Hi Mik,
Okay, it can be pretty confusing, but here's the basics...
If you take a basic resistor and connect it to a DC voltage source, you know that a certain current will flow through the circuit, depending on the size of the resistor. This can be worked out with Ohms Law. Nice and easy.
If you then connect the same resistor to an AC voltage source- e.g. the secondary winding of a power transformer, you can again work out the current flow due to the voltage using Ohms Law.
This is because the resistance of the resistor is independent of the frequency of the voltage- from 0Hz (i.e. DC) up to about 1MHz the resistor is purely resistive. Above 1MHz it's a different story but lets not worry about that now.
Okay. Lets have a look at capacitors. The simple analogy of a capacitor is that it blocks DC and passes AC...simplistic, but a working theory. We can place a capacitor between the power supply rails and once it has filled with charge it is "blocking" DC.
But when does DC become AC? Easy- as soon as its frequency increases from 0Hz.
So if a capacitor blocks DC, will it also block 0.0001Hz? IOW, will it also block a very slow AC signal?
The fact that this capacitor "blocks" DC can also be seen as the fact that the capacitor has a very high resistance once charged- which is exactly the case, because once it is charged with DC only a very small current will pass- the leakage current.
But a capacitor connected to an AC voltage will charge on a positive-going cylce and discharge on the other side of the cycle, so a current will appear to be flowing during this charge-discharge cycle. Speed this charge/discharge cycle up a bit and more current will be seen to pass...
Something is happening here- as the frequency of the voltage is increased, more current is passing "through" the capacitor...therefore it's resistance appears to be falling....but a resistance has to remain constant no matter what the frequency as described above!
:?
This is the Reactance of the capacitor. Put simply, a reactance is the AC Resistance of a component- more accurately the AC Impedance.
There are two equations for reactance because there are two types of component which exhibit frequency-dependent-resistance:
1. Capacitative Reactance Xc for capacitors.
2. Inductive Reactance Xl for inductors.
Capacitative reactance:
Xc= 1/(2*pi*f*c)
Inductive Reactance:
Xl= 2*pi*f*L
Looks complicated, but it's not. Both equations are basically the same- we're taking the value of the component in Farads or Henries (notice we use the largest unit of value- you have to convert uF to Farads and mH to Henries etc) and multiplying it by the frequency in Hertz (the frequency at which we want to know the components Reactance), and multiplying this by 2*pi, which is roughly 6.3 for on-the-spot calculations. For capacitative reactance Xc, 1 is then divided by this number. For inductive reactance Xl this is the actual value. Reactance is measured in Ohms (which is cool- because we can then work out the overall impedance of a combination of DC Resistance, Xl and Xc in a circuit and have the overall result in Ohms at a certain frequency... :grin: )
Equations can be a bit scary, but lets look at these again.
Xl= 2*pi*f*L
or,
Xl= 6.3*f*L
Here we can see that Xl increases if the frequency increases, or the Inductance increases or both values increase. Conversely, we can see that Xl decreases if f decreases or the value of the inductor L decreases, or both- this is correct behaviour for an inductor- a power supply choke is a big coil of wire of large inductance which allows DC (0Hz) to pass, but which has a higher reactance to power supply ripple frequency (60/120, 50/100Hz etc)
For capacitative reactance Xc, the same equation as above is done, except that the 2*pi*f is multiplied by the value of C (in Farads). This is then put into the equation below 1.
1/"anything" is called the inverse of "anything".
If you plot a graph of "something" vs. "anything", and then plot the graph of "something" vs. 1/"anything", the graph will be inverted.
This is exactly the way to think of inductive and capacitative reactance- with Xc, as the frequency increases the reactance decreases (remember with Xl the value increases for increasing frequency...) and when the frequency decreases, Xc increases.
More simply, (and a handy way to remember) a capacitor "blocks" DC (as in a PSU smoothing cap) and an inductor "passes" DC (as in a PSU choke filter) with the effect reversing for increasing frequency for each component...
Right, more later on combining Reactances, got to go now!
:guinness:
Mark
