# Impedance matching question

Discussion in 'Homework Help' started by boks, Nov 17, 2008.

1. ### boks Thread Starter Active Member

Oct 10, 2008
218
0
Do we get max. power transfer by setting $Z_S = Z_L$ both in AC and DC circuits?

2. ### KL7AJ AAC Fanatic!

Nov 4, 2008
2,071
334
For an AC circuit, you get maximum transfer when the load impedance is the COMPLEX CONJUGATE of the source impedance.

3. ### boks Thread Starter Active Member

Oct 10, 2008
218
0
And for a DC circuit simply when $Z_L = Z_C$ because there's no phase shift?

4. ### KL7AJ AAC Fanatic!

Nov 4, 2008
2,071
334
that is correct. For a DC circuit, it's pretty easy to prove that maximum power transfer occurs when the load resistance equals the source internal resistance. Rather, I should say, it's easy to demonstrate....while a rigorous mathematical proof is a bit trickier.

If you model a battery as being a voltage source with a fixed value of resistance in series, with a load resistance equal to that value of resistance, you can do a few simple calculations. Calculate what the load's dissipated power would be with a resistance matching that of the battery internal resistance. Now change the value of that load resistance to anything else, and rerun the calculation. You will not find any value that results in MORE power dissipation in the load.

eric