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For my own learning, I derived the following relationships for basic two-element impedance-matching networks. Apologies that I cannot create diagrams; they are not supported by touch devices.

If \$R_S < R_L\$: put Ra in parallel with Rs; then Rb in series with Rl.

$$ R_A = \frac {R_S} {\sqrt {1-R_S/R_L}} \\ R_B = R_L {\sqrt {1-R_S/R_L}} $$

In the opposite case, if \$R_S > R_L\$, make Ra in series with Rs, and Rb in parallel with Rl, and in the equations exchange Rs with Rl and Ra with Rb.

In both cases, Rs will see an impedance of Rs looking forward, and Rl will see an impedance of Rl looking backwards.

But is the backwards criterion necessary if power is only ever transferred from source to load? Would this criterion only need to be enforced on a bidirectional line?

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  • \$\begingroup\$ I'm not sure what you mean by "backwards criterion." Could you please clarify that? \$\endgroup\$ – esilk May 18 '18 at 16:46
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    \$\begingroup\$ As in, how important is it that the load see a resistance equal to its own resistance? \$\endgroup\$ – Reinderien May 18 '18 at 17:09
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I assume you are talking about L-Pads in your post. I am far from an expert, but I believe that bi-directional impedance matching is only important when you are concerned about issues such as reflections and standing waves, such as RF applications (or any other time transmission line effects are significant). In these cases, then yes, the primary design constraint is the matching of the impedances in both directions, and the insertion loss is often a secondary consideration.

Conversely, in situations such as audio attenuation, the impedance matching doesn't matter in the "reverse" direction nearly as much. A common use of L-pads are attenuating the output of, say, a tube amplifier that expects to be presented with a certain nominal impedance. The speaker, on the other hand, doesn't care so much what it is being driven by (consider the fact that most solid state power amplifiers are often lower impedance than the speakers they drive). The primary design consideration here is attenuation (insertion loss) and matching in one direction, whereas there often is no consideration as to what the speaker will see.

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  • \$\begingroup\$ Yes, I am thinking of an L-pad, though I didn't know what it was called. Thanks! \$\endgroup\$ – Reinderien May 18 '18 at 17:52

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