What is impedance? And why does it do those terrible things?
Beginners with electronics get down Ohm's law pretty quickly. The concept that Voltage, Current, and Resistance to electrical flow are related by the simple expression V=IR seems to
What is impedance? And why does it do those terrible things?
Beginners with electronics get down Ohm's law pretty quickly. The concept that Voltage, Current, and Resistance to electrical flow are related by the simple expression V=IR seems to set pretty easily. They usually learn about capacitors and inductors as "something else", not like resistors at all, but as perhaps a way to store energy or filter some frequencies from others. But sooner or later, they run up against the need to understand the effect of source impedance and/or load impedance, and things get un-simple quickly. Impedance seems to become a vague concept of something like electrical strength or drive capability, not simple at all, especially if the impedance in question involves capacitors or inductors, or (ugh!) both.
It's not that complicated.
Impedance is the generalization of the concept of resistance from DC to AC. That is, it's a way to represent how much current will flow with a specified (AC) voltage across the impedance. That is, if you have one volt AC across an impedance that lets one ampere of AC current flow, the impedance is defined by the AC version of Ohm's law and is one ohm.
Since AC has not only amplitude, like DC, but also frequency and phase, this introduces the possibility that an impedance will not only allow a current to flow, but will change the phase of the signal, and respond with different amplitudes and phases as frequency changes. You can have a resistor, a capacitor, and an inductor that each have an impedance of one ohm (or a Kohm or a Mohm) at any given frequency.
The resistor (ignoring the "imperfections" of parasitic capacitance, lead inductance, etc., which is usually valid at audio frequencies) will have the same impedance at every frequency. The capacitor will have an impedance that goes down with frequency (making the same assumptions as with the resistor, ignoring parasitics) and the inductor will have an impedance that goes up with frequency (ditto).
We can calculate the impedance of any of these, given a frequency to work with.
The cap is Xc = 1/(2*pi*F*C) and the inductor is Xl= 2*pi*F*L, so they vary linearly with frequency. As to phase, the inductor's voltage is always 90 degrees ahead of its current (the current takes some time to change); the capacitor's current leads the voltage across the cap, as the capacitance slows down voltage changes. If you can remember "E" for voltage, I for current, you can keep this straight by the phrase "ELI the ICEman", which is a nonsense way to remember "E leads I in inductors (L's)" and "I leads E in Capacitors (C's).
In AC power line circuitry, where the "signal" on the line is always a fixed frequency, fixed amplitude sine wave, inductors and capacitors make perfectly good current limiters, better than a resistor would be because they cause no heat to be dissipated as a result of their current limiting. In fact, the impedance of inductors and capacitors is so different from a resistance that it's given a special name - "reactance". In engineering schools, impedance is expressed as a "complex" number represented by "Z". This Z is the sum of a resistance and some reactance, Z = R+jX. You won't need to know this, but I thought I'd mention it in case you had run across it and wondered.
Ok, so how do we do some quick calculations of impedance?
There are ways to do it that are analytically correct, but very confusing. There are more intuitive ways to find some approximations; we can ignore some things and simplify. I'm going to skip the correct-but-tedious stuff entirely.
Any series element that has a very small impedance compared to the other things in series with it can be replaced with a wire for the purposes of calculations. Any parallel impedance that is very large can be replaced by an open circuit; these simplifications produce only tiny errors. When we come to things with similar (less than 10:1 differences) values in series we add them, and in parallel, we compute the parallel values.
Using these approximations, we can usually get a pretty good idea of the source impedance (how much impedance is inherent inside a signal source) and the input or loading impedance (how much current it takes to drive a signal into it)
Example: The input to an NPN transistor amplifier, with a pull down resistor of 1M to ground at the input, a capacitor of 0.1uF in series to the base, which also has a resistor of 220K to the positive supply and a resistor of 22K to ground, and a 1K emitter resistor from the transistor emitter to ground.
Unstated but assumed is that the supply voltage is that, a pure voltage source with an impedance that is vanishingly small. We approximate that with a battery, which may have an internal resistance of only a few ohms. Since this is by far the smallest impedance here, we replace it with a short, our first approximation. So now we have the 220K and the 22K in parallel to ground from the base.
Let's see about that input cap. The impedance can be as high as 1/2*pi*82Hz*1E-7 = 19.4K at the low end of the guitar range, and as low as 79.5 ohms at 20KHz. The 1M is much higher than the cap at all frequencies of interest, so we replace it with an open circuit and ignore it.
So now we have a seri