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The pi pad

In the world of electronics we have impedance; the combination of all forces which oppose the flow of electric current. Often times we have circuits with different impedances, 50 ohms for RF, or 75 for cable TV. It’s pretty important to use the right coax in these circuits, else you’ll be wondering why your RG-58 antenna feed line doesn’t give you anything good to watch.

It’s pretty important to match impedances when connecting different circuits. Apart from the obvious flaws such as a 50 ohm load blowing up a 300 ohm amplifier, there are subtler things such as signal reflection and destructive interference which might just be enough to break whatever it is your playing with. RF mosfets are not cheap! But how could we match impedances? Well we could always use a transformer, but those are rather expensive and bulky. What if we only have a box of resistors to play with? Well, we could build an attenuator! Most of you probably know what an attenuator is; if not, it’s a de-amplifier. Simply put, it’s a circuit which reduces the strength of a signal. Often these are called ‘pads’ in the RF world, and the pad most often used is the pi pad. By looking at the network’s schematic it becomes rather obvious *why* we call it that.

It looks like a ?.

Now our guests want a 50 ohm signal attenuation of 3dBm, or 50%. Let’s pick some toppings for our pi then, shall we?

When Z=50, R1 and R3 equal…

[292.4 ohms].

Now R2 equals…

[17.61 ohms]

Well that was a pain. Luckily, there’s a cheat sheet for this.

So now we have our values, and assuming a 50 ohm load everything should work just fine. But wait! Somebody F*cked up and put a 300 ohm feed line on the end of the pad! Crap. Let’s look at the resistance values of the network now, from A to ground. I’m assuming you should know how to calculate resistances…

…105.7 ohms. That’s near double the 50 ohm input impedance and is going to wreak all hell upon the other circuitry. Sure, it does its job of reducing the signal 3dBm but still.

Now here’s the neat thing. Let’s pick some new resistor values so that we attenuate by 10dBm, or about 90%. According to our cheat sheet we’d need 71.75 ohms of attenuating resistance and 96.25 ohms to ground on either end. What’s the impedance mismatch now?

57.78 ohms, or 7.78 away from 50. That’s a lot better than before, and should actually be usable as an impedance matching network. Sure, you lose 10dBm or about 90% of your signal strength, but that’s nothing that can’t be compensated for by putting a Class-C amplifier in series with the attenuator. Even with an active component it’s still cheaper and smaller than a transformer. What I’m trying to prove here is that pi pads can be used as the poor man’s impedance matcher; as attenuation goes up the impedance mismatch goes down.

What’s nice about resistive pi pads is that they are ultra-wideband; since there are no reactive components this network will always attenuate by 10dBm and always match the impedance by 7.2 ohms. An inductive network such as a transformer might not work at both 200kHz and 200MHz. Actually, it certainly won’t work! Capacitive networks would have the same limitations.

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