was dVout/dVin ~ 1/Vin, which makes it
approximately logarithmic.  These were different from the usual
successive-detection DLVAs, because they actually performed logarithmic
compression on the RF, not just the detected signal.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal
ElectroOptical Innovations
55 Orchard Rd
Briarcliff Manor NY 10510
845-480-2058
hobbs at electrooptical dot nethttp://electrooptical.net

On Mar 10, 7:32 pm, Phil Hobbs
pcdhSpamMeSensel...@electrooptical.net> wrote:
[....]
At lowish frequencies, you can do this:

---------------------------------------/\/\---+----Out
! !
+-----------------/\/\----+-/\/\---+---/\/\----+
! ! ! !
! --!-\ ! !
In ---+--------!+\ !>-- !
!>---+--/\/\--+---!+/ !
--!-/ ! ! !
! ! ---/\/\--GND !
GND--/\/\--+--/\/\---+------------------------/\/\--

With rail to rail op-amps, you can get a total of 6 knees from Vee to
Vcc in the output
swing.

[....]
Plessey used to sell packaged RF amps that worked a bit like that--they
were meant to be cascaded to form logarithmic IF strips. They had a
gain of 10 dB for small signals, dropping to 0 dB when they saturated.
With a string of them in series, upping the signal input by 10 dB railed
another amplifier, and so reduced the overall gain by 10 dB.

That way, the differential gain was dVout/dVin ~ 1/Vin, which makes it
approximately logarithmic. These were different from the usual
successive-detection DLVAs, because they actually performed logarithmic
compression on the RF, not just the detected signal.

I have often thought that the same sort of thing would be good in an
FM IF
strip. In that case, the 3rd power part of the series is what does
the most
to remove the noise. The odd numbered terms are less effective. As a
result,
it would be very nice to be able to make the limiting stage have the
right
amount of 3rd power and less of all the others.

On 3/11/2010 9:10 AM, MooseFET wrote:
On Mar 10, 7:32 pm, Phil Hobbs
pcdhSpamMeSensel...@electrooptical.net> wrote:
[....]
At lowish frequencies, you can do this:

---------------------------------------/\/\---+----Out
! !
+-----------------/\/\----+-/\/\---+---/\/\----+
! ! ! !
! --!-\ ! !
In ---+--------!+\ !>-- !
!>---+--/\/\--+---!+/ !
--!-/ ! ! !
! ! ---/\/\--GND !
GND--/\/\--+--/\/\---+------------------------/\/\--

With rail to rail op-amps, you can get a total of 6 knees from Vee to
Vcc in the output
swing.

[....]
Plessey used to sell packaged RF amps that worked a bit like that--they
were meant to be cascaded to form logarithmic IF strips. They had a
gain of 10 dB for small signals, dropping to 0 dB when they saturated.
With a string of them in series, upping the signal input by 10 dB railed
another amplifier, and so reduced the overall gain by 10 dB.

That way, the differential gain was dVout/dVin ~ 1/Vin, which makes it
approximately logarithmic. These were different from the usual
successive-detection DLVAs, because they actually performed logarithmic
compression on the RF, not just the detected signal.

I have often thought that the same sort of thing would be good in an
FM IF
strip. In that case, the 3rd power part of the series is what does
the most
to remove the noise. The odd numbered terms are less effective. As a
result,
it would be very nice to be able to make the limiting stage have the
right
amount of 3rd power and less of all the others.


If you use an FM detector that's insensitive to AM, e.g. a wideband PLL,
it'll work better than a limiter at low SNR. Essentially all reasonable
demodulation schemes work equivalently at high SNR, where the AM and PM
fluctuations are linear functions of the additive noise amplitude.

At low SNR, limiters start suppressing the signal in favour of the
noise. That leads to dropouts--periods during which the signal
disappears and only the noise is left--which really set the threshold
for detection. PLLs using wideband AGC instead of limiting don't
exhibit threshold, although the detected signal does get noisier as the
SNR declines. (You need the AGC to keep the loop bandwidth reasonably
constant.)

The Plessey scheme can be thought of as a kind of ultrawideband AGC, I
suppose--as long as the compression comes after the narrowest IF filter,
it should be nearly equivalent.

The only other problem there would be AM-PM conversion. Most kinds of
amplifiers slow down when you rail them, which leads to phase errors.
(The good news for FM is that this needs only a 1-D calibration, instead
of 2-D as in I/Q schemes.)

Cheers

Phil Hobbs