# how to derive resistance vaules (attenuator)?

Let's say we have this types of attenuator pads:

How do we derive their resistance values? like shown below

Where did Zo, k come from? How about R5, R3 and R7?

edit:

Zo represents the characteristic impedance, k represents the ratio between V out and V in and R5, R3 and R7 are simply the designations for resistors across different configuration

The question looks likely to be closed, but here's a start :-

Taking the 'T' attenuator, 'k' represents the reciprocal gain. For example, a required attenuation of 20dB (ie a gain of -20dB) gives a 'k' of 10.

$Z_0$ is the required characteristic impedance of the circuit into which the attenuator is to be placed. With a source impedance of $Z_0$, the output impedance of the attenuator will also be $Z_0$, and with a load impedance of $Z_0$, the input impedance will also be $Z_0$. The calculated attenuation will only be achieved with this source and load impedance. The resistor values are derived from three simultaneous equations for gain, input impedance and output impedance.

For the 'L' pads things are different since the source and load impedances cannot be the same. For the first pad, with a matched load impedance, the input impedance will also be matched. However, even with a matched source impedance, the output impedance will not be matched.

The second 'L' pad is similar but allows the output impedance to be matched at the expense of the input impedance.

I haven't checked the formulae for the other pads but it's all just Ohm's law, KVL & KCL from there.

• this answers the question :) +1 – WantIt Jul 24 '13 at 15:47