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# Square wave AC?

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#### grrr_arrghh

##### New Member
I am a little bit confused. i know that you can only step up/down the voltage of an AC current, and you can turn DC into AC using an osscilator, something as simple as a 555 astable. Thats fine.

BUT: how is a square wave AC? it is only changing for a very short ammount of time. For the rest of the time the wave is either 'High' or 'Low', i.e. it is not changing, making it DC for that period of time....????????

Can someone explain how this works?

Thanks

Tim

The square wave signal is "built up" from many components. Each component is an AC sinusoid with a specific frequency and amplitude. This is known as the Fourier series for that waveform. A square wave has an easy series to remember. It is composed of only odd harmonics and the amplitude of each harmonic is 1/h where h is the harmonic number.

A square wave then has the following series:

1 sin(t) + 1/3 sin(3t) + 1/5 sin(5t) + ....

If you plot this wave, as you add more and more harmonics, you will get closer to a perfect square wave.

Note that any wave with an average value of 0 has no DC component (which would be sin(0t)).

In this case, the wave is composed of all AC components. Hope this helps.

ermm, thanks

it does help, or at least it would if i understood it!! :?

whats a harmonic?

does the fact that you can step up only AC have nothing to do with the fact that it is always changing, but more to do with the fact that it changes from high to low (or inverse or whatever) quite quickly?? or have i gone an assumption too far?

also, are you saying that a square wave is made up of lots of more traditional AC type waves, and they all sort of average out at a wave that looks square-ish? And in the equation, is each bit (the bits that are added together, appart from the first one) a sinusoidal wave?

i did understand the last two lines of your post!

don't get me wrong, i do appreciate the help, but i'm only a beginer, and I don't really get the 'nitty-gritty' bits!

Harmonics are frequencies that are multiples of the fundamental. The 2nd harmonic of 60 Hz is 120 Hz, 3rd harmonic is 180 Hz, etc. And, you are correct, the square wave is made up of odd numbered sine wave harmonics added together.

The fact that AC can be transformed has everything to do with the fact that it is always changing. You need to understand inductance and inductors to appreaciate that. When voltage is applied to an inductor, the magnetic field starts charging up. Everything is fine as long as the magnetic field does not reach steady-state because when it does, the back EMF goes away, the current increases and something burns up (hopefully a fuse).

so how come it doesn't burn up when the square wave is in its 'high' or 'low' phase? How does the transformer 'know' that it is made up of lots of 'curvy' waves?

I'd rather not add to the confusion but thought it good to point out that what I understand as AC (alternating current) alternates or changes polarity once per cycle. The voltage rises from zero to some maximum, drops to zero then goes "minus" to some level below zero then back up to zero. The voltage generated by an alternator rises/falls as a sine wave because of the rotation of the alternator - or as a result of the oscillator or source.

A square wave can do the same thing - rise above zero, dwell, drop past zero to some negative value, dwell, then rise to zero.

Be careful not to mix this up with a "square wave" that isn't really alternating. An example might be the output of a logic or clock circuit that is actually square in shape but is only rising from zero up to some value, dwelling, drops to zero, dwells at zero then rises again. I'd call this pulsating DC - if there's a better term I'd appreciate knowing what it is.

Whether AC sine/square or pulsating DC, a magentic field builds and collapses as a result of the changes in voltage presenting a different load than just a simple resistor - which is why it doesn't burn up like it would if pure DC were applied for a time.

The transformer doesn't really "know" that it is made up of lots of sinusoids. In fact, this is precisely the concept of superposition. For instance, lets treat the transformer as a black box. We are putting a signal in that is composed of many other signals, x1, x2, x3, etc. We have some composite output y, that is made up of y1,y2,y3, etc. Rather than do the complex analysis (which would probably require a simulation), we can find what y1 is from x1, y2 from x2, y3 from x3 and then just add those up to find the composite signal y.

So why did I got through that. Mainly because you can think of the transformer of looking at it the same way. For simplicity, we put in three signals, f1, f3, and f5, which are the fundamental and two harmonics. The transfore is designed for f1, so it works the best at that frequency. At the f3 frequency it will work, but might not be as efficient so it gets warm. f5 might be so far off that none of the energy is converted and it all goes to heat.

So in summary, when you stick your signal into the transformer, you are putting in lots of AC frequencies, your transformer will have some frequency response to each one.

ok, i think i get it

thanks guys

Tim

thats a good answer STEVEZ, i never really understood it until now - ill prob forget it in time though.

cheers
andy

Another way to explain it is that the voltage induced into a conductor is proportional to the rate of change of the magnetic field. So when a step is applied to the primary of a transformer, the magnetic field changes at a rate that induces a voltage in the primary that almost exactly equals the applied voltage (Lenz's law). The changing magnetic field also induces a voltage into the secondary so the secondary voltage is dependent on the number of turns on the secondary compared to the primary.

It is equivalent to a RC differentiator circuit. The capacitor blocks DC, but an AC square wave will pass through it provided the frequency is high enough.

The same applies to a transformer. The frequency must be high enough, otherwise the waveform at the secondary will not be square.

Len

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