Question about phase reversal...

[vadoom]

Put the schematics down for a second Rob, and explain to me how in a situation of DC offset that phase inversion is identical to polarity inversion. Explain where that original diagram I had of the three sine waves is incorrect. Put another way, pick up the math and show me how the math describing both of the processes is results in the same solutions regardless of the input values. Because I just don't see how that is possible.

Polarity inversion is simply a change in sign. Phase inversion is not. Phase inversion is a change in relative value, measured in degrees. No sign. Tell, me, is 180° positive or negative? If the change is instantaneous and not a shift, then it's neither.

The fact that by man-made design the input voltage values are purposely constrained and insured to conform to favorable values that make polarity inversion look identical to phase inversion does not make them the same...not any more than automatically subtracting 1 from 6 to make 5 means that 6 is equal to 5.

G.

Yes, I think I got caught in the same loop as Robert D did a while back (feel free to look it up). Nothing wrong with that.

Anyways, now that I think I see the argument better, I would say that it is not the same. Polarity inversion flips the waveform upside down, as was shown in an experiment (you had two waves cancel each other out). Mathematically (I've shown some math before), polarity inversion multiplies your waveform by a negative 1.

Original: y = sin(x) + d
Inverted: y' = -sin(x) - d


"Conventional phase inversion" (phase shift) works like this:

Original: y = sin(x) + d
Inverted: y' = sin(x+pi) + d or sin(x-pi) + d



So in other words, polarity inversion affects the dc offset (d), phase shift does not. Phase inversion moves the wave right or left on the x axis a distance of pi rads.

Now, coming back to real world, two things pop into my mind.
1. Sound reproduction
2. Conventional phase inversion (phase shift) of more complicated waves.

1. You should hear the sine wave the same. Whether changing polarity or shifting the phase, it will be the same compression and recession of air molecules just different relative to each other. DC offset may simply bias the speaker cone one way or the other and perhaps create some noise..........

2. Like I mentioned before, if you have a 10kHz wave riding a 1kHz wave. If you do phase shift, of which wave do you shift phase? If the polarity is inversed, it inverses both waves. You can't match that wave by simply shifting phase of the original wave.

So from a from purely academical point of view, polarity inversion and phase inversion are not the same..................................


However, at the end of the day, once we filter out the dc offset and just look at a simple sine wave, we stubbornly call polarity inversion a phase inversion just because:
1. It looks like that
2. "phase" sounds cooler than "polarity"
3. That is just how we've been told and how we heard it over and over again...


I hope this puts this phase vs polarity to rest.

 

[SouthSIDE Glen]

Vadoom,

Excellent post!

I will actually play Devil's advocate here and say that if you remove the element of time from the equation, i.e. talk about an instantaneous "inversion" instead of a "shift" to phase, that two interesting things happen.

First, the phase change is no longer frequency-dependant (since frequency is based upon time). This allows one to actually perform the 180° inversion on a complex wave and not have to worry about aligning either/or the 1k or 10k freuency. They both invert.

Second, when the element of shift over time is removed, so are all signs of positive or negative. The formulas you show indicate shift; this is why the forumula has two versions one with addition and one with subtraction. The sinage here basically indicates direction in shift. Subtract 180 from 0 and you get -180, by shifting the wave back. Add 180 to 0 to get +180 by shifting the wave forward. However, when the phase change is instantaneous (an inversion) all plusses and minuses are removed, it's just 180°. This is what I meant when I said that phase inversion (not phase shift) has no sign.

The rest of what you explain remains correct as far as I can see however. You are absolutely correct that outside of any physical limitations in loudspekaer design that there is no audible differece.

That's not the question, however. The questions were, "does an inversion switch perform a phase inversion or a polarity inversion?" and "are a polarity inversion and a phase inversion the same thing?" The only correct answers are, it is inverting the phase by performing a DC normalization and a polarity inversion, but in the raw polarity inversion and phase inversion are not the same thing because one is rest-voltage dependant and the other is 0DC dependant.

G.

 

[vadoom]

Vadoom,

Excellent post!

I will actually play Devil's advocate here and say that if you remove the element of time from the equation, i.e. talk about an instantaneous "inversion" instead of a "shift" to phase, that two interesting things happen.

First, the phase change is no longer frequency-dependant (since frequency is based upon time). This allows one to actually perform the 180° inversion on a complex wave and not have to worry about aligning either/or the 1k or 10k freuency. They both invert.

Second, when the element of shift over time is removed, so are all signs of positive or negative. The formulas you show indicate shift; this is why the forumula has two versions one with addition and one with subtraction. The sinage here basically indicates direction in shift. Subtract 180 from 0 and you get -180, by shifting the wave back. Add 180 to 0 to get +180 by shifting the wave forward. However, when the phase change is instantaneous (an inversion) all plusses and minuses are removed, it's just 180°. This is what I meant when I said that phase inversion (not phase shift) has no sign.

The rest of what you explain remains correct as far as I can see however. You are absolutely correct that outside of any physical limitations in loudspekaer design that there is no audible differece.

That's not the question, however. The questions were, "does an inversion switch perform a phase inversion or a polarity inversion?" and "are a polarity inversion and a phase inversion the same thing?" The only correct answers are, it is inverting the phase by performing a DC normalization and a polarity inversion, but in the raw polarity inversion and phase inversion are not the same thing because one is rest-voltage dependant and the other is 0DC dependant.

G.

Hummm... but I don't have time (t) part of the equation... I also don't have frequency (f) or wavelength (lambda), or any other reference (velocity of the wave, etc, etc). The equations purely represent a sine wave in a regular x-y cartesian coordinate system in terms of position of the wave, i.e. you give me x I give you y...

General form of the wave would be:

y = A sin(wt - kx + phi) + d

where:
A = amplitude
w = angular frequency
t = time
k = wave number
x = spatial position
phi = phase
d = offset

k is related to wavelength by 2*pi/L
L = wavelength


....

Sorry, need to take a break. I'm currently moving from one place to another, so gotta move some stuff...

....


And as a side note, I think -180 moves the wave to the right and +180 moves to the left...

 

[SouthSIDE Glen]

And as a side note, I think -180 moves the wave to the right and +180 moves to the left...

Yep, I think you're right. You are good at catching my dyslexic thoughts I was thinking that it moved the time "pointer" to the left and got mixed up.

Hummm... but I don't have time (t) part of the equation... I also don't have frequency (f) or wavelength (lambda), or any other reference (velocity of the wave, etc, etc). The equations purely represent a sine wave in a regular x-y cartesian coordinate system in terms of position of the wave, i.e. you give me x I give you y...

OK, I am admittedly dancing on a rope without a safety net here, I admit. But when I saw you equations:

Inverted: y' = sin(x+pi) + d or sin(x-pi) + d

I interpreted the sign in the parentheses as direction of phase shift. That's why there are two equations with two solutions; one rotates the value "clockwise" the other "counterclockwise". Is that a correct enough interpretation? If so, then time is implied in the equations because the value of that sign defines the direction of shift on the timeline. Or am I way off on that interpretation?

An inversion of the type being theoretically debated in this thread has no component of time; i.e. there is no "shift" or rotation per se. It is a "flipping in place" on the X axis. Therefore any equation that defines it as a rotation or a shift in either direction loses it's meaning in this context. The wave isn't shifted -180°, nor is it shifted +180°. It's *inverted*, and that inversion happens to resemble a 180° shift...just without the actual shift .

It's also for this reason that the frequency components of the wave don't play in. Regardless of the complexity of the wave and of the number or frequencies of the component wavelets, all are equally inverted by 180°. This is not possible (AFIK) with a simple shift or rotation because each component wavelet has a different phase relationship over a set period of time.

Now, what I don't know is just what the algebra would be for such a time-independent phase inversion...or even whether there IS one. Since what is actually physically being done is a normalized polarity inversion, the question perhaps is: is the math actually the same for each?

Or perhaps there IS NO algebra for a time independent phase inversion, and all that can really be done that way is a polarity inversion. In which case, that would pretty much seal the deal on this whole debate.

G.

 

[vadoom]

DISCLAIMER: Math buffs, feel free to correct me... I'd like to see where I've gone astray. However, I think I'm pretty solid...

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Inverted: y' = sin(x+pi) + d or sin(x-pi) + d

I interpreted the sign in the parentheses as direction of phase shift. That's why there are two equations with two solutions; one rotates the value "clockwise" the other "counterclockwise". Is that a correct enough interpretation? If so, then time is implied in the equations because the value of that sign defines the direction of shift on the timeline. Or am I way off on that interpretation?

Yes, 'cw' and 'ccw' is a good interpretation. However, we still don't have time, t, part of the equation. We are simply dealing with a wave frozen in time. Or in other words, observing how the wave behaves at t=0. When we shift phase of original wave and compare the new wave with the original wave.

We can take a wave and multiply by another wave:
y = sin(x) * .3*sin(10x)

You now get a wave 10x of frequency of the original wave riding the original wave. If we shift phase of both waves:
y' = sin(x-pi) * .3*sin(10x-pi)

The new wave, y', will look exactly like if you multiplied the wave y by a negative:
y' = -[sin(x) * .3*sin(10x)]

This example shows that polarity inversion and phase shift produce exact results even if the wave is more complex than just a simple sine wave.

Now, let's add add some offset, d.
y = sin(x) * .3*sin(10x)

If we shift phase, we supposedly achieve the following result:
y' = sin(x-pi) * .3*sin(10x-pi) + d
Obviously multiplying the wave y by -1 does not produce same results:
y'' = -[sin(x) * .3*sin(10x) + d]
y' != y''
where != means 'does not equal to'
Waves y' and y'' are not equal because the offset, d, has changed signs in y'' equation.

But then you are not performing the same function to each term of the equation (mathematically speaking).

For example, sin(x-pi) = -sin(x) are interchangeable.
So is sin(x-pi) * .3*sin(10x-pi) and -[sin(x) * .3*sin(10x)]
So when I'm distributing -1 for every term in the following equation:
y'' = -[sin(x) * .3*sin(10x) + d]
Then y'' = -sin(x) * .3*sin(10x) - d

You must agree that by multiplying the sine wave by -1 I have performed a equally valid phase shift since I can equally write down y'' as the following equation (substitution property):
y'' = sin(x-pi) * .3*sin(10x-pi) - d


So if I go back to the original equation
y = sin(x) * .3*sin(10x) + d
and decide to shift phase, why should I ignore to multiply second term, d, by -1? It is as if I took my original equation, y, multiplied it by -1 as a whole, except that I forgot to multiply one of the terms by -1. It would be considered bad mathematics, right? We need to make sure we are consistent.

If you mark a point on the wave, you will think of it as moving one way or the other due to phase shift, but mathematically it is irrelevant. We are not tracking a single point on our equations are not tracking a single point as well. We are dealing the wave as whole. There is also no time delay to worry about because time is not an element of the equation.


----


We can also write our wave equation as
y = (wt + phi)
where
w= angular frequency
t = time
phi = phase

However, this only describes where the wave in terms of time. We don't know where it is in space. In fact, we are looking at one point x=0 and how the wave looks like in terms of time.
Same arguments/mathematics applies as described above. Do we have delay? No - our wave is not moving anywhere. We are still looking at a frozen wave (in space now) and seeing its y position in terms of time.


-----

To describe a wave in terms of x-axis space and time, we need to use the following equation:
y = sin(wt - kx + phi) + d

Well, ok, we are now treading into a differential equation territory...

Are we going to get a delay now? Actually, why should we? All phi does is allow us to describe the phase of a wave relative to a wave that we consider 'original'. The wave with it's shifted phase is still there (it's not coming in late) - it's just has a different y value. It's peak might be coming in late, but then we observe that when we flip polarity as well.



Humm... I think I proved that phase shift and polarity inversion are the same thing - literally. At least mathematically. This explains why we call polarity inversion a phase shift - because it is just that.

An inversion of the type being theoretically debated in this thread has no component of time; i.e. there is no "shift" or rotation per se. It is a "flipping in place" on the X axis. Therefore any equation that defines it as a rotation or a shift in either direction loses it's meaning in this context. The wave isn't shifted -180°, nor is it shifted +180°. It's *inverted*, and that inversion happens to resemble a 180° shift...just without the actual shift .

Again, keep in mind that there is no element of time. We have cut out that dimension and only dealing in two dimensional space now. Whether you flip the wave or shift the phase, your wave will look the same. Period. The above examples show that it shouldn't even matter if we have an offset.

Think of the phase shift as a partial inversion. Limiting yourself to just "inversion", your wave is either upright or upside-down. Phase shift allows you to partially "invert" the wave. Is not the same as physically turning a 2-d wave in a 3-d space, but i think that particular concept is irrelevant here...

It's also for this reason that the frequency components of the wave don't play in.

Actually, since we have no time, frequency becomes irrelevant. You need time to measure frequency.

Regardless of the complexity of the wave and of the number or frequencies of the component wavelets, all are equally inverted by 180°. This is not possible (AFIK) with a simple shift or rotation because each component wavelet has a different phase relationship over a set period of time.

Now, what I don't know is just what the algebra would be for such a time-independent phase inversion...or even whether there IS one. Since what is actually physically being done is a normalized polarity inversion, the question perhaps is: is the math actually the same for each?

Or perhaps there IS NO algebra for a time independent phase inversion, and all that can really be done that way is a polarity inversion. In which case, that would pretty much seal the deal on this whole debate.

G.

I think I demonstrated a counterargument in the above example(s).


Well, I guess here you have it, practicality and hardware aside - pure mathematics.........................

 

[andyhix]

I think I liked this thread yesterday better when everyone was hugging and appologizing and buying each other beers... this recent mathy twist is freaking me out.

 

[SouthSIDE Glen]

If we shift phase, we supposedly achieve the following result:
y' = sin(x-pi) * .3*sin(10x-pi) + d
Obviously multiplying the wave y by -1 does not produce same results:
y'' = -[sin(x) * .3*sin(10x) + d]
y' != y''
where != means 'does not equal to'
Waves y' and y'' are not equal because the offset, d, has changed signs in y'' equation.

But then you are not performing the same function to each term of the equation (mathematically speaking).

For example, sin(x-pi) = -sin(x) are interchangeable.
So is sin(x-pi) * .3*sin(10x-pi) and -[sin(x) * .3*sin(10x)]
So when I'm distributing -1 for every term in the following equation:
y'' = -[sin(x) * .3*sin(10x) + d]
Then y'' = -sin(x) * .3*sin(10x) - d

Correct me if I'm wrong, but if you multiply the term by -1, you are not performing a phase shift, you are inverting the polarity. Of course it's going to be "the same" as a polarity inversion, because that's exactly what you are doing! .

What would you do, for example, if you wanted to shift phase by 90 degrees? or 270 degrees? You wouldn't multiply the entire term by 0.5 or -0.5, would you?

If not, there's no reason why you would multiply by -1 for 180 degrees either. 180 degrees is just another number, and it should be manipulated by the same methods as any other number between 1 and 359. If that's true, the prejudice is setting in again that just because 180 degrees resembles an inversion, that one multiplies by -1 to acheive it. But that's actually flipping the polarity, not executing a phase change.

G.

 

[Robert D]

You guys are cracking me up! Before you hurt yourselves, why don't you just do the very simple experiment of passing a 100hz mixed with 1Khz wave through an inverting unity gain buffer (voltage follower), and take a look. It only takes one op-amp and two resistors of the same value (or no resistors if you don't care about setting the input impedance). Compare the output and input and tell me they are not 180 deg out of phase for both freq components.

 

[SouthSIDE Glen]

You guys are cracking me up! Before you hurt yourselves, why don't you just do the very simple experiment of passing a 100hz mixed with 1Khz wave through an inverting unity gain buffer (voltage follower), and take a look. It only takes one op-amp and two resistors of the same value (or no resistors if you don't care about setting the input impedance). Compare the output and input and tell me they are not 180 deg out of phase for both freq components.

The question is, Rob, not whether they are 180° out of phase, but whether there are any other differences as well. Flipping polarity will always throw something 180° out of phase. That has never been in debate, AFIK.

My point is, and has always been, that throwing a polarity inversion at the wave form inverses the phase around 0 DC. Straight phase change does not, it inverts it around the waveform's rest voltage. If the rest voltage for the waveform is not 0DC, however, simply inverting the phase will not result in the same thing that an inversion of polarity will. The two processes in and of themselves are not equal.

Now, you keep saying that any engineer in their right mind will normalize the rest voltage around 0DC first - and you're right. You use that to conclude that therefore the two process ARE equal. The way I see that is that proves that the are NOT equal, because the phase inversion requires that extra step to ensure the equal result.

One of the effects, but not necessarily the only effect, of polarity inversion is a phase change of 180°. OTOH, a phase change of 180° does not necessarily result in a polarity inversion at all. Phase change of ANY degree - whether it's 180° or 1° - in and of itself happens independant of voltage polarity.

Remember, phase itself is not even dependant upon electricity. The exact same principles, the exact same math, the exact same definitions reamin true whether we are talking electriical voltages in a circuit, electromagnetic waves, sound waves, waves in the ocean, or even phases of the moon. In at least three of those versions of phase, there is no polarity to even consider. Yet we can still talk about 180° phase changes in all of them.

A 180° phase inversion in the ocean waves does not flip around an arbitrary and uniform measurement called "sea level". Nor does a phase inversion in sound pressure waves flip around the silence of an atmospheric vacuum. And phase in and of itself of an electrical current does not flip around an arbirary reference level of 0DC. Each of them flip around the ambient "rest" condition, whether it matches some standard reference level or not. Ocean waves would invert around the local level of a calm sea, which more often than not is not a standard measurement we call "sea level". Sound waves would flip around the ambient Brownian noise level, not some theoretical rest level based upon total silence. And it's the same with electricity; a pure phase change flips around the "rest voltage" of the waveform, not what we humans arbitrarily refer to as 0DC.

G.

 

[bennychico11]

I have a feeling when this thread finally ends it will be the end of the phase/polarity discussion as we know it. Scholars will reference this for years to come....books will be written about this discussion. A multimillion dollar movie will be made by Darren Aronofsky which will be his sequal to Pi....called Phase (with the symbol phi used on the cover). But instead of a mathematical genius being driven to insanity...it'll be the members of an online recording forum that do.

lol

 

[SouthSIDE Glen]

I have a feeling when this thread finally ends it will be the end of the phase/polarity discussion as we know it. Scholars will reference this for years to come....books will be written about this discussion. A multimillion dollar movie will be made by Darren Aronofsky which will be his sequal to Pi....called Phase (with the symbol phi used on the cover). But instead of a mathematical genius being driven to insanity...it'll be the members of an online recording forum that do.

lol

LOL, you're probably right, Benny. It's alread driving me to madness that this debate even need to take place. It's not like we're talking string theory and multiple universes here. We're talking very basic physics that's been a known quantity for damn near a couple of centuries. Phase is phase. Polarity is polarity. Under special, constrained and, frankly, man-made circumstances, the two yield equal results. But the true nature of the two are entirely different altogether.

G.

 

[Robert D]

So, the user of the channel strip is supposed to care about all of this? The button needs to be labled "phase invert plus decoupling"? When the user pushes that switch, the end result is that a phase inversion has occured. My point all along has been that the button is named appropriately for what it does, not how it does it. There are several ways to affect the inversion, and most of them don't invert the signal around 0 Vdc. The DC component is a detail to be sorted out by the EE, not the AE.

 

[SouthSIDE Glen]

So, the user of the channel strip is supposed to care about all of this?

The people in a forum asking (and answering) the questions of what the button does and what the difference is between polarity and phase SHOULD. For someone who DOES understand phase - even if it's just remembering it from their high school physics - and comes in here as a newb to recording technology, telling them that all that button does is invert phase will give them the wrong picture, the wrong impression and the wrong idea of what is actually going on because that is NOT what the button is doing.

The button needs to be labled "phase invert plus decoupling"?

No, it really should be labeld "polarity invert".

When the user pushes that switch, the end result is that a phase inversion has occured.

NO. The end result is that a polarity inversion has occured, which has a coincidental side effect of also inverting phase.

My point all along has been that the button is named appropriately for what it does, not how it does it.

And my point is that it isn't.

There are several ways to affect the inversion, and most of them don't invert the signal around 0 Vdc. The DC component is a detail to be sorted out by the EE, not the AE.

Unless the AE thinks that all the buttion is doing is inverting phase and nothing else, in which case he's not expecting it to "sort out" the DC component, but rather expecting it to be handled like it would in a standard vanilla phase change of any other degree. What it does and what he'd expect it to potentially do based solely on the name "phase inversion" are two different things.

And I probably just gotta leave it there, Rob. You and I are going to butt heads on this from now until doomsday and never agree, as long as we're looking at it from the two different perspectives that we are; me from the theoretical physics aspect and you from the practical engineering aspect, we're never going to quite see eye to eye. What'dya say we just leave it at that, at least for now. I'm tired of the topic and am frankly running out of different ways to try to explain it. And I usually wind up agreeing with you far more than I disagree with you on ths forum; Id' rather not fuck that up by getting into such a fine point on an esoteric detail.

Besides, 99.98% of those reading our words here have no idea what either one of us are talking about anyway.

G.

 

[vadoom]

I think I liked this thread yesterday better when everyone was hugging and appologizing and buying each other beers... this recent mathy twist is freaking me out.

Wait till we start resorting to imaginary numbers!!

 

[vadoom]

Correct me if I'm wrong, but if you multiply the term by -1, you are not performing a phase shift, you are inverting the polarity. Of course it's going to be "the same" as a polarity inversion, because that's exactly what you are doing! .

What would you do, for example, if you wanted to shift phase by 90 degrees? or 270 degrees? You wouldn't multiply the entire term by 0.5 or -0.5, would you?

If not, there's no reason why you would multiply by -1 for 180 degrees either. 180 degrees is just another number, and it should be manipulated by the same methods as any other number between 1 and 359. If that's true, the prejudice is setting in again that just because 180 degrees resembles an inversion, that one multiplies by -1 to acheive it. But that's actually flipping the polarity, not executing a phase change.

G.

Humm... you do have a point....

 

[SouthSIDE Glen]

Wait till we start resorting to imaginary numbers!!

-i carumba!

G.

 

[vadoom]

I'll try to contemplate on this for some time... It has been a good brain exercise for me (remembering waves, etc, etc). Hadn't had this opportunity since college...

However, I must agree that a phase shift can occur without affecting the offset since the wave is a function of space and/or time. And, yes, multiplying the whole wave by -1 is just inverting the wave and it happens that the results resemble a 180deg phase shift but the offset is also affected.

Nevertheless, I've tried arguing different things just to "massage" my brain. I find this topic very fascinating and will continue to think some of this out. Will post if I come up with anything...

At this point I see your point and must agree that even though phase shift and polarity inversion may produce same results, due to the fact that our offset seems to end up being different in both cases, we must conclude that phase shift and polarity inversion are not exactly the same thing (not interchangeable in all cases).





Humm... when you integrate the wave y, you get rid of the offset so then you can do whatever you want with the integral and differentiate back to original wave... Does this seem to have any merit?

 

[SouthSIDE Glen]

At this point I see your point and must agree that even though phase shift and polarity inversion may produce same results, due to the fact that our offset seems to end up being different in both cases, we must conclude that phase shift and polarity inversion are not exactly the same thing (not interchangeable in all cases).

Thank you! It is sure lonely when no one understand what one is talking about. Knowing that even one person come around is gratifying.

Humm... when you integrate the wave y, you get rid of the offset so then you can do whatever you want with the integral and differentiate back to original wave... Does this seem to have any merit?

I have no idea, to be honest. When you talk about "integrating the wave", you are at the edge of my understanding of mathematics terminology.

I have just stuck to a simple mental picture all along. A phase inversion is nothing more than a phase change of a specific value that happens instantaneously (t=0). It is no different than any other phase change in that the phase rotates around the rest voltage; i.e. the rest voltage is not affected. This means that phase inversion only has the equivalent result of polarity inversion in one special circumstance, when the rest voltage is 0.

Then I add the idea that phase change is not limited to a value of 180°. If one wanted to, they could change the phase by any damn degree they wished. There is nothing special about 180° in that regard. It's just another number. And regardless of degree value, the same formula should be used for all of them. One should just need to plug the value into the equation and away you go.

Changing the sign, OTOH (a.k.a. multiplying the terms by -1) - which is basically all a polarity inversion is, is an artificial manipulation that has nothing to do with any phase change methodology. The fact that a polarity shift resembles a 180° phase change in some (but not all) aspects is nothing more than a happy coincidence that does nothing to actually make phase and polarity the same thing.

G.

 

[MCI2424]

Thank you! It is sure lonely when no one understand what one is talking about. Knowing that even one person come around is gratifying.I have no idea, to be honest. When you talk about "integrating the wave", you are at the edge of my understanding of mathematics terminology.

I have just stuck to a simple mental picture all along. A phase inversion is nothing more than a phase change of a specific value that happens instantaneously (t=0). It is no different than any other phase change in that the phase rotates around the rest voltage; i.e. the rest voltage is not affected. This means that phase inversion only has the equivalent result of polarity inversion in one special circumstance, when the rest voltage is 0.

Then I add the idea that phase change is not limited to a value of 180°. If one wanted to, they could change the phase by any damn degree they wished. There is nothing special about 180° in that regard. It's just another number. And regardless of degree value, the same formula should be used for all of them. One should just need to plug the value into the equation and away you go.

Changing the sign, OTOH (a.k.a. multiplying the terms by -1) - which is basically all a polarity inversion is, is an artificial manipulation that has nothing to do with any phase change methodology. The fact that a polarity shift resembles a 180° phase change in some (but not all) aspects is nothing more than a happy coincidence that does nothing to actually make phase and polarity the same thing.

G.

If you had a properly desingned pre-amp then the DC offset will be 0vDC. It is in this case that the 180 degree polarity change would be a phase shift compared to another source. If you had a pre-amp with bad decoupling caps, then all that math applies.

The one way out here would instead of applying all that math, get the pre-amp fixed so it works correctly.

 

[SouthSIDE Glen]

[Removed non-helpful post. - G.]