Return loss derivation question using reflection coeffiecient

I have a question about the formula for return loss: RL = -20 log (Γ) where Γ is the reflection coefficient.

Γ can never be a negative number because you cannot take the log of a negative number, according to the RL equation.

But if I use the Γ equation ZL-Zs/ZL+Zs where in one case ZL=50 and Zs=25 I get Γ = .33, and RL = 10.458

But if I use the Γ equation ZL-Zs/ZL+Zs where in another case ZL=25 and Zs=50 I get Γ = -.33, RL is 10.458 according to bessernet'd demo. http://www.bessernet.com/Ereflecto/tutorialFrameset.htm

So my question is it possible to get a RL c=value when you have a negative value for Γ ? How so?

Is it such the case that the Zs will never be larger than ZL?

your formula for RL is not completly correct.

The correct one is RL = -20 log |Γ|

The sign of Γ is related to the phase of the reflected wave with respect to the incident one.

Thanks for a clear and precise answer. Now that I got that resolved could you explain to me why open circuit, maximum reflection results in a reflection coefficient of +1 and a short circuit , maximum reflection results in -1? I am reading that it has to do with the voltage magnitude at different locations along the transmission line but it is still not clear. The attached files come from the book that explains short termination and open circuit termination in respects to magnitudes of voltages.

Try this;

http://www.microwaves101.com/encyclo...vswr.cfm#other

Extract from above; ... the reflection coefficient can distinguish between short and open circuits. A short circuit has a value of -1 (1 at an angle of 180 degrees), while an open circuit is one at an angle of 0 degrees.

But return loss, a scalar quantity, is derived from scalar (unsigned) reflection co-efficient which ranges from 0 to 1.

So; plug-in a scalar reflection co-efficient between 0 and 1 into the equation RL = -20 log |Γ| kindly supplied by albbg and see what you get.

Can you tell me why/how -1 for short circuit and +1 for open circuit? How is this determined?

The voltage along the trasmission line will be due to the superposition of incident wave + reflected wave. This means that, if the amplitude at generator side is A and supposing the generator impedance matches with the line impedance:

1. Vincident(end)+Vreflected(end)=0 ==> Vreflected(end) = -Vincident(end) if the end of the line is shorted
2. Vincident(end)+Vreflected(end)=2*A ==> Vreflected(end) = 2*A-Vincident(end) if the end of the line is left open

This is a simple intuitive explanation, valid after initial transient and supposing total reflection.