> I understand the text book definition is resistance to A/C, but I fail to understand impedence matching, coax cable ratings, high impedance inputs, and pretty much anywhere else the term is used.

Actually, it's easy to understand the basic concepts in pure DC. Let's see...

high impedance inputs - this is the easiest one to explain. A device with high-impedance input only allows a small, often negligible amount of current to flow into it, as if nothing is connected.

Imagine a 5-volt power source followed by an 10k ohm output resistor in series, and we put it in a blackbox. If you connected another 10k ohm resistor across the blackbox, you create a voltage divider, and the voltage across your resistor would be 5 x (10k / (10k + 10k)) = 2.5 volts, and a current of 0.25 mA flows.

But if you increase the value of your inserted resistor to, e.g. 10M ohm, now the 99.9% of the voltage is now across your resistor, and you get 4.995 V, and there is almost no current flows across the power source, as if nothing is connected, minimizing the "observation effect".

This allows you to measure the voltage without disturb it by drawing power from a circuit. Example:

ideal voltmeter - gives a voltage measurement.

ideal oscilloscope probe - just an ideal voltmeter that takes many measurements and display a line on a chart.

ideal ADC - just an electronic voltmeter.

ideal transistor switch and logic gate - output only depends on the voltage reading of the input, it doesn't absorb power.

ideal buffer and operational amplifier - measures the voltage at the input without affecting it, and creates a replica of this voltage by using its own power source.

impedence matching - This one is difficult if we're talking about reflections, S-parameters, and standing waves, but it's easy understand if we only talk about impedence matching for maximum power transfer. People often say that, to get the maximum power transfer, the impedance of the source and the load should be matched. But it's misleading. Theorem of Maximum Power Transfer is actually telling us how to choose our load, given a known source, not vice versa.

Imagine an ideal 5-volt DC voltage source. The maximum available power from such a power source is infinite, and only depends on the impedance of your load. By connecting an infinitesimal resistor, infinite power will be absorbed by the resistor.

Now imagine an ideal 5-volt DC voltage source followed by 10 ohm of output resistor in series. This is closer to a real power supply, or a signal generator, or a radio antenna, whose internal impedance sets an upper limit of available power.

What the Theorem of Maximum Power Transfer is telling is that, if we want to absorb the maximum available power out of this power source, our load must be equal to the source impedance, in this case, 10 ohm.

If our load has the same impedance as our source, the voltage across our load will be Vcc x R2 / (R1 + R2), or 5 x 10/(10+10) = 2.5 V, and the power is absorbed by our load is V^2 / R, or 0.625 W.

If our load is much smaller than the source, there will be more current but less voltage. A 1-ohm load will get a voltage of 5 x 1/(1+11) = 0.416 V, and absorb only 0.173 W.

If our load is much bigger than the source, there will be more voltage but less current. A 100-ohm load will get a voltage of 4.54 V, and absorb only 0.206 W.

It's simple if the following misconceptions are cleared.

* Misconception 1: If I have a 300-ohm load, the output impedance of the power supply should be matched to 300-ohm for maximum efficiency.

False. Maximum Power Transfer does not imply Maximum Efficiency. Efficiency is the ratio, Useful Power / (Useful Power + Wasted Power), and it has nothing to do with maximum power transfer.

Recall the example above, when a 100-ohm load is connected to a 10-ohm power source, the voltage across the load is 4.54 V, drawing 0.206 W. Meanwhile, the voltage across the internal impedance of the power is 0.46 V, drawing 0.021W. The efficiency is 91%. But when impedance is matched, 100-ohm load is connected to a 100-ohm power source, the efficiency is "only" 50%.

Often, the efficiency is the best when there's low power transfer. You don't waste a lot of power if you don't take away a lot of power.

* Misconception 2: If I have a 300-ohm load, (e.g. a headphone), the output impedance of the power supply (e.g. a headphone amplifier) should be 300-ohm for maximum power transfer.

False. Maximum Power Transfer is only about how to select our load to absorb maximum power when we have no control over a given source, not vice versa. In real-life, for non-RF circuit, if we have control over the source, the solution is to make the output impedance of the power source close to zero.

For a 5-volt DC source with a 300-ohm impedance, connected by a 300-ohm load, only 0.02W of power comes out because there's only 2.5 V across the load. But if we have the output impedance to be 0.1-ohm, 4.998 V is now across our load, and drawing 0.083 W of power.

This is called impedance bridging, and it's how power supplies and modern headphone amplifiers are designed - they are designed for maximum efficiency by minimizing their output impedance, while the headphones themselves only draw a little bit of power.

On the other hand, a radio receiver is a good example when we have no control over the source impedance, given the same antenna, it cannot be changed. In this case, the better our receiver is matched to the impedance of the antenna, the higher its sensitivity.

BTW, in RF-circuit, even if we have control over a signal source, we use matched impedance, in this case, the purpose is not to get the maximum power transfer, but for avoiding reflections, a completely separate issue.

* Misconception 3: 50-ohm coax cable has 50-ohm of electrical impedance.

False. The "50 ohm" and "75 ohm" for coax cable is its characteristic impedance, not electrical impedance.

This is when things get complicated and when we must think electrical signals as waves. But the other comment has a good explanation, so it won't be repeated. In short, when a wave hits an impedance discontinuity in its medium of propagation, some of the energy is reflected, so in an RF system, 50-ohm everywhere is desirable.

A small piece of lossless coax cable can be modeled as an inductor in series and a capacitor in parallel, it's the radio of the inductor and the capacitor that determines its characteristic impedance that we can match to avoid a discontinuity in the circuit, thus avoiding reflection. Or we can say that the characteristic impedance is the input impedance when the length of the lossless coax is infinite.

It's not an actual electrical impedance that we can measure by an ohmmeter. A 10-meter coax has an electrical impedance of less than 1 ohm.