# What is AC actually?

What is actually alternating current (AC)? And direct current (DC)? I've been reading several books about basic electric circuits analysis and they are contradictory.

1. Some books say that AC is the same as the sinusoidal stationary state. That is, a sine or cosine function (actually, they are the same only shifted horizontally). For instance, $v(t) = A \sin(\omega t + \phi)$. Acording to these books, DC is totally stationary (static), that is, the voltage and current are not time-dependant ($v(t) = k$, where $k = \mathrm{const.}$). Currents have the same form as voltages on each of these cases.
2. According to other books, AC is any current that is changing (that is alternating) his sign over time ($t$). With maths notation: $i(t_1) < 0$ and $i(t_2) > 0$ for some $t_1$ and $t_2$ where $t_1 \neq t_2$. It could have any shape as long as it's alternating his sign.

I'm inclined to think that in practice wins the first option but maybe it's better the etymology of the second option.

Some other cuestions have relation to this:

1. Is AC a voltage that is the sum of a sinusoidal stationary state and a constant voltage? For instance, $v(t) = A \sin(\omega t + \phi) + k$.
2. Is AC a shawtooth wave?
• What is your purpose? Understanding "AC analysis" aka "small signal analysis" af amplifier circuits? Power distribution? Power supply design? All your contradictory views are correct, in different contexts (though AC isn't usually a sawtooth, you can find examples of pure sawtooth AC waveforms if you know where to look). Without giving any context this is too broad. – user_1818839 Sep 29 '17 at 12:29

AC does not have a precise meaning, its meaning can be context dependent. It's probably better to identify various waveforms and ask whether they could be called AC.

A sinewave waveform with a zero average would certainly count as AC.

A square, triangle or any other waveshape with a zero average would also count as AC.

If any of these waveforms had a small non-zero average, they could be described as AC with a small DC component.

Generally with AC, the 'alternating' part of the description suggests (but it's only as weak as suggests) that the waveform reverses polarity from time to time. If one of the waveforms above had a large DC average, such that it didn't reverse, then it could be described as fluctuating DC, or DC with ripple (as Michael K points out), or could be called AC on top of DC, or AC with a large DC component. All would be correct, or at least, none of them are wrong.

In all cases, if it really matters what the waveform is, then describe the waveform voltage as a function of time, don't get hung up on how different people try to name it. If it's in an exam or class assignment, then memorise what your tutor expects to see (it will be in their notes), and just reproduce that for the marks.

• You might want to mention too that OP might come across the term "ripple" especially in relation to fluctuating DC (being a relatively large DC voltage with a small AC component). Ripple, of course, not directly relating to the wave form of the voltage, but being the change of peak-to-peak value of the non-DC component of a mostly-DC voltage. (Example: "This 13.8 V DC power supply has a maximum ripple of 30 mV peak-to-peak with full load.") – user Sep 29 '17 at 18:24
• That said, I'm giving this a +1 even just for the final paragraph alone. That's the real take-home (or take-to-work?) lesson from all this; in the absence of clear definitions, if it really matters, don't rely on your definitions being the same as the person you are communicating with; instead, describe what you really mean. – user Sep 29 '17 at 18:32
• "AC does not have a precise meaning, its meaning can be context dependent." That's now how I've learned and probably contradicts with all books I got, so I'm quite curious where you get this from. – Mast Sep 30 '17 at 8:37

That's actually a more complex question than you imagine.

At face value we think of the sinusoidal volts that come out of the wall as AC and the volts that come out of a battery as DC, but in reality those are just two, almost pure, commonly available examples.

As @ThePhoton mentions, in reality all voltages can be expressed as having two components. A DC part and some AC time function. The time function can be anything. A simple sine, a triangle, pulse wave, anything you like with an average amplitude of zero.

Obviously the wall socket has, or should have, a zero DC part, and the battery should have a zero AC function. However, in reality most every signal has both to some extent or another.

In practice whether we call a signal AC or DC depends to the most part on what information the signal is carrying and how we intend to use it.

Example 1: Consider the output of a bridge rectifier.

Obviously the input here is AC, but what do we call the output.

If we are going to use it for the regular function to generate a DC power source, we call it DC, despite the fact it is really an AC function with a DC component.

If however we intended to feed that full rectified wave into an amplifier as a signal we would call it an AC signal.

Example 2: Consider a simple DC biased amplifier

Again the input is obviously classical AC, but in order to function correctly, a DC voltage component is added and the output ends up with a DC component of Q. However we would still call the output an AC signal despite the bias.

In fact this still holds true even if the input signal is removed. On the scope the output may look like a DC voltage, but we would refer to it as a zero amplitude (biased) AC signal.

Example 3: Is it AC or DC?

You could call this waveform a DC voltage with a ripple, or you could call it an AC voltage with a large DC offset.

Either could be correct. Which one is more correct depends entirely on how the signal is being used. In some applications, both could even be true.

In Conclusion:

Other than the simplest examples of line and battery voltages the terms AC and DC are relative and application specific. Which term you use or hear should invoke a certain higher utilitarian meaning.

• Hi, Trevor. +1. I'm not sure if you are aware that you can size the imgur images by adding a letter before the dot in the filename. e.g. i.stack.imgur.com/IOl0Wm.jpg converts it to a medium size 320 x 320 image. The handy ones are 't' for thumbnail, 'm' for medium, 'l' for large and 'h' for huge! See bitmapcake.blogspot.ie/2015/05/… for more. It can help make images such as in your Example 1 better proportioned to the text of the post. – Transistor Sep 29 '17 at 17:08
• As long as the bias DC voltage is constant, couldn't you just consider the resultant DC+AC voltage to be at some other ground reference? After all, there's nothing special about a DC bias of +676 volts (or any other value, for that matter); that only really depends on what you measure against. If you do, then it becomes obvious (or does it...?) that a pure DC bias is irrelevant to whether a voltage waveform is AC or DC. – user Sep 29 '17 at 18:31
• @MichaelKjörling indeed, the bias is a relative term, good point. – Trevor_G Sep 29 '17 at 18:33

There are two different definitions of AC and DC that don't entirely agree with each other.

1. A signal is DC if it always has the same sign, either always positive or always negative. A signal is AC if it is sometimes negative and sometimes positive.

2. A signal is DC if it does not vary in time, and AC if it varies in time and has a mean value of 0. (N.b.: this means that not every signal can be categorized as purely AC or purely DC, as we'll see below)

I don't know where the first definition comes from or what sub-field prefers it, but I have seen it used and vigorously defended a few times on Stackexchange and other online sites.

The second definition is the one used in circuit theory and most academic work in EE, in my experience. The value of this definition is that any signal can be broken down into AC and a DC components like

$$v(t) = v_{dc}(t) + v_{ac}(t),$$

where the DC part is actually constant ($v_{dc}(t) = {\rm constant}$), and the mean value of the AC part is 0.

With these definitions, we can in many circuits find ways to understand the circuit behavior by analyzing the effects of the DC and AC components of the signal separately. For example, if the amplitude of the AC component is small, it might be possible to analyze its behavior in a linearized model of a circuit, even if the circuit is a nonlinear one.

• +1 RE: "I don't know where the first definition comes from"... probably from the fact that once AC is passed though a rectifier we call it DC even though we know it's just a folded sine-wave. – Trevor_G Sep 29 '17 at 16:11
• @Trevor, Yes, I'm guessing it's from the power world, but I don't really know. – The Photon Sep 29 '17 at 16:13
• Of course in some sense there is no true DC that will be constant for all time. Your circuit had to be turned on before you could start using it and it will eventually be turned off. – Peter Green Sep 29 '17 at 17:59
• @PeterGreen, that's true. If you consider that there's also no true ideal wires with no resistance or circuits small enough to produce zero radiation, the whole of circuit theory is founded on useful approximations rather than perfect models. – The Photon Sep 29 '17 at 18:05
• A fluctuating voltage with stable polarity is DC. Anything crossing the polarity ('going through 0') is AC. Direct Current isn't the same as Constant Current. – Mast Sep 30 '17 at 8:39

As you've noticed, "AC" is a term with multiple definitions.

• AC means alternating current! Period! Don't listen to any others!!!

:)

• AC means sine waves only: AC voltage and AC current. (Well, cosine is acceptable too.)

• AC means "dynamic" or "changing." If it's not changing, then it's static and DC.

In that case, a narrow voltage-spike isn't AC, because it's not current, yet also it's purely AC, since it's changing fast. But really it's not AC, since it has just one polarity; it doesn't cross zero or change back and forth. But also it's not AC because it's not sinusoid!!!

Avoid stupid arguments, and always beware of chasing after the "Single True Meaning" of words. That's called a "Swiftian Battle."

This was well parodied in Gulliver's Travels, where the Liliputians had a war between Big-endians and Little-endians. Looks like Johnathan Swift could see the future and the internet coming. The stupid Liliputian war involved: vast and teeming hoards ...of tiny little people ...at each others' throats ...fighting about the One True Way way to crack an egg.

Current is the movement of charge. The charge carriers in a conducting material such as a copper wire are electrons.

If there is a force on an electron it will move. When dealing with electricity we are concerned with the electromagnetic force.

For alternating current, the electrons on average go back and forth, back and forth, etc. but their average position does not change.

For direct current, the electrons on average go in one direction.