Error in simulation results for balanced pi type attenuator

Question

I wish to design a balanced pi type attenuator to give attenuation of 20dB and characteristic resistance of 500 ohms.

I have found out the necessary resistances required to design the attenuator. However upon simulation on ISIS proteus, the results are not what I expected. For input of 40V, the output is 7.92V instead of 4V. Where am I making a mistake?

Answer 1

Try adding the 500 ohm source resistance and 500 ohm load resistance... If you remove the three attenuator resistors, you'll get 6 dB attenuation from V1-to-load resistor R3.
If you insert the three attenuator PI-resistors, you'll get 26 dB attenuation from V1-to-load resistor R3.

Normally, V1 is not accessible as a bare voltage source...its source resistance of 500 ohms (R4) is part of the source. You would measure attenuator input across R1 (below). Then the attenuator output across R3 (below) would be -20 dB.

^{simulate this circuit – Schematic created using CircuitLab}

Answer 2

Where am I making a mistake?

You forgot to add a 500 ohm termination resistor across the load side. Doing this makes the net resistance seen after the 2475 ohm resistor into 275 ohms and this provides 20 db attenuation. Your source also needs to drive via 500 ohms and this means that without an explicit attenuator in place, there is an implicit attenuation of 2:1.

I wish to design a balanced pi type attenuator to give attenuation of 20 dB and characteristic resistance of 500 ohms.

Also, your circuit isn't a balanced attenuator because you have one side earthed. Maybe you mean balanced in respect of both input and output being the same? Wiki quote from the above link: -

In telecommunications and professional audio, a balanced line or balanced signal pair is a transmission line consisting of two conductors of the same type, each of which have equal impedances along their lengths and equal impedances to ground and to other circuits.

Wiki also tells us about unbalanced transmission lines: -

In electrical engineering, an unbalanced line is a transmission line, often coaxial cable, whose conductors have unequal impedances with respect to ground; as opposed to a balanced line. Micro strip and single-wire lines are also unbalanced lines.