Updated July 11,
This page is in response to the
following question: how do you solve attenuator equations?
It's so simple that even a 47-year-old
can do it, using Ohm's Law! We'll look at one example here, then
you are all on your own. If you can't do this math, you need to
consider a new career, perhaps in your company's Six Sigma organization.
The only "formula" you have to remember is that resistors
in parallel have a net value of the product over the sum.
Start by drawing a picture of
the attenuator, and include the voltage source and its impedance.
Remember to use "2V" for the voltage source, and Z0 for
its impedance. Then under the matched condition, ZIN and Z0 will
form a 50% voltage divider and the load will get the maximum power
Now, let's start
by calculating the attenuation, which is given by Vout/Vin. What
you have is a two-step voltage divider. We can write two equations
Note that if you
work on the above expressions you can solve for VIN/VOUT in terms
of RA, RB and Z0.
An important property
of the attenuator is that ZIN must be matched to Z0. This gives
the following expression:
of sheet resistance variation on attenuators
Let's jump ahead
to a common attenuator problem. What happens when you are unable
to laser trim the resistors in a tee or pi attenuator to 1% values,
when you are making thin-film attenuators? This is often the case,
because the way the network is hooked up it is hard to separate
R1 from R2, etc.
It turns out attenuators
are a lot more forgiving than you'd think, because of the combination
of errors in series and shunt elements tends to cancel each other
Yes, we will post
the equations for this soon... but we checked our answers against
an ADS model, so we are confident that the plots are correct.
Below is a plot
showing the attenuation error for either a tee or a pi, when sheet
resistance is varied from 0.6, 0.8 and 0.9 of its nominal value.
By the way, it makes no difference if you use a tee or a pi, the
error you create when sheet resistance drifts is exactly the same.
If you are off the mark in the opposite direction (Rsh=1.66, 1.25
and 1.11 of nominal) you get the same errors. The sheet resistance
has to be 40 percent low (or 66% high) to make the error more than
0.55 dB. Sweet!
Here's a look at
the input return loss with the same sheet resistance errors. Here
even if you are under the nominal by 40%, you still get 12 dB return
More to come!