The difference between impedance and resistance

Al covered lots of good details but I would like to summarize it for those that might have gotten lost.

The fundamental difference has to do with frequency, as in frequencies of the recorded music, for example. There are innate qualities of capacitance and/or inductance in certain components (like capacitors and inductors) but they are not called into action until there is a signal composed of frequencies (such as music) interacting with them.

As the frequency of the signal increases, the way the signal sees every electrical part in the system changes dramatically. The higher the frequency, the more inductance and capacitance, quite literally, appear. Eventually you get to a point where even a resistor acts like a capacitor and an inductor! And then after that, even a wire exhibits inductive and capacitive effects! It is a crazy world - and it's no wonder cable and component break-in occurs.

Since music is not a DC signal (frequency of zero), technically speaking there is no such thing as a pure resistance in a stereo system. Everything has some sort of reactance associated with it, be it capacitive or inductive, which requires the use of the term "impedance." This is ever more accurate as frequencies go above human hearing, but there is no mathematical lower limit for this effect. This is why it pertains to our stereos.

As far as a "bad load" is concerned, it is tougher to drive a capacitive load than an inductive or resistive one. Capacitive loads can be seen in impedance plots as negative phase angles, meaning the current is ahead of the voltage. Not only does the efficiency of the circuit decrease if the load is capacitive, but the current demands during transients can be significantly more than looking at resistance alone. That double whammy is hard on an amplifier.

Arthur

The reason radians are used is because the derivative of sin(x) is directly cos(x) when using radians. This is why the formulations using radians come out cleaner.

I would like to add too that you very rarely get 90 degrees in a circuit. The parasitic effects will cause the angle to be all over the map, positive and negative, the extent of which is dependent on the frequency of the signal.

Simply-q: Break-in effects are largely due to parasitic capacitance effects through the air, insulation, cable sheaths, PC boards, etc., surrounding the signal-carrying wire(s). The capacitance is formed between the wire and "ground," which can be just about anything at a lower potential, and everything in between ground and the signal is the dielectric. These effects are part of what I was talking about. The fact the ground is indeterminate is what leads to the mystery of break-in. As time goes on, the more-dominant capacitances charge to a "neutral" level and finally break-in "ends." This is in addition to any physical material changes due to heat or an applied field.

There has been extensive research done by the French government (and the Germans to a certain extent) on this effect as it relates to high-power transmission lines. It is easier to witness when you're dealing with MV instead of mV. (When you stand under a power line, you are quite literally standing inside a capacitor.) They have shown that just the heavy ions in air can have a big impact on the capacitive resonance effects that affect a signal. But they are far from nailing down all the variables in all instances, of course.

Arthur

Bob - the difference between the derivative in radians and degress is the scalar multiplier of k*pi. The key thing to note in my description is the word "directly". I found this description that should go into enough detail for you to understand what I was saying:

http://mathforum.org/library/drmath/view/54181.html

As for lead and lag, you can do a search for "ELI the ICE man" and the first few links that pop up offer good explanations.

Arthur