I've been looking at impedance matching a circuit, but I'm struggling to find an equation for calculating the values of the resistors in the output network.

Given this circuit:

How are the values 475R and 56.2R calculated?

Say $$R1 = 475, R2= 56.2, Rload=50, Rsource=500$$

You simply want from the source side: $$R1 + (R2*Rload)/(R2+Rload) = Rsource$$

So lets try that: $$475 + (50*56.5)/(50+56.5) = 501.5$$

So this shows that it works.

But as you can see there are 2 unknowns, ie $$R1$$ and $$R2$$. So you need atleast two equations. The one I did above was looking in from the source side. You can form a similar equation from the load side and solve simultaneously:

$$R2||(R1+Rsource) = Rload$$

• That's one of the equations. The other is to obtain the effective impedance of 50 looking the other direction. Then both must be solved simultaneously. Commented Sep 18, 2019 at 1:46
• Yup was editing before accidentally publishing..Editing now..
– MAM
Commented Sep 18, 2019 at 1:49
• @AdilMalik - Thanks! Dumb question, but to what operation does the || operator refer to? Absolute value, logical OR, etc? Commented Sep 18, 2019 at 2:30
• || = Parallel..
– Chu
Commented Sep 18, 2019 at 7:35