# Stuck on an approach to a simple problem. Need a nudge in the right direction.

#### profbuxton

Joined Feb 21, 2014
421
problem is as follows:
An attenuator is designed to conform to the condition that,
eqn 1: (R1 + R2 + Ro) /R2 = 5

where Ro = sqrt(R1R2 +( R1^2) /4) = 60

find value of R1 and R2 (note in practice no negative resistance)
I am working through some of my very old books and have got stuck on procedure to break this code. I have the answers but need a nudge on how to go about this one. Any help is much appreciated so i can stop having sleepless nights and mathematical nightmares.
Thanks for you help

#### Ian0

Joined Aug 7, 2020
8,378
Start off my getting all references to R2 to the right hand side of the eqn1.

#### WBahn

Joined Mar 31, 2012
29,150
problem is as follows:
An attenuator is designed to conform to the condition that,
eqn 1: (R1 + R2 + Ro) /R2 = 5

where Ro = sqrt(R1R2 +( R1^2) /4) = 60

find value of R1 and R2 (note in practice no negative resistance)
I am working through some of my very old books and have got stuck on procedure to break this code. I have the answers but need a nudge on how to go about this one. Any help is much appreciated so i can stop having sleepless nights and mathematical nightmares.
Thanks for you help
Since there's no circuit schematic, there's no way for us to know if your starting equations make sense.

For Ro, which of the following do you mean:

$$R_o \; = \; \sqrt{R_1R_2 \; + \; \frac{\left( R_1^2\right)}{4}}$$

which is what you wrote, or

$$R_o \; = \; \sqrt{\frac{R_1R_2 \; + \; R_1^2}{4}}$$

which is what someone might easily have meant.

If R1 is supposed to be ~71 Ω, then you meant the first, but if R1 is supposed to be ~101 Ω, then you need the latter.

In either case, solving it is pretty straight forward if you tackle it in two steps.

The first step is to use the first equation to solve for R2 in terms of R1.

Then substitute this into the second equation and solve the resulting quadratic equation.