Here's a simple practical problem to figure out what combination of
available resistors would work best to configure a ham transmitter dummy load -
one that I needed to solve recently.
I acquired a bunch of 20 Ohm, 200 watt, non-inductive resistors last
year. Non-inductive, and non-capacitive for that matter, is necessary for an RF
dummy load, which wants to be as purely resistive as possible, just like your
perfectly cut and tuned antenna system. In working this, draw equivalent
schematic circuits as Alex has shown, and draw one for each step in the
process.
The problem for you to solve as homework (should you choose
to accept it) is:
What is the simplest way to connect some number of these
resistors together in a series/parallel arrangement to result in a total
resistance of 50 Ohms, which, as you know, is what most transmitters want to see
as a matched load?
Note: Given that you have a large number of these resistors, there
are many ways to interconnect them to get 50 Ohms; but, I'm looking for a way to
use the least number of them, which is less than six. (I won't tell you the
exact number)
Extra Credit Questions: Solve the following as you
would for a DC power source although in reality we would be dealing with a
transmitter's RF AC source. Alex will later show that AC
voltages can be conveniently expressed as their AC RMS value (root of
the mean square) which is equivalent to a DC value for power calculations and
the associated currents and voltages.
1.) For the 50 Ohm resistor network you come up with, and given that
each resistor can only dissipate 200 watts, what is the maximum continuous power
you could apply to your 50 Ohm dummy load without over stressing any
resistor(s)? Big Hint: You should calculate the maximum current permitted
in a single 20 Ohm resistor to yield 200 watts. Then calculate how much power
that current yields as being applied to the total load resistance of 50
Ohms.
3.) Let's say you've got your 50 Ohm dummy load connected so that
your load resistance is now fixed. But, let's also say you can
vary the tuning of the transmitter to either increase or decrease its
source resistance above or below 50 Ohms. Also given is that, in
changing the Tx source resistance, the voltage of the
ideal RF voltage source driving the series combination of the
source resistance and the 50 Ohm load resistance stays the same as for
the solution of question 1.). Then, what happens to the
power dissipated in the fixed 50 Ohm dummy load if you reduce the Tx
source resistance? What happens to that power if you increase the source
resistance?