# Question on matched 3dB attenuator

For the second picture below, how to derive the expression for Vo?

I suppose there is some inbetween maths that I missed.

Note: 41.44 Ω is the parallel equivalent for (50 Ω + 8.56 Ω) || 141.8 Ω.

• So, what answer did you get and what is the correct answer? Commented Aug 15, 2019 at 9:50

You are on the rigth way with the $$\41,44 \Omega\$$ calculation.

The schematics are simplifications from top to bottom. For example the middle schematic shows on the right hand side the part from the top schematic that can be expressed by an equivalent R (left side).

$$\R_{eq}= \frac{R_p*(Rs_ + R_L)}{R_p+(Rs_ + R_L)} = 41.44 \, \Omega \$$

Derivation:

$$\1) V_{R_s} = R_s*i \$$

$$\2) V_{R_{eq}} = R_{eq}*i \$$

$$\V_1 = V_{R_s} + V_{R_{eq}} = R_s*i + R_{eq}*i = i*(R_s + R_{eq})\$$

$$\i =V_1 /(R_s + R_{eq})\$$

Subsituting i in 1) and 2):

$$\V_{R_s} = R_s*(V_1 /(R_s + R_{eq}))\$$

$$\V_{R_{eq}} = R_{eq}*(V_1 /(R_s + R_{eq}))\$$

$$\V_0\$$ being $$\V_{R_{eq}}\$$:

$$\V_0 = \frac{V_1*R_{eq}}{R_s + R_{eq}}\$$

for $$\V_1=1V\$$:

$$\V_0 = 0.829 V\$$

• I do not understand why Req is a standalone resistor in your second circuit above ? Commented Aug 16, 2019 at 2:44
• Req is the equivalent of the right hand side (Rp||(Rs--RL). That's exactly what you had calculated to be 41.44 Ohm. Commented Aug 16, 2019 at 15:32