# Pi Network Attenuators: Impedance Matching For The Strong Of Signal

If you catch a grizzled old radio amateur propping up the bar in the small hours, you will probably receive the gravelly-voiced Wisdom of the Ancients on impedance matching, antenna tuners, and LC networks. Impedance at RF, you will learn, is a Dark Art, for which you need a lifetime of experience to master. And presumably a taste for bourbon and branch water, to preserve the noir aesthetic.

It’s not strictly true, of course, but it is the case that impedance matching at RF with an LC network can be something of a pain. You will calculate and simulate, but you will always find a host of other environmental factors getting in the way when it comes down to achieving a match. Much tweaking of values ensues, and probably a bit of estimating just how bad a particular voltage standing wave ratio (VSWR) can be for your circuit.

If LC circuits aren’t for you and you have plenty of RF power to play with, there is of course another way to preserve impedance matching, and it’s one in which you’ll never have to tweak a recalcitrant inductor again. Simply use a resistive attenuator, and put in enough power to compensate for the fact that some of it will be lost as heat. Your impedances are set by resistor values, which are reliably available over a huge range.

A Pi network attenuator is a simple three-resistor circuit, as shown in the diagram to the right. Both input and output are terminated by resistors, in this case R1 and R3, and the degree of coupling, or attenuation depending which way you want to look at it, is set by R2. From an impedance perspective each end sees an impedance equivalent to its termination resistor in parallel with a resistor made by the other two resistors in series. In practice for high degrees of attenuation in which R2 is quite large, the total  impedance as seen from the outside tends towards that of the terminating resistor, so for example if R1 and R3 were each 50 Ohm, and R2 was sufficiently large, the impedance seen at each end would still be pretty close to 50 Ohm.

This property of Pi networks in which R2 is much larger than R1 or R3 also has a side effect which is the point of this article. If you were to remove R3, the impedance as seen across R1 would be equal to R1, while if you were to short R3 completely the impedance as seen across R1 would still be pretty close to the value of R1. Thus not only does a resistive Pi network provide impedance matching at the expense of attenuation, it also provides a measure of isolation in the event of a significant impedance mismatch. Thus you can use a Pi-network attenuator to isolate your RF generator from the adverse VSWR effects of a severe mismatch, and create a bench RF source that is effectively bulletproof and can be connected to any impedance without damage. The injection clamp shown in our February feature on EMC testing uses an attenuator for just this purpose.

So how do you calculate those resistor values? The formulae are readily available, as for example on the Wikipedia page, so there is little point in regurgitating them here as if we weren’t just pretending to be an authority while merely cut-and-pasting them. Of more use though are a host of online calculators that are just a Google search away. Most of them will allow you to input preferred resistor values, and to tweak for the best results to fit your needs.

If you’ve never used an attenuator for this purpose, we hope you’ve had your eyes opened to the possibilities they offer, and we’ve liberated you from the tyranny of the LC circuit when it comes to quick matching of RF sources on your bench. Maybe in a distant future where grizzled old subspace amateurs down synthehol in a holodeck bar, the Wisdom Of The Ancients will involve attenuators for a somewhat lazier version of impedance matching.

Attenuator image: Miikka Raninen [Public domain].