Attenuator calculations

[glias]

Hello all,
I'm interesting attenuator circuit and would want to know how can I calculate this type of circuits :

I don't understand how we can write expressions of R5 and R6 :

(from this site : https://www.allaboutcircuits.com/vol_3/chpt_1/7.html)
how does the expression of R5 and R6 comes from ? how can we write them like this ?


I hope that you could help me
regards

 

[FvM]

The resistance values are unequivocally determined by two conditions
- attenuation
- 50 ohm input impedance

In contrast the T and pi attenuators discussed in the same lesson have in- and output impedance matching, requiring three resistors to fulfill all conditions.

 

[RCinFLA]

This type of attenuator is often used as a minimum loss attenuator for matching Z where Zin is higher then Zout.

It is not a very good attenuator for other applications unless return loss is unimportant. You need a PI or T arrangement to get general attenuation and keep input and output Z to a desired specific value.