X and R channels

[Repwoc]

I'm trying to get my head round the X & R channels theory. In ITMD2 p.70 in the section headed "Phase Demodulation" there are some equations:

X = Acosθ (eq. 7-1)
R = Asinθ (eq. 7-2)

Could someone define what "A" and "θ" are in this context? They aren't defined in the text and so I've been trying to reverse-engineer to deduce what they are but as I'm trying to learn this stuff reverse-engineering it is ambiguous. "θ" is fairly ubiquitous in meaning an angle, but which one? "A" could mean another angle, or something else - amplitude?

Anyway if someone could put me out of my misery I'd be grateful.

paul

[Altra]

Google Inverse Trigonometry. A= ARC

[Carl-NC]

Target receive signals have some amplitude (A) and some phase (θ) relative to the transmit signal. To extract these we use quadrature demodulation to get an X and R voltage value and then compute A = sqrt(X²+R²) and θ = arctan(R/X).

Here are 5 targets that all show the same amplitude (A) but different phases. Phases are backwards from normal trig; ferrite is 0°, foil is 95°, and the silver quarter is 155°.

[Repwoc]

Google Inverse Trigonometry. A= ARC

OK - I'm not convinced by that.

1. A few equations further down (7-5), arctan is spelled out fully (ie "arctan" not "Atan"). Why would the style change from one equation to the next?
2. In equation 7-4, the A term is eliminated when R is divided by X, (R/X = Asinθ/Acosθ = sinθ/cosθ).

I suppose that since A is eliminated in a subsequent step then its meaning is academic. I'd still like to know what it is, however.

[Repwoc]

Target receive signals have some amplitude (A) and some phase (θ) relative to the transmit signal. To extract these we use quadrature demodulation to get an X and R voltage value and then compute A = sqrt(X²+R²) and θ = arctan(R/X).

Here are 5 targets that all show the same amplitude (A) but different phases. Phases are backwards from normal trig; ferrite is 0°, foil is 95°, and the silver quarter is 155°.

Thanks! I guess that image is from your new book?

Just going to read up on quadrature demodulation now. :-)

[Carl-NC]

Thanks! I guess that image is from your new book?

Yes, and quadrature demodulation is covered extensively.

[Altra]

OK - I'm not convinced by that.

1. A few equations further down (7-5), arctan is spelled out fully (ie "arctan" not "Atan"). Why would the style change from one equation to the next?
2. In equation 7-4, the A term is eliminated when R is divided by X, (R/X = Asinθ/Acosθ = sinθ/cosθ).

I suppose that since A is eliminated in a subsequent step then its meaning is academic. I'd still like to know what it is, however.

I stand corrected, some programming languages use atan, asin and acos for inverse functions. That's my reference for being wrong.

[Repwoc]

I stand corrected, some programming languages use atan, asin and acos for inverse functions. That's my reference for being wrong.

Actually when I read your post I thought "jeez why didn't I think of that?" but then it didn't fit with the following text.

[Altra]

I didn't have any context and made a sloppy post. Carl wrote the book, A is for voltage amplitude, post #3

[Carl-NC]

It is confusing, and it's my fault. I should have used A·cos(θ) instead of Acos(θ).