In transmission line does reflected wave travel on the path before impedance or after impedance?

Question

I was taught in class that 2 port RF networks have the following structure below, where V2+ is the reflected wave if load at end of port 2 does not match the characteristic impedance of lines at port 2:

^{simulate this circuit – Schematic created using CircuitLab}

Let's take a simple circuit that we can make practically, it consists of 2 ports where input is being applied at port 1. The network consists of a single resistor whose value may not match with characteristic impedance of either lines resulting in reflection:

^{simulate this circuit}

What I want to understand: If frequency of source is so low such that wavelength of input wave is much greater than L1 and L2 then the circuit doesn't need reflection consideration. What I mean is it would be like a 10 Hz source powering an appropriate load of wire length say 5 cm. This means voltage at load and source vary exactly as each other.

Statement 1: So, in above case, when we reduce it to simple network theory and we say that the current will travel thru Path 1 and return thru Path 2 (which we usually call ground path).

Statement 2: When we increase frequency such that wavelength is comparable to network, then also current should return thru Path 2. But according to first diagram, the reflected voltage/current returns thru path 2.

So, my confusion is does the reflected current wave, I1- (according to first diagram) returns on path 1 or path 2. If it returns on path 2, then does it add with the returning I1+?

Answer 1

Statement 1: So, in above case, when we reduce it to simple network theory and we say that the current will travel thru Path 1 and return thru Path 2 (which we usually call ground path).

Correct, for low speed analysis we can consider current flowing in a loop: -

• down path 1,
• through the load R1 and
• back along path 2.

We "say" (for the ease of the mathematics) that the current takes zero time to do this. Then it's easy to use basic circuit theories (like Kirchhoff's). But, strictly speaking we are not being absolutely correct.

Statement 2: When we increase frequency such that wavelength is comparable to network, then also current should return thru Path 2. But according to first diagram, the reflected voltage/current returns thru path 2.

No, this is not correct; we cannot talk in full circuit loops any more. What actually happens is that Path 1 and Path 2 form a transmission line (that's the name we use when analysing high speed data transmissions). Even before the signal has reached load R1, current is circulating back to the input source due to the input impedance of the transmission line called "the characteristic impedance" or \$Z_0\$.

If the load (R1) doesn't match the \$Z_0\$ impedance, we get a mismatch of voltage and current when they reach R1 and the "excess" (of both voltage and current) has to be sent back to the source in order to avoid ohm's law being violated. That excess is the reflection; it is both voltage and current.