Single Phase Theroy

[LarryFine]

First of all, I want to mention that I side with Rick on this topic, so he's not alone.

The counterpoint, which has been made many times over, is that for a single frequency system, 0? and 180? doesn't simply 'look like' 0? and its inversion; the two are _indistinguishable_ and completely _equivalent_.

Second, although Jon is correct on this point, I say it's irrelevant.

While it may be factual when referring to a single frequency, let's see someone create an inverted signal using time shift for a complex signal, like audio.

I have made transistor-based phase-splitters for bridging audio amps, and center-tapped transformers are used to create phase inversion in push-pull circuitry.

It can't be done using time-shifting, because each frequency requires a different amount of time delay for a 180-degree signal shift. One set time doesn't do it.

A real transformer ... will produce an imperfect sine wave . . . you also need to look at possible different flux coupling to the different halves of the transformer...making one half of the common center tapped secondary not necessarily a simple inversion of the other half.

True, but "bi-filar" winding is used when the halves must match. Instead of winding half the secondary, creating a tap, and winding the other half, they wind both halves using two conductors, and then connect them in series.

 

[LarryFine]

Yes, they are indistinguishable on a scope, but they are not mathematically equal. An inversion is a minus sign. A phase shift is a time delay.

Agreed, as my comments, especially those starting on page five, illustrate.

 

[LarryFine]

My answer: a single phase system has 2 phase angles, so by adding an additional transformer you can get 6 phase angles, which we call three phase.

If one can derive six phases from two, why can't one derive three phases from one?

 

[LarryFine]

My revision is:
The counterpoint, is that for a single frequency system, a sine wave produced by a 180? delay and a sine wave produced by inversion do not simply look the same, they are _indistinguishable_ and completely _equivalent_.

I won't argue that they "resemble," to quote myself, but the reality is that, even using the from-the-neutral perspective, the two lines are of opposing polarity, and not of a time difference.

Furthermore, since the outputs are equivalent, I can use either method to create the output for either application. Say I need a time delay of exactly 1/2 cycle; I don't have to invest in a delay line; I can use a simple inversion.

As long as you're inverting a single frequency, of course.

Because the outputs of the different mechanisms are the same (again, in the idealized case), then it is reasonable and correct to use names derived from either mechanism in order to describe these outputs. IMHO it is just as reasonable to say '0? and its inverse' as to say '0? and 180?' to name the legs on a single phase supply.

I can't agree with either of these statements. The "mechanism" of a time delay certainly isn't used, while that of an inversion of polarity is dead accurate.

Actually, the only reason even an inversion is accurate is because one chooses to use the center tap as the reference. But, the "arrows" all point one way, line to line, like the batteries in series.

 

[LarryFine]

In other words,

-120V @ 0 = +120V@ 180

Either value will provide the same result.

Mathematically, yes, but I've only seen the "inversion" used in the real world of power.

 

[winnie]

If one can derive six phases from two, why can't one derive three phases from one?

Whoops, I should have supplied a bit more context.

If I have single phase power, with two hot wires and a neutral from the power company, and need three phase power, then the POCO can install a _single_ additional transformer, and supply me with a _single_ additional hot wire, and now I have three phase power. If I start with single phase, and by adding an additional wire I get three phase power, where does the second phase come from?

-Jon

 

[rattus]

Mathematically, yes, but I've only seen the "inversion" used in the real world of power.

Maybe so, but mathematically is what it is all about. If you are analyzing the circuit with phasors, you must include phase angles. The phase difference is there whether you recognize it as such or not.

We are of course assuming pure sinusoids and ideal circuit elements in order to perform a linear analysis. If we get off on the imperfect world argument, we cannot assign phase angles to a 3-ph system for example.

And, while it is true that an ideal transformer does not add a time delay, one voltage lags the other, or does it lead? WYSIWYG!

Simply put, the notion that an inversion does not produce a phase difference is baseless. No one has produced a valid reference to justify that claim.

Still single phase though!

 

[jim dungar]

If I have single phase power, with two hot wires and a neutral from the power company, and need three phase power, then the POCO can install a _single_ additional transformer, and supply me with a _single_ additional hot wire, and now I have three phase power.

Maybe and maybe not.

Many utilities in rural areas only provide 2 conductors (hot and grounded)on many of their distribution circuits. They reserve 3 and 4 conductor circuits for those that parallel 'county roads' and concentrated industrial locations.

 

[SAC]

Whoops, I should have supplied a bit more context.

If I have single phase power, with two hot wires and a neutral from the power company, and need three phase power, then the POCO can install a _single_ additional transformer, and supply me with a _single_ additional hot wire, and now I have three phase power. If I start with single phase, and by adding an additional wire I get three phase power, where does the second phase come from?

-Jon

By their addition (voltage sources in series). If I have one battery, say 2 volts, I can get 2 volts (or -2 volts). If I add another battery, say 1 volt, I can now get 2 volts, 1 volt, or three volts, depending on how I connect them (or the inverse of each of those). Two batteries, but three voltages. It works the same way with AC sources, but now the resulting voltages also take phase into account. Note that you can't just use two AC voltages of arbitrary phase and get the desired 3rd phase - the two phases need to be chosen carefully so that the sum of them gives the desired third phase. Same with the battery example - if they both were 2 volts, I could only get 2 volts or 4 volts (zero volts doesn't count!).