Transmission Line with Multiple Loads Along the Way

I have a 2 port/4 terminal transmission line with characteristic impedance Z0. Input Port is I+/I- and Output Port is O+/O-.

When doing impedance matching, I understand you can put an input resistor Rs=Z0 and make RL=Z0 between O+/O-.

But throughout the transmission line I have loads on it as well, say B+/B-, C+/C-, etc. I have to believe that this situation is common in high frequency RF signal distribution with multiple
"taps" along the way.

If the loads are, say, capacitive, such as driving transistor gates, how do you "account" for them in terms of overall transmission line and impedance matching? Do you put in some matching resistors along those taps?

Also what if there are resistive loads along the transmission line, what effect would that have on the overall transmission line?

Is this basically where you need to go deeper with multi-port s-parameter type analysis (which I am weak in, admittedly).

Any insight on how to deal with this is appreciated!

Is this basically where you need to go deeper with multi-port s-parameter type analysis (which I am weak in, admittedly).

Click to expand...

Everything can be described with S parameters, but there probably more visual ways.

Capacitive loads (e.g. MOSFET gates) can be matched by locally reducing transmission line parallel C, or adding series L. Operation principle of distributed amplifiers.

Resistive loads at a transmission line of constant Z0 will cause signal attenuation in any case. To compensate for the signal reflections at the discontinuities, you need to add series R. A transmission line with staggered Z0 could keep the voltage level along the line constant while sourcing power to the loads.

One common way this might be done is with use of a directional coupler.

A very small sample of the signal can be removed without substantially effecting the impedance (or loss) through the main signal path.
It will however probably require a gain stage to raise the level of the small stolen sample back up to a usable level.
Google "20db coupler" for more info.

Conjugate matching works pretty well for simple lumped reactive loads.

If the load involves very complex impedance changes, a four port quadrature hybrid can work quite well.

A well matched Transmission Line cannot be tapped-off as you desire.Otherwise matching and everything will go worse..
Tapping off from a Transmission Line for any kind of circuit needs a circuit "Tap-Off" like a Directional Coupler to prevent unwanted distrubings from the line.

The basic concepts of transmission-line theory are broken when you load the line. I would think the best you can do is determine the input impedance, and make sure that you match to this. It's up to each of your components to make sure that they do the same.