# 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].

## 29 thoughts on “Pi Network Attenuators: Impedance Matching For The Strong Of Signal”

1. Alex says:

Nice Article…impedance matching inductors and coils can be very difficult….time, patience and experience does go a long way in those situations!

2. for the hopeless peasant like me, i will invariably revert to buying whatever pre-fabricobbled radio module i can get out of Shenzhen the cheapest, i wish i had the time to learn this all

1. So what do you do when they’re running hot and you’re getting 1/10 of the performance you expected, from X spiffy module and Y spiffy antenna? Buy another one?

In this instance it’s almost like saying “I wish I had time to learn to drive, but I spend every spare second hunting for beater cars because they keep crashing on me..”

1. Daniel says:

1. Surfingtheither says:

Ham gets hot over RF feedback…or something whitey like that, ill leave it for the next guy to make a good ham/pork joke about radio operators.

2. Because the Mini Circuits catalog and a credit card can save you two months of screwing around with design-by-committee and sourcing quantity-one parts? I dunno. Just a thought. :-)

3. Daniel says:

I really enjoyed this read regardless the absence of hack. Next episode: The mixer

1. Doug says:

Learning the basics can be beneficial to the hacker, but I hear that some can’t be bothered to find the time to learn.

4. Mr Master says:

“Strong” is an adjective. The name you are looking for is “strength”.

1. notarealemail says:

It may have been a reference to something…

1. Ren says:

Like, “Strong’s Biblical Concordance”?

B^)

2. Jenny List says:

I’m afraid you’ll have to do better than that.

5. Moryc says:

It should be pointed out that most resistors, especially high-power ones also have both inductance and capacitance. And in case of RF circuits it might have quite an impact on performance and attenuation…

1. t_diddy says:

I meant to say for chip resistors at <2GHz.

6. Simon says:

When was the last time you saw a ham in a bar?
Bars are for people who actually leave their houses.

1. Gotta leave the basement before you can leave the house.

7. Gravy_enthusiast says:

Good read and interesting subject :) Thanks, Jenny :)

8. John Phillips says:

Isn’t the whole point of being a ham to want to do things the fiddly time consuming way?
If it was purely to contact others we could just email each other, I like the fact that each individual “improvement” involves trial and error and a few more “deadbugs” for the how not to do it museum.

1. For some perhaps, but for me if I want an oscillator i grab an SI5351a or a mixer i get something from mini circuits and use modern building blocks rather than make everything at the component level. the thrill is in building simple transmitters and receivers and being able to use it to make contacts with others as well as having fun playing with electronics.

9. Jenny you are missing a point in RF engineering,.
In RF design you use a matching network to preserve the power of the signal between stages.
If you do impedance matching with an attenuator you might as well NOT do any matching at all to start with. The miss-match would give you less loss than matching with an attenuator.

1. It is obviously not a panacea to be used instead of proper matching transformers, but there are instances where using a pi pad is actually beneficial. Its also not always about preserving power, it can also be to stop one stage loading down another, removing excess gain and providing the correct impedance to termination sensitive things.

2. Jenny List says:

Completely understood. This is for times when you want an impedance mismatch proof RF source, and aren’t bothered how much power you put in.

10. jenningsthecat says:

A couple of things the article didn’t mention:
1) Tee attenuators can usually be substituted for Pi attenuators, and the calculating programs I’ve seen will give values for either topology. Theoretically, one can be substituted for the other at will; in practice, parasitics may occasionally cause them to behave a bit differently;.i(I theory, there’s no difference between theory and practice; but in practice, there is)… Sometimes changing from a Pi to a Tee or vice-versa will get you closer to the desired impedance(s) with standard E24 resistor values.
2) Within certain limitations, (depending on the amount of attenuation and the difference between the two impedances), Pi and Tee networks can be used for impedance matching. This is useful if you have, for example, a 50 ohm generator and a 75 ohm load, or vice versa. Of course you’re throwing away some of your signal, but it may be worth it to have cheap, transformerless impedance ‘transformation’. Again, the calculating programs I’m familiar with allow for specifying both the input and output impedances.

11. Luke Weston says:

“Your impedances are set by resistor values, which are reliably available over a huge range.”

The resistive pi pad is just a special case of the general pi network – with three impedances Z1, Z2 and Z3. And that network, in general, has a great many applications – as a filter, as an attenuator, or as an impedance match including complex impedances.

Of course there’s no such thing as a perfect resistor with no inductance or capacitance – you still have parasitics, whether you’re building a system with capacitors and resistors, or a system that only has resistors.

Real-world tolerances in component values, and parasititic resistance, capacitance or inductance, apply to “pure” resistive devices just like they do to devices with inductors or capacitors. You’re still going to have some usable frequency limit beyond which the pi attenuator does not behave as you expect it to.

It’s still a really common and useful circuit, and it’s useful to recognize common resistor values (for example 300 ohm shunt resistors on both sides and 18 ohm series, for 3dB attenuation in a 50-ohm system without impedance mismatch) which are handy building blocks.

Of course matching impedances with a resistive network assumes you have only real impedences on either port – good luck matching impedances with a resistor where the imaginary component of the impedance is non-zero :)