Transmission line and infinite reflection coefficient

[Boorglar]

Hello,
I am taking some microwave engineering courses and was trying to explain the concept of reflection coefficients to my friend, but he asked me a question I am unable to answer...

So we know that given a transmission line with characteristic impedance $Z_0$ terminated with a load impedance $Z_L$, the voltage reflected is related to the incident voltage by the reflection coefficient, $\Gamma_L = \frac{Z_L - Z_0}{Z_L + Z_0}$.

Now what happens if we pick $Z_L + Z_0 = 0$? This could happen if both $Z_L$ and $Z_0$ are purely imaginary, and one is the negative of the other (maybe some inductive and some capacitive reactances cancelling each other). Normally in our courses we considered $Z_0$ being a real number, usually 50 ohms. But if I assume it to be complex, then the reflection coefficient can become larger than 1, and even infinite like in that case.

So what's the physical meaning of an infinite reflection coefficient / reflection coefficient larger than 1? That seems to contradict conservation of power, because you get more power reflected than input power...

 

[tech99]

So what's the physical meaning of an infinite reflection coefficient / reflection coefficient larger than 1? That seems to contradict conservation of power, because you get more power reflected than input power...[/QUOTE]
The load is storing more energy than the generator is supplying each cycle. It is similar to a series resonant circuit, where application of very small power can produce large voltages across L and C, each of them storing a large amount of energy.
Notice that a transmission line with a purely reactive characteristic impedance is a rare beast indeed.

 

[marcusl]

A little thought would go a long way before making an assertion like this. A pure imaginary impedance is not a transmission line. Look at the characteristic impedance $$Z_0=\sqrt{\frac{R+j\omega L}{G+j\omega C}}$$There is no way to make this purely imaginary.

 

[Jeff Rosenbury]

A little thought would go a long way before making an assertion like this. A pure imaginary impedance is not a transmission line. Look at the characteristic impedance $$Z_0=\sqrt{\frac{R+j\omega L}{G+j\omega C}}$$There is no way to make this purely imaginary.

That is not clear to me. There is currently research into advanced metamaterials with odd electrical characteristics.

However such a material would need to provide energy to the line, which can be done.

There's no free lunch, but sometimes we can steal a bit from nature.

(Of course there will always be some small real parasitics since nothing is perfect.)