Characteristic impedance of a transmission line - why is there a minus sign?

Hello all,

If I understand correctly, characteristic impedance of a transmission line is ratio of forward voltage wave to forward current wave or reflected voltage wave to reflected current wave.
It makes sense that Z_0 = (V+/I+). But why is Z_0=-(V-/I-)?
I searched for answers online and only explanation I found was "minus sign is because I- is traveling in -Z direction"
But V- is also traveling in same direction (-Z direction). So shouldn't minus signs cancel out and Z_0=(V-/I-)?

Thanks,

Your physical understanding is fine and it's only a definition thing how to measure the voltage (polarity).

In my opinion, V+ and I+ are different than V- and I-. so there is no way they are gonna cancel each other.Because first two quantities are actually desired signals(larger amplitudes) moving towards the load while others are undesired signals are undesired signals(smaller magnitudes) because of impedance mismatch. there ratio should be same as per impedance of the line.

Why?

For a single moded transmission line with two conductors, we have one voltage between the conductors. And because we have single mode propagation, all current in conductor "a" must return through conductor "b".

To have different currents, you would need a third conductor -> multimode propagation. That is usually not desired.

You are talking about incident and reflected waves, not voltage/current ratio.

Incident and Reflected waves can be interpreted in terms of voltage/current. Waves conversion to circuit theory.
this seems right for low frequency signal. For high frequency signal it is point to point travelling of waves as described by the lumped circuit model.
What I talking is, There is actually no scenario in which two kinds of signals can gather at one point on transmission line because of same source. This is only possible unless waves are reflected back. The direction is just a reference.

Ps:Volker if yo have idea about feeding network design please do comment my other post.

Sure. And one thing we must be careful with: when talking about waves and modes (not individual nodes), this implies well defined signal and return path. The currents in signal and return are dependent, and this is why Ia=-Ib

Voltage and current exist in high frequency and transmission lines also. We can convert wave representation to voltage/current representation. But we should not mix both concepts in discussion. The initial question was about voltage and current.

I didn't mean V-,I- will cancel V+,I+.
Both V- wave and I- wave are traveling in -Z direction.
So shouldn't Z_0={-(V-)/-(I-)}=(V-/I-)?

I will suggest you to look at the derivation for Lumped circuit model.

http://www.ittc.ku.edu/~jstiles/723/...el_package.pdf