Is current with a frequency less than 1 Hz still considered DC?

Question

We had a big argument last night with vague conclusions. Is the current with a frequency less than 1 Hz considered DC?

It would still resemble a wave...

Answer 1

AC and DC are relative terms. If you're looking at a 10kHz waveform for 100ns, you will think it is DC. It works the other way around too: if you forget about what's providing you with "DC", who knows if this waveform is not going to change in the next seconds, minutes, days, years? Think the voltage of a capacitor for example during slow discharge. If you monitor the voltage on an oscilloscope, you'll see a flatline. DC you say? Wait longer, and the flatline will decrease in voltage towards zero, which means there is some AC in there as well.

Besides, no signal is actually pure DC, you always have AC components as well due to noise and all sorts of causes. It is only "DC-enough" or "AC-enough" for the application you're intending to use it with/for.

Fourier transforms are a good way to picture what DC and AC components are in a waveform. The transform is constant for periodic signals and depends on time for any non-periodic signals like the capacitor example. For the square wave: (source: wikipedia)

Answer 2

Yes, you can have AC with a frequency less than 1Hz, in the same way you can have numbers between 0 and 1.

Frequency isn't an integer number, but a "real" number. You can quite happily have a waveform of \$1 \times 10^{-100}Hz\$ if you wanted. You'd have to be quite patient to see it change, but it will change, and given time it would trace an AC waveform.

Answer 3

As with any AC voltage, frequency is the inverse of the period in seconds, and vice versa:

$$f = 1 / T$$ $$T = 1 / f$$

As f gets asymptotically close to 0, T correspondingly becomes very large.

As a practical example, I have a function generator that generates any frequency up to 5MHz in 0.01 Hz steps. So at its lowest setting (0.01 Hz), it can generate a sine wave with a period of 100 seconds.

Answer 4

If you want to be strict, all real current is AC. I'll explain why.

Looking at it from a thermodynamic point of view, a direct current (which never changes magnitude) would require two terminal points of fixed charge; that is, one relative positive, one relative negative. (I'm using charge here instead of voltage or current in order to stick to my thermodynamic approach, and keep things simple.) The relative positive would dispense into the relative negative, without ever changing magnitude itself; thus, an infinite source of charge, dispensing into an infinite well. This is of course an ideal.

Since such black boxes do not exist in the real world, it is safer to say that "direct current" is simply a model. The rules that apply to it have been calculated and can be applied to a slowly varying voltage source, such as a gradually draining AA battery; but all sources of current will ultimately reach zero, and thus have a frequency.

So, in a broad sense, there are cases in which /any/ current frequency can be described as DC; and the AC laws can be derived from the DC laws. As to whether 1 Hz looks like DC, it depends on how short a time frame you are using it over, and how close it appears to be to level during that time. It's really up to you.

Answer 5

As others have already pointed out, you can have AC of as low a frequency as you wish.

I think it's worth adding, however, that at such low frequencies it mostly won't act much like most of us usually think of AC acting.

Just for an obvious example, you can typically think of a capacitor as allowing AC to flow through it, but as stopping DC. At extremely low frequencies like you're considering, you're probably not going to see any significant current flow, even though it is technically AC.

In particular, a capacitor basically acts like a (very gentle) high-pass filter. To pass such a low frequency well, you'd need a tremendously huge capacitor. By far the most common type of large capacitor is an electrolytic capacitor. An electrolytic capacitor is a little like a specialized battery--that is, part of how it works is chemical, not purely electrical. Like batteries, electrolytic capacitors can self-discharge over time. I've never tested to figure out an exact rate of self-discharge, but it wouldn't surprise me a lot if it were to self-discharge faster than (for example) a 0.01 Hz signal was charging it--if so, the net result would be that the capacitor never charged, and it would basically act like there was no capacitor there at all.¹

The bottom line is that most AC circuits are designed for much higher frequencies, so even though there's no sharp cutoff below which a signal is no longer AC, quite a bit of typical thinking about AC circuit design may easily start to sort of fall apart as you reach such...subterranean frequencies.

Just for reference, the lowest frequency of AC in really common/wide use is probably in audio circuits. Although (again) it's not a hard cuttoff, the typical number used as the bottom-end of the audio range is 20 Hz.

There has been some work done in Extremely Low Frequency radio, but the lowest frequency of which I'm aware was around 50 Hz or so. For a 1 Hz signal, a half-wave dipole antenna would be substantially larger than planet earth.

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^{1. In fairness, most electrolytic capacitors are polarized, so you normally use them for things like filters on DC power supplies. Here I'm assuming an (admittedly, less common) non-polarized electrolytic capacitor.}

Answer 6

Of course. 1 Hz is once per second, and a second is a fairly arbitrary amount of time. If we had settled on 100 seconds per minute, 60 times per minute would have been 0.6 Hz.

Answer 7

Yes, you can have alternating current (AC) that alternates with a frequency less than 1 cycle per second (a period longer than 1 second). If you connect a battery and a resistor using a properly wired DPDT switch, you would be able to reverse the voltage across the resistor, at will. So if you manually throw the switch once per second, or once every 2 seconds, or once every 100 seconds, etc. you would have "alternating current" with a frequency less than 1 cycle per second.

Answer 8

Whether a voltage is AC or DC has nothing to do with frequency, but more to do with whether the voltage is alternating or not. If it's not alternating it's DC.

If a voltage always stays above zero (ie; positive) it is 'DC', although it may have a small 'AC' component. Such voltages have a mean value above zero (the DC level).

On the other hand, if the voltage alternates from positive to negative (no matter how slowly) it is 'AC'. Such voltages have a zero mean value.

Answer 9

Yes. Hertz is a measure of how many cycles happen in a given time frame (1 second).

Since time is subjective, and a second is a unit defined by humans, you could (for example) have a "Zecond" that lasts 0.4 seconds.

Hence the definition of Hertz could be different but retain its meaning.