Vectors vs Phasors

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Re: Vectors vs Phasors

Because reactance and impedance are based on pure sinusoids and cannot be used with any other waveforms.
Of course you already knew that!
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No, I didn't know that. :D
one could compute the RMS value of a full wave rectified single phase voltage. It would be 0.707 * Vp.
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If Vp is Peak or Maximum value of the AC supply, I can't agree.

The AVG (average) value of a full wave rectified single phase voltage is 0.637 x Emax. Example below.

And, TTBOMK, we shouldn't be using RMS to denote a rectified voltage.

Ed

Rect9.gif


[ February 03, 2005, 08:40 PM: Message edited by: Ed MacLaren ]
 
Re: Vectors vs Phasors

Ed, I am speaking of an unfiltered, full wave rectified waveform as in your diagram. We are interested in the heating effect which is not provided by the average value. We must compute the RMS value of this fluctuating DC waveform.

Vrms = sqrt[int(v(t)^2)dt/T], (integrated over one period)

where v(t) = Vp*sin(wt)

Since we are integrating voltage squared, it matters not that the rectified wave contains only positive lobes while the AC wave contains both positive and negative lobes. The result is the same.
 
Re: Vectors vs Phasors

Vrms = sqrt[int(v(t)^2)dt/T], (integrated over one period)
where v(t) = Vp*sin(wt)
Click to expand...
Rattus, I don't speak "math". :D You might as well be speaking Gaelic. (Thats what my ancestors spoke)

But, I know what the DC output voltage of a rectifier circuit is. I've connected and used many, single and three phase, half-wave and full-wave, filtered and unfiltered, and I've measured the voltages.

Are you saying the voltages in my examples above are incorrect, or are you saying that they should be referred to as RMS instead of AVG?

Ed
 
Re: Vectors vs Phasors

Ed, I am saying that the full wave rectified waveform has both an average and an effective value, just like the sine wave has an average and effective value. In this case, these values are the same for both waveforms.

And, in both cases it is the effective (RMS) value which should be used to compute power in a resistive load.

What I am saying is that the positive and negative lobes of an AC wave have the same heating effect.

If we have only positve (or negative) lobes, the heating effect is the same as that of the AC wave. Therefore, we use the RMS value which is 0.707Vp.

I don't speak Gaelic or even Erse, but I am fluent in Gibberish.

[ February 03, 2005, 11:43 PM: Message edited by: rattus ]
 
Re: Vectors vs Phasors

I am saying that the full wave rectified waveform has both an average and an effective value,
Click to expand...
Can you show me any statements agreeing with that?
Any one here on the board?

Therefore, we use the RMS value which is 0.707Vp.
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Rattus, when you say we, don't include me, if you are referring to rectified DC. :D

What is your current and power calculation for the circuit below?

Ed

Rect10.gif
 
Re: Vectors vs Phasors

my 1.5 cents:

it seems intuitively correct that Rattus is right on this one. The heating effect is the same, regardless of whether the second half-cycle is negative or positive.

I would go with the .707 x peak as the "effective" value for either the AC voltage or the rectified DC voltage.
 
Re: Vectors vs Phasors

Ed, here is a site which explains it mathematically:

http://en.wikipedia.org/wiki/Root_mean_square

We can also think of the instantaneous power in the AC wave or the full wave DC.

For the AC wave:

p(t) = (Vp(sin(wt))^2/R

You don't need to evaluate this formula, just realize that the heating effect will be the same at any instant for either wave since the shape of the lobes is identical (assuming ideal rectifiers).

Now if you filter out the AC components to create pure DC, the average and effective values will be equal.
 
Re: Vectors vs Phasors

Rattus, you didn't tell me yet if your calculation of the current and power in the load (diagram above) is different than mine, and if it is, what your values are. ;)

Ed
 
Re: Vectors vs Phasors

Ed, yes, there are differences.

Your average current is correct, but the power is too low.

The effective voltage is 120V, the effective current is 12A, and the average power is 1440W.

RMS voltages and currents can be computed for any periodic waveform, not just sinusoids, e.g., a square wave which swings between +/- V, has an average value (over a half period) of V. The effective (RMS) value is also V.

A triangular wave would have different average and RMS values as does a sine wave.

You can demonstrate this to yourself by measuring the full wave voltage with a true RMS voltmeter, but you must make allowances for the rectifier drop.
 
Re: Vectors vs Phasors

Rattus,
We will have to agree to put this on hold until I get a chance to build this circuit and check the power with a wattmeter. :)

Ed
 
Re: Vectors vs Phasors

Ed, when you do your test, be sure your wattmeter will handle a DC component in the waveform. It would be sufficient though to measure the true RMS voltage since power equals voltage squared over R.

You could also measure the line current which should be 12Arms for your example. The rectifier merely commutates it. Rattus
 
Re: Vectors vs Phasors

Oops,

I made a mistake; thought I was wrong! No, really, a phasor is written as,

e^jwt = cos(wt) + jsin(wt) (Euler's eqn.)

not the other way around, and no one noticed.

Rattus
 
Re: Vectors vs Phasors

Definition of a Vector,
"A straight line representing the magnitude and direction of a quantity."

Definition of a Phasor,
"A quantity that has magnitude and direction in the time domain; i.e., is constantly changing as instantaneous value of a sine wave." :D :D
 
Re: Vectors vs Phasors

I've been around here for a month or so... have learned a lot! I used to think that vectors and phasors were the same thing. Now I see the difference.

I am looking at some things as I have never seen them before.

For example, the sine wave you mention represents the magnitude of a voltage which can be represented as a vector at any instant in time. Essentially this can be represented by a one-dimensional graph with the second added dimension of time... as in vertical coordinate = magnitude and horizontal coordinate = time.

Now, consider a particle which is moving in a plane. We have two spacial dimensions and then a third dimension of time. Could be x and y coordinates define the plane, and z is the time dimension. I can visualize that as the plane moving along the z axis through time, and the position of the particle can be plotted.

Then take a particle moving in three spacial dimensions... add the fourth dimension for time... wow! The three dimensional coordinate system is moving through time. Something I never realized before makes a little sense.

Will I be solving General Relativity tomorrow? No, but at least I have an inkling...
 
Re: Vectors vs Phasors

Sparks1,

I must agree with your definitions of vectors and phasors. Then impedances as well as steady state voltages and currents are vector quantities because they are NOT functions of time.

Now can you come up with some examples of the application of phasors? We have already seen the cute little rotating arrows, but how would you use phasors in a real problem?
 
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