How vector network analyzer measures S-parameters of lumped element?

Question

i've seen video lecture where S-parameters of 50 Ohm resistor placed in series between input and output port of VNA with reference resistance also of 50 Ohm are calculated by hand. S11 was calculated as equal 1/3 by formula of reflection coefficient S11 = Г = (Rin - Z0) / (Rin + Z0) = (100 - 50) / (100 + 50) = 1/3. So question is why resistor have reflection? It is not waveguide, what reflections can it have? And if it have reflection, how VNA measures it? Does it simply measures amplitude on its port or somehow measures amplitude of outcoming and reflected wave? I also heard that reflected wave can be detected somehow via directional coupler but anyway i don't understand what reflection do i have in case of lumped resistor? Sorry if I mix different questions in one.

Answer 1

why resistor have reflection?

First, you're not measuring just a resistor, you're measuring a resistor whose other end has been connected to the input of a transmission line whose far end is (pretty close to) ideally terminated.

But to answer your question, the signal coming out of the first transmission line can only propagate forward without reflections if the ratio of its voltage (measured between the inner conductor and outer conductor for a coaxial line) to its current (measured on the inner conductor) is equal to the characteristic impedance of the transmission line.

Since the termination you provided (a resistor plus another transmission line with an ideal termination) has an effective impedance of 100 ohms, the ratio of voltage to current at this termination will be 100 V/A, rather than 50 V/A. This means that a backward travelling wave (a reflection) must be produces so that the voltage-to-current ratio in the termination can be 100 V/A while the voltage-to-current ratios in the forward and reverse travelling waves on the feed line are both 50 V/A.

And if it have reflection, how VNA measures it?

The VNA (speaking broadly) separates the reflected wave from the outgoing wave with a directional coupler and measures its amplitude with an RF detector (a diode-based device that converts RF signals to DC voltages). If the reflected signal is mixed with a local oscillator before being measured, the phase of the reflected signal can also be determined.