I'm pretty sure the answer to this should be obvious - even to me ...
It's been a while I've been reading and attempting to construct simple electronic circuits. The supply almost always is either through a battery/cell, or AC duly rectified to DC.
I have the impression electronic circuits rarely ever work off an AC supply.
Your impression is correct.
AC flips polarity very often. Most semiconductor devices have been designed with very particular polarity conditions in mind. If one were to reverse the polarity between two inputs on many different components, you would get magic smoke coming out of it.
For example take mosfet operation. An NMOS is expected to block current from drain to source until the gate is activated. If you have AC across drain to source, then it allows current to flow backwards (losing gate control).
It's not impossible to design an electronic circuit with active devices around AC, but it makes it much more challenging. I should also qualify this statement: many electronics circuits do have signals with AC components to them, but they usually have a DC offset to them to prevent the polarity switching. That would be something like 5VppAC with a 2.5V DC offset would be an AC signal from 0-5 V. That remains the same polarity at all times even though it's passing an AC signal.
A keyword - in context with the question - is LINEARITY.
Let us take the simple example of an electronic circuit, which is widely used: Transistor-based "linear" amplifiers (lumped circuits or integrated). Transistors are highly non-linear devices.
In order to produce sinusoidal output signals exhibiting low signal distortion it is necessary to use only a certain part of the input-output charcteristic. Hence, we use a dc voltage/dc current to BIAS the device at a suitable operating point (within a limited quasi-linear part of the input-output function). Then, the input signal causes a swing around this operating point resulting in an acceptable output quality.
You are right, circuit are seldom powered with AC. Some analog circuit may work on AC, but digital doesn't. This is due to the very nature of how it has been design and how it has proven to be efficient and easy to implement. There are system which uses AC signal to encode data on some very old systems, but it requires lots of high power components, which is not practical with current technology. An example would be old casino slot machines which used an analog signal to make the reels turn and the coin dispenser drop coins one by one. Also, some mechanical counters used AC signal toggling to count.
Transistors as they are now are designed to be efficient with DC signals (if you consider digital data as DC, since some purist would say it actually is offset AC). It is what is the most power efficient and space-wise efficient in integrated circuits. Also, encoding data on AC signal (while possible) is much more complex than with DC signal, since you can use a simple edge detection mechanism. In order to do so with AC, you need to use peek detectors or circuits like that, which is not practical.
Now if you want to understand why technology moved toward DC, consider this: imagine you are trying to turn on/off complex circuits with DC, it is easy, because your signal has only two states: full on and full off. With AC, you would have (as a guess): an AC signal or no signal. Relays could be compatible with your AC signal, but they work simply because of magnetic field. In order for your relay to remain firmly on, you would need to rectify your signal (so it doesn't swing) thus yielding rectified AC...
In short, it is both due to historical and technological reasons.
First electron tube was the diode and the main property is to produce DC voltage from AC (one way). Triode tube is based on diode (DC) and was the first device with stable amplifyication or switching properties. This was realized controlling the electron flow from a negative cathode to a positive anode via a grid. So the weak grid voltage modulates a DC voltage (dc swing) and those an amplifier is made. This device needed mainly by Telegraphy and early Radios area . To use an AC power makes the amplification extremily coplex and finaly useless.
After that a lot of applications with electron tubes introduced in the market and industry around the globe.
Transistor invented as a direct replacement of triode tubes, based exactly at the same concept, and today IC’s consists of million transistors that needs a DC power.
However there is a semiconductor device like Thiristor or Triac that can be powered with AC power, but in most cases needs a zero-crossing circuit with a proper input signal that should be related somehow with the frequency of the AC power and so on
Most interesting circuits maintain some internal state, that means: they store information. In order to do this, the circuits needs electrical energy. Pure AC (current and voltage in phase) by its nature regularly goes through a period in which no energy is supplied. This makes it difficult to make a circuit that can store state: it is as if the circuit has to start anew every AC period. You can circumvent this problem by storing energy in some other form (magnetic, mechanic, in a capacitor, etc) but why bother? DC can supply energy all the time, so most circuits work with DC.
The above is mostly about digital circuits. An analog circuit could be AC powered, but then the AC component would be present in the output, which in most cases would present a problem (especially when the output is fed into a human ear).
