What is impedance? I'm looking at impedance in the regime of a waveguide. I have not been able to find much on what impedance actually is apart from (ratio of electric over magnetic field strength). But what really is it. Can you think of it like the resistance of free space for EM waves? So a lower impedance up to the free space limit the faster the wave?
Also what is impedance miss matching? I've been told its caused by imperfections in the wave guide but not what is actually is.
 A: The concept of impedance pops up all over physics, you'll see it in energy transfer equations involving waves in everything from vibrating ropes to LC oscillator circuits in analog electronics to waveguide propagation. Here is some background:
In the most general sense, impedance is the ratio of the effort variable (for example, voltage) to the flow variable (for example, current) in a network in which power (effort * flow) is being transferred.
If the power transfer occurs with high voltages accompanied by small currents, the circuit is said to be high impedance; if the power transfer occurs with small voltages accompanied by large currents, the circuit is said to be low impedance.
For perfect transmission of power between different components of a system, you need the impedance of the driver to be equal to that of the load- a condition known as matched impedance. An impedance mismatch causes the load to "fight" the driver in a way which reduces power transmission.
The perfect example of this is a car with a manual transmission, in which the effort variable is torque and the flow variable is RPM. The driver is the engine and the load is the car's mass.
If you are stopped at a traffic light when it turns green and you stick the transmission into 4th gear, the engine's torque versus RPM characteristic is badly matched to that of the car and its wheels, and little power is transmitted: the engine groans and stalls. You need 1st gear to match those impedances when starting the car off from a stop.
Similarly, if you are cruising at 60 MPH in 4th gear and suddenly downshift into 1st, the engine revs up like crazy trying to drive the load and it cannot push the car; instead it burns up. You need 4th gear to match things up.
In this context, the transmission in the car is a variable impedance matching transformer which lets you match impedances between the engine and the wheels across a variety of speeds.
