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AC waveforms - questions

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gjpollitt

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After learning complex numbers for ac phase etc I have a question. If there are 2 sine waves out of phase they can be added and seen as a single waveform on a scope. My question is how do you know that there is more than one waveform when you connect the scope to the signal?

Second if current and voltage are 90 out of phase and you can see the voltage side on the scope what do you see the current side with to prove they are out of phase by 90?

Thanks
Graham
 
Well if you're unsure as to what your signal contains here is what I suggest:

If you're using newer scope then it should come equipped with an FFT option under the math menu. Have the scope compute the FFT of the signal you're interested in looking at. If for example you have s(t) = sin(2*pi*1000*t) + sin(2*pi*1000*t + 37 deg), you won't be able to make the distinction on the scope because the FFT is only a magnitude FFT, and not the phase FFT.

However, if you have for example s(t) = sin(2*pi*1000*t) + sin(2*pi*200*t + 37 deg), you will see 2 very large spikes at f = 1000 and f = 200. So that will tell you that your signal is composed of a sum of sines that have respective frequencies of 200 hz and 1000hz.

As for your second question. I believe you're thinking of ELI ICE. ELI - Voltage leads Current in inductive circuits. ICE - Current leads Voltage in capacitive circuits.

That is because if you are supplying v(t) = sin(w*t), and i = c*dv/dt (for capacitors) then i(t) = c*cos(w*t)/w. Which means current is leading. As if you'll recall cos(w*t) = sin(w*t + 90).

Conversely, if you're dealing with an inductive circuit v = L*di/dt, and the same math follows as above.

So, only in these special cases does current lag/lead by 90 degrees as you've stated below.
 
gjpollitt said:
After learning complex numbers for ac phase etc I have a question. If there are 2 sine waves out of phase they can be added and seen as a single waveform on a scope. My question is how do you know that there is more than one waveform when you connect the scope to the signal?
You can't tell by looking at the waveform.

Second if current and voltage are 90 out of phase and you can see the voltage side on the scope what do you see the current side with to prove they are out of phase by 90?
You need a current probe, or a low-value series current sampling resistor.

Thanks
Graham
 
If the waveform displayed on the scope is anything but a sinewave, then it is composed of two or more waveforms of different frequencies added together.

But if you have two sinewaves of the same frequency but of different phase, which are added together the result is another sinewave. Unless they are of equal and opposite amplitude, in which case they cancel out to zero.

JimB
 
you must have a dual trace scope display voltage wave form on one channel and the current wave form on the other channel...or a out of phase second voltage wave form. With the x-y setting you will get one display that shows the addition or difference of the two wave forms

joe
 
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