# The devil is in the detail – real world transmission lines and ReturnLoss

We are traditionally taught transmission line theory starting with the concept of complex propagation constant γ and then dealing with them as lossless lines (means Zo is purely real) or low loss distortionless lines (means Zo is purely real).

Let's explore theoretical calculations of ReturnLoss for a very short section of common RG58 at 3.6MHz.

By definition, $$ReturnLoss=\frac{ForwardPower}{ReflectedPower}$$ and it may be expressed as $$ReturnLoss=10log_{10}\frac{ForwardPower}{ReflectedPower} dB$$.

The scenarios are:

• open circuit termination; and
• short circuit termination. Above is the RF Transmission Line Loss Calculator (TLLC) input form. Note that it will not accept Zload of zero or infinity, instead a very small value (1e-100) or very large value (1e100) is used. Above, the input for the shorted termination.

Now lets compare the outputs side by side. Items of interest are highlighted. Note that the input Zload figure is different, open at left and shorted at right.

The calculated ReturnLoss wrt Zo=50+j0Ω (RL(50)) is different in both cases, one is 28 times the other.

You might have expected that based on classic transmission line theory that $$ReturnLoss=20log_{10}(2 l |\gamma|) dB$$ where l is length, and Zload does not appear in that expression, so ReturnLoss should be independent of Zload.

You would be quite correct in that thinking, and if you look to the second last line, you will see RL calculated as 0.058dB in both cases… this is the ‘true' ReturnLoss calculated wrt the actual Zo=50.02-j1.37Ω. You will see also that the calculated matched line loss is exactly twice the ‘true' ReturnLoss.

Beware of assuming that ReturnLoss(50) as might be measured by nominal 50Ω instruments is the actual ReturnLoss in terms of the transmission line Zo.