L-pad attenuators

Updated August 17, 2007

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Updated August 2007! We've fixed some typos in the equations, thanks to David from Jakarta!

L-pad attenuators are popular with audio geeks throughout the world, but they don't get much play in the microwave industry. Here we'll tell why that is.

L-pads can be used to perfectly match one impedance to another, but the solution is lossy. In microwave engineering, this is usually unacceptable, we'd rather match two impedances with near-zero loss by using reactive components, which limits the bandwidth of the solution. Note that for a given input and output impedance, only one solution exists for an L-pad where the input and output are to be perfectly matched; this is often called the "minimum loss matching pad".

This schematic and others are in a Microsoft Word file you can download for presentations, look for it in our download area!

L-pads can be also be used as variable attenuators, if you allow one of the impedances to be mismatched, which is usually not a good idea for microwave circuitry because the effects of voltage standing waves (VSWR). Audio geeks do this all the time, they keep the generator side matched (so you don't blow up an expensive power amp), and to heck with the speaker side! At audio frequencies you don't have to worry about the effects of standing waves, unless your amplifier is in New York and your speaker is in California and they are hooked up by a lossless transmission line. Good one!

Here's a web page that has an L-pad calculator:

http://www.webervst.com/lpad.htm

Just remember when you use this the output won't be matched.

Equations for impedance-matched L-pads

This configuration is often called the "minimum loss matching pad". It is used to match one real impedance to another real impedance, a typical application is to match 50 ohm stuff to 75 ohm stuff (we'll use that as an example below).

The equations are simple to derive using Ohm's Law, or you can look them up in the ITT Handbook or other resources. For Z₁>Z₂,

R1=Z₁xSQRT[1-(Z₂/Z₁)]

R2=Z₂/SQRT[1-(Z₂/Z₁)]

The attenuation (or insertion power lost) is defined as (Power out)/(Power in). Here you have to be careful to include the effects of the disparate input and output impedances.

Pout/Pin=1/[SQRT(Z₁/Z₂)+SQRT(Z₁/Z₂-1)]^2

(linear, not dB!)

Update August 2007! Thanks for the corrections, David! These calculations are in an Excel spreadsheet that is available in our download area, check it out!

Let's look at an example. Suppose you wanted to create the perfect match between a 50 ohm system and a 75 ohms system. Using the above equations,

R₁=43.3

R₂=86.6

Attenuation (dB)=-5.7 dB.

This begs the question... why would anyone want to throw away almost 75% of their available power, when the mismatch loss between the two impedances is only 0.2 dB? Probably not an experienced microwave engineer!

Let's look at a broad range of impedance mismatch from 50 ohms. Even for small mismatch, you pay a big attenuation penalty. So the phrase "minimum loss pad" is a cruel joke indeed!