# Trigonometry terminology

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Phil Hobbs
Guest

Mon Feb 11, 2019 5:45 pm

On 2/10/19 1:58 PM, Joseph Gwinn wrote:
Quote:
On Feb 6, 2019, Don Kuenz wrote
(in article <20190206a_at_crcomp.net>):

bloggs.fredbloggs.fred_at_gmail.com wrote:
On Wednesday, February 6, 2019 at 11:09:01 AM UTC-5, Jeroen Belleman wrote:
Do we have a handy term to say that two sinusoidal waves
of equal frequency differ only by amplitude and phase?
I would say 'correlated', but would that be the most
common term?

Jeroen Belleman

Those types of signals are called coherent. It is a very broad area of
study, but, when you say coherent sine waves, the people who know the
field will understand it to mean exactly what you describe.

Yes indeed. My _IEEE Dictionary_ says it this way:

coherent (1) (fiber optics). Characterized by a fixed phase relationship
between points on an electromagnetic wave. Note: A truly monochromatic
wave would be perfectly coherent at all points in space. In practice,
however, the region of high coherence may extend only a finite distance.

Thank you, 73,

_Coherent_ is correct, and it applies to reference signals generated from one
another by frequency multiplication or division. The key is that the ratio of
the rates of phase advance is constant. In the case of a signal and a
frequency-doubled (or -halved) version of the same signal, that ratio is
exactly two.

All correlated signals are coherent, but not all coherent signals are
correlated. A signal and a frequency doubled version of that signal are
coherent, but are uncorrelated.

The original definition of coherent was simply that coherent beams of light
could be made to interfere and cancel. This was subsequently expanded to
handle such things as frequency-doubled light.

Useful ref: "A unifying view of coherence in signal processing", William A.
Gardner, Signal Processing, Volume 29 Issue 2, Nov. 1992, Pages 113 - 140.

Joe Gwinn

That's too restrictive a definition. For instance, I've built coherent
detection systems with offset frequencies as high as 8 GHz. (That one
was a homodyne interferometer for detecting submicron tin droplets
moving at up to 3 km/s [Mach 9].)

The basic definition of optical coherence is the ability to form
fringes. The fringes don't have to stay still. I took Joe Goodman's
statistical optics class long ago, and his book is an excellent read:
<https://www.amazon.com/exec/obidos/asin/1119009456>.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

Guest

Mon Feb 11, 2019 8:45 pm

Have you ever used a delay line discriminatory to measure oscillator phase noise ? It can only be used to see phase noise a fair distance from the carrier

Phil Hobbs
Guest

Mon Feb 11, 2019 10:45 pm

On 2/11/19 2:10 PM, bulegoge_at_columbus.rr.com wrote:
Quote:
Have you ever used a delay line discriminatory to measure oscillator
phase noise ? It can only be used to see phase noise a fair distance
from the carrier

Yup. The first engineering thing I ever built for hire was a 12-GHz
cavity discriminator, which I still have. It was built for measuring
close-in phase noise. Eventually we got an HP 8566A, so we didn't need
the discriminator any more.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
https://hobbs-eo.com

Joseph Gwinn
Guest

Tue Feb 12, 2019 4:45 am

On Feb 11, 2019, Phil Hobbs wrote
(in article <q3s5us\$v50\$1_at_dont-email.me>):

Quote:
On 2/10/19 1:58 PM, Joseph Gwinn wrote:
On Feb 6, 2019, Don Kuenz wrote
(in article <20190206a_at_crcomp.net>):

bloggs.fredbloggs.fred_at_gmail.com wrote:
On Wednesday, February 6, 2019 at 11:09:01 AM UTC-5, Jeroen Belleman
wrote:
Do we have a handy term to say that two sinusoidal waves
of equal frequency differ only by amplitude and phase?
I would say 'correlated', but would that be the most
common term?

Jeroen Belleman

Those types of signals are called coherent. It is a very broad area of
study, but, when you say coherent sine waves, the people who know the
field will understand it to mean exactly what you describe.

Yes indeed. My _IEEE Dictionary_ says it this way:

coherent (1) (fiber optics). Characterized by a fixed phase relationship
between points on an electromagnetic wave. Note: A truly monochromatic
wave would be perfectly coherent at all points in space. In practice,
however, the region of high coherence may extend only a finite distance.

Thank you, 73,

_Coherent_ is correct, and it applies to reference signals generated from
one
another by frequency multiplication or division. The key is that the ratio
of
the rates of phase advance is constant. In the case of a signal and a
frequency-doubled (or -halved) version of the same signal, that ratio is
exactly two.

All correlated signals are coherent, but not all coherent signals are
correlated. A signal and a frequency doubled version of that signal are
coherent, but are uncorrelated.

The original definition of coherent was simply that coherent beams of light
could be made to interfere and cancel. This was subsequently expanded to
handle such things as frequency-doubled light.

Useful ref: "A unifying view of coherence in signal processing", William A.
Gardner, Signal Processing, Volume 29 Issue 2, Nov. 1992, Pages 113 - 140.

Joe Gwinn

That's too restrictive a definition. For instance, I've built coherent
detection systems with offset frequencies as high as 8 GHz. (That one
was a homodyne interferometer for detecting submicron tin droplets
moving at up to 3 km/s [Mach 9].)

We do this kind of thing all the time in radar, and we would consider this a

But we would not claim that the doppler was coherent in the same sense as we
use for reference signal generation. Even though the whole radar is
frequency terms, although phase is nonetheless lurking below. There is a
implied distinction in there somewhere.

Quote:

The basic definition of optical coherence is the ability to form
fringes. The fringes don't have to stay still. I took Joe Goodman's
statistical optics class long ago, and his book is an excellent read:
https://www.amazon.com/exec/obidos/asin/1119009456>.

Forming fringes is exactly what happens when interference leads to
cancellation, so that part is the same. That definition sounds awfully like a
moire beat note, but another angle is always good. IŽll read the book.

Joe Gwinn

Guest

Tue Feb 12, 2019 1:45 pm

On Monday, February 11, 2019 at 4:02:43 PM UTC-5, Phil Hobbs wrote:
Quote:
On 2/11/19 2:10 PM, bulegoge_at_columbus.rr.com wrote:
Have you ever used a delay line discriminatory to measure oscillator
phase noise ? It can only be used to see phase noise a fair distance
from the carrier

Yup. The first engineering thing I ever built for hire was a 12-GHz
cavity discriminator, which I still have. It was built for measuring
close-in phase noise. Eventually we got an HP 8566A, so we didn't need
the discriminator any more.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
https://hobbs-eo.com

Was the cavity used to provide the delay?

Guest

Tue Feb 12, 2019 4:45 pm

Quote:
Yup. Â The first engineering thing I ever built for hire was a 12-GHz
cavity discriminator, which I still have. Â It was built for measuring
close-in phase noise. Â Eventually we got an HP 8566A, so we didn't need
the discriminator any more.

Was the cavity used to provide the delay?

Sort of. It used the cavity to make a 90-degree phase shift. IIRC it used a circulator and a coax mixer, so we tuned it to null the DC, which also gets rid of most of the AM noise as well.

A high-Q resonator has a higher phase slope (d phi/df) than any feasible length of coax.

An unbalanced Mach-Zehnder interferometer is also a delay discriminator.

Cheers

Phil Hobbs

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