terminology : phase

[JohnDenker]

Minor point: In section 32.5 on page 859 in connection with equation 32.16, the variable ϕ is conventionally called the phase. I've never heard anybody call it the "phase constant" nor can I imagine any good reason for doing so. It's just the phase.

By way of analogy, you wouldn't call I the "amplitude constant" and you wouldn't call ω the "frequency constant".

[ericmazur]

I did this to avoid confusion with the argument of the sine (or cosine) which is often called "phase". As you said it is a bad idea to use the same name for two different things. An alternative would be to call it "initial phase". Not sure anymore why I decided against that -- I thought about it a long time, and reversed my decision several times. When I'm back in the US I can look up my notes.

Eric Mazur Harvard University Area Dean of Applied Physics Balkanski Professor of Physics and of Applied Physics

Vice President, Optical Society of America

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On Nov 27, 2015, at 9:27 PM, JohnDenker notifications@github.com wrote:

Minor point: In section 32.5 on page 859 in connection with equation 32.16, the variable ϕ is conventionally called the phase. I've never heard anybody call it the "phase constant" nor can I imagine any good reason for doing so. It's just the phase.

By way of analogy, you wouldn't call I the "amplitude constant" and you wouldn't call ω the "frequency constant".

— Reply to this email directly or view it on GitHub.

[JohnDenker]

OK, good point. I agree that the term "phase" is ambiguous.

The problem runs deeper than terminology. The deeper problem is that there are three different _concepts_ that are similar enough to be deceptive yet different enough to cause problems. Suppose we write ϕ(t) = ωt + ϕ₀ Then we might care about:

1. ϕ₀, and/or
2. ϕ(t), and/or
3. ϕ(t) mod 2π.

Giving the same name ("phase") to all three concepts exacerbates the problem. Using the same conventional symbol (ϕ) for all three concepts further exacerbates the problem.

You mentioned "initial phase" which is consistent with the approach outlined above. If you are content with that concept then I suggest:

• avoiding the unadorned symbol ϕ entirely
• defining ϕ(t) to be the phase at time t, aka the total phase
• using ϕ₀ to represent the phase at time t=0 ... i.e. ϕ₀ ≡ ϕ(0)
• adding a footnote to explain that the literature is inconsistent. Sometimes "the" phase refers to ϕ₀ [i.e. the phase at time t=0, aka the initial phase], sometimes to ϕ(t) [aka the total phase], and sometimes to ϕ(t) mod 2π [aka the reduced phase]. Sometimes these distinctions doesn't matter, but sometimes they do.

I can see that there might be drawbacks to calling ϕ₀ the "initial" phase. However, calling it the phase "at time t=0" seems completely unambiguous.

Certainly calling ϕ₀ the "phase constant" is problematic, because (a) it is nonstandard terminology, (b) ϕ₀ doesn't have to be a constant, and (c) it doesn't explain the concept, i.e. it doesn't say what is the problem we are trying to solve.

[JohnDenker]

Here are some reasons why people can "usually" get away with being ambiguous:

1) At least 99 times out of 100, especially in introductory courses, we are comparing one signal with another. The frequency is the same for both, and the time is the same for both.

Therefore Δϕ(t) = Δϕ₀ = Δϕ = the "relative" phase.

Furthermore usually the reference is obvious or well-standardized, in which case we can drop the Δ and drop the word relative, and just call it "the" phase.

Examples include the the phase and amplitude of the gain function. This includes the overall gain (final output versus original input) as well as various other gains (including loop gain, open-loop gain, and closed-loop gain in a feedback system).

2a) When using phasors, the ωt contribution has already been factored out, so ϕ(t) = ϕ₀ = ϕ = "the" phase of the phasor.

2b) As another example of the same kind, in NMR and ESR one typically works in the rotating frame, so once again the ωt contribution has already been factored out. Once again ϕ(t) = ϕ₀ = ϕ = "the" phase.

The more I think about it the more I like defining the total phase as ϕ(t) = ωt + ϕ₀ in general. Then in special cases we can drop the subscript zero, if-and-when we are sure it doesn't matter.

[JohnDenker]

While we are in the vicinity: The minus sign in the definition of phase in equation 32.16 is non-standard. It looks like a bad idea to me. I am not persuaded by the explanation in the associated text.

Again I recommend defining the total phase to be

       ϕ(t) = ωt + ϕ₀

That means that for positive frequency, the phase angle increases with increasing time and/or with increasing ϕ₀.

Compare standard usage e.g. http://www.ittc.ku.edu/~jstiles/622/handouts/Phase%20and%20Frequency.pdf https://faculty.unlv.edu/eelabs/docs/labs/cpe400L/ee400L_13_exp3.pdf https://web2.ph.utexas.edu/~shih/interference%20and%20diffraction.pdf http://www.ele.uri.edu/courses/ele436/FM_mod_demod_lab/AnalysisoftheFMspectrum.pdf

Those are the first four examples I came across. They all used the plus sign. I didn't find any counterexamples.

Furthermore, the minus sign makes it impossible to interpret ϕ₀ as the "initial" phase.