# Why is residential wiring known as single phase?

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#### jim dungar

##### Moderator
Staff member
It is silly because I have already demonstrated my expertise, such as it is.
I can surmise, it is your concern over what the results will be.

But the question is about an inequality:
What part of cutting a single winding in half creates an inequality?

I do not know how to make it any straighter.
By cutting a single winding in half you created two identical voltages. Your are free to assign any direction you want to them. Your are free to make one waveform the inverse of the other. But when you are done the math must be repeatable for A+B=C, A=C-B, B=C-A or for A-B=C, A=C+B, and -B=C-A.

However you have been asking about a single voltage wave form and it inverse.
Inverting a single waveform does not shift it in time, it simple changes the magnitude, I have posted a link to an application that graphs this for you..
When applying phasors, and a negative magnitude is encountered, the common practice is to multiply the magnitude by (-1) and modify the angle by either adding or subtracting PI radians, or 180?. So a purist would never use Vbn=-Vnb as a final result. Instead they would say Vbn=Vnb@180? which is still just a single waveform, with its reference point swapped.

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#### Rick Christopherson

##### Senior Member
If they were "vectors" say forces, they would cancel, but they are not "vectors", they are phasors representing a voltage magnitude (always positive) and phase angle. The rules are different. You subtract one potential from the other to get the potential DIFFERENCE--phasorially that is.

Good reason to use the term "phasor" instead of "vector".
I sure would like to see a reference that says phasors are not vectors.

#### jim dungar

##### Moderator
Staff member
You certainly implied that the delta method was the correct method.
Actually I stated the fact, that a center-tapped winding is physically connected like a delta, 'identified terminal' connected to 'unidentified terminal' (i.e. X2 to X1) versus a wye where all of the 'identified terminals' or all of the 'unidentified terminals' are connected together (i.e. X2-X2).

Yes there are other possible connections of two isolated windings,but not of a center-tapped one.

#### Besoeker

##### Senior Member
To which point do you disagree?
the difference between the two is purely semantic.
The difference is pragmatic for the reasons I gave in post #2411.

#### Besoeker

##### Senior Member
Your circuit works because of the way you have it wired not because there is a phase difference.

I responded to this thus:
Which is just the same way as residential 120-0-120.
The SCRs don't change that.
Now if it's just one phase why does it require two firing pulses per cycle?

I note you have not explained the requirement for two pulses, phase displaced by 180deg per cycle of the supply.
Nor has anyone else for that matter.

And why does the circuit produce two pulses of current every cycle of the supply if there is only a single phase?
Just to be be clear about it, the SCRs don't make the currents flow from each half of the centre-tapped transformer at those times. Those are the times the currents would flow from each half into resistive loads without SCRs.

#### rattus

##### Senior Member
However you have been asking about a single voltage wave form and it inverse.
Inverting a single waveform does not shift it in time, it simple changes the magnitude,

The magnitude cannot be changed. It is always 120Vrms in this case. The inversion creates a phase difference, which is commonly called a phase shift, of PI radians.

When applying phasors, and a negative magnitude is encountered

No such thing as a negative magnitude, ALWAYS positive.

The common practice is to multiply the magnitude by (-1) and modify the angle by either adding or subtracting PI radians, or 180?
Would not do both, the minus sign changes the phase constant.

. So a purist would never use Vbn=-Vnb as a final result. Instead they would say Vbn=Vnb@180? which is still just a single waveform, with its reference point swapped.

It is incorrect to say Vnb@180 because Vnb is a phasor in its own right. It carries its own angle. No need to tack another angle on it.

But, you have yet to explain away the differing phase constants! You have been sidestepping this one issue.

You must agree that it is permissible to write the two voltages as,

Van = 120Vrms @ 0
Vbn = 120Vrms @ PI

It doesn't matter that they may have come from a transformer secondary. and you have already agreed that it is permissible to use the neutral as a reference. Now for the \$64 question:

How can these two waveforms be of the same phase when their phase constants differ by PI.

#### jim dungar

##### Moderator
Staff member
I responded to this thus:

I note you have not explained the requirement for two pulses, phase displaced by 180deg per cycle of the supply.
Nor has anyone else for that matter.

And why does the circuit produce two pulses of current every cycle of the supply if there is only a single phase?
Just to be be clear about it, the SCRs don't make the currents flow from each half of the centre-tapped transformer at those times. Those are the times the currents would flow from each half into resistive loads without SCRs.
I thought you understood how to different voltages could be interconnected?

Va is connected to an SCR that is triggered to allow current to flow on the "1st half' of the cycle.
Vb is connected to an SCR that is triggered to allow current to flow on the "2nd half" of the cycle.
Two voltages and two triggers, phase really has nothing to do with it.
Oh yeah, then you inverted the reference on one of the two waveforms, but you kept the triggerings pulse the same. The effect is mathematically the same as having non-identical waveforms.

#### rattus

##### Senior Member
I sure would like to see a reference that says phasors are not vectors.

[Tang, Alternating Current Circuits, International, 1960]

#### jim dungar

##### Moderator
Staff member
First post the phasors toanswer my question

It doesn't matter that they may have come from a transformer secondary. and you have already agreed that it is permissible to use the neutral as a reference. Now for the \$64 question:

How can these two waveforms be of the same phase when their phase constants differ by PI.

Given the single center-tapped winding there are identical waveforms.
Inverting a waveform does not shift it in time.
If the waveforms are identical, their phase constants (wt+phi) are identical.
You just don't seem to agree that you are the one adding PI, 180?, to the phase constnat and then you claim you have a different wave.

But the whole issue of the 120/240V output from a single center-tapped transformer is the entire argument, so it makes no sense to exclude their reference.

#### gar

##### Senior Member
120321=0835 EDT

Rick:

The following quote is from "Analysis of A-C Circuits", by M. B. Stout, 1952. There is supporting discussion prior to this quote. The quote is from p 11. Some of the supporting material specifies a sine wave.
The phasors used for this purpose are a very special form of vector, and should not be confused with the more conventional space vectors. The electrical quantities are rotating radii or time vectors which show time relationships. The direction of an electrical diagram in space has , in general, no particular significance. The important matter is the relationship between the various quantities shown on the diagram. Turning the diagram as a whole does not alter these relationships.

There are various suggestions that the word "vector" be dropped as the name of the electrical symbols, and that some other name be adopted in its stead. This idea has merit in avoiding confusion with the broader mathematical uses of "vector", and "phasor" is now coming into general use. The term "vector" will be used in a few places in this book to tie to past practice in this field, with special application to time vectors. However, the newer term "phasor" will be given general preference for the time-vector idea.

#### rattus

##### Senior Member
Given the single center-tapped winding there are identical waveforms.
Inverting a waveform does not shift it in time.
If the waveforms are identical, their phase constants (wt+phi) are identical.
You just don't seem to agree that you are the one adding PI, 180?, to the phase constnat and then you claim you have a different wave.

But inversion does create a phase DIFFERENCE, therefore the waveforms are NOT identical. AC waves must have the same magnitude and phase to be identical.

Van carries a phase of (wt)

Vbn carries a phase of (wt + PI)

I didn't add anything to the phase constant, the phase constant of Vbn is PI, period.

Again, a deceptive answer and a lecture on transformers.

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#### Rick Christopherson

##### Senior Member
But inversion does create a phase DIFFERENCE, therefore the waveforms are NOT identical. AC waves must have the same magnitude and phase to be identical.
But you didn't invert the waveform. You only inverted your measurement of it. That's the equivalent of saying you have two waveforms between A and N, Van and Vna and they are out of phase.

#### rattus

##### Senior Member
But you didn't invert the waveform. You only inverted your measurement of it. That's the equivalent of saying you have two waveforms between A and N, Van and Vna and they are out of phase.

Nonsense!

#### Rick Christopherson

##### Senior Member

[Tang, Alternating Current Circuits, International, 1960]
Gee, why bother narrowing it down to a whole book. Wouldn't it have been easier for you to simply say, "The Library of Congress"? :dunce:

120321=0835 EDT

Rick:

The following quote is from "Analysis of A-C Circuits", by M. B. Stout, 1952. There is supporting discussion prior to this quote. The quote is from p 11. Some of the supporting material specifies a sine wave.
Reread your own citation. He does not say that phasors are not vectors. Just that they are special vectors. Nor does the reference suggest that vector math does not apply. Moreover, what makes them "special vectors" is that they rotate. However, when we work with them, we treat them as fixed, or instantaneous. When you write V<w?, you fix the vector in a single position.

#### Rick Christopherson

##### Senior Member
Nonsense!
Really? Did you physically disconnect that transformer and invert the winding?

#### Rick Christopherson

##### Senior Member
Nonsense!
P.S.: If by "nonsense" you mean that Van and Vna are not two waveforms out of phase, then you are absolutely right. It is nonsense. But it is the same nonsense that you are using when you claim the two waveforms between A, N, & B are out of phase. It's only because you measure them that way, not because they are. That is the nonsense.

#### gar

##### Senior Member
120321-1007 EDT

Rick:

I did not provide you with all the background leading up to the actual quotes. Phasors and mechanical vectors are not the same thing. You may use some similar tools and concepts, but mechanical vectors, such as in static force balance equations, are quite different than the concept of electrical phasors.

.

#### Rick Christopherson

##### Senior Member
120321-1007 EDT

Rick:

I did not provide you with all the background leading up to the actual quotes. Phasors and mechanical vectors are not the same thing. You may use some similar tools and concepts, but mechanical vectors, such as in static force balance equations, are quite different than the concept of electrical phasors.
Their origination and meaning may be different, but the mathematics surrounding them is not, and that is what is at issue.

#### rattus

##### Senior Member
Their origination and meaning may be different, but the mathematics surrounding them is not, and that is what is at issue.

No so. Treat them like force vectors and the opposing phases of the split phase system cancel--not expected.

Treat them like phasors and the opposing phases, subtracted phasorially, yield 240V-- as expected.

#### rattus

##### Senior Member
P.S.: If by "nonsense" you mean that Van and Vna are not two waveforms out of phase, then you are absolutely right. It is nonsense. But it is the same nonsense that you are using when you claim the two waveforms between A, N, & B are out of phase. It's only because you measure them that way, not because they are. That is the nonsense.

No. It is because they are DEFINED that way. You can always measure voltages in two ways. I choose the way that makes the voltages out of phase. You can do it your way.

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