Explaining return current and propagation on a transmission line

[Analog]

In texts the edge of a signal is often shown propagating down the transmission line with a return current shown leading back to the source (top example). The waveform being constant back to source. Would a better conceptual/teaching model be a narrow pulse propagating with no return currents to the source (bottom example)? To me this seems better although Bogatin, Brooks, Et al. all use the first model. I know in practice that PCBs are unlikely to have leading and falling edges present on the transmission line at one instance in time however the narrow pulse concept seems better in explaining the nature of return current and the importance of a constant dielectric and conductive structure along the trace. Opinions?

[T3sl4co1l]

Well, it would be inappropriate to show signals that far out of scale.  What you've drawn is a few picoseconds long, hard to generate at board level, let alone move around within the board for any useful distance in typical materials!  It also wouldn't have much time to spread out between nearby traces/planes, or really affect much of anything else nearby unless it also has bandwidth as extreme as the source.

It's also not much of a distinction, as you can do this.



Tim

[Analog]

Thanks for the feedback. I've seen figure 3 before and although it helps illustrate a wave transition moving without current flowing from the TX side of the line is still bothers me that there is current illustrated as going all the way to the load although I've seen emphasis made on current at the transition illustrated.  In my opinion the return current to the source (leading edge) or load (trailing edge) reinforces the complete circuit or battery and light bulb way of thinking. For me the pulse concept seems to better show independence of the transition from source or load at the ends of the line. I'm viewing this from a TDR/RADAR/wave on a rope viewpoint where the wave is traveling free from influences of sources but still propagates in it's Zo environment. Of course the whole point of this is a better conceptual model and if the pulse concept just confuses people it is not good.

[T3sl4co1l]

The Kirchoffian battery-light-switch form doesn't entirely stop being true at high frequencies, it just moves to smaller and smaller scales.  At some point, that scale becomes differential, and we have to integrate Maxwell's equations to solve the problem.  For most board-level problems, we can still treat a transmission line as two ports, each port being a Thevenin source of Zo, with the signal and return currents being instantaneous, at the port +/- terminals.

We then assume a whole lot of nothing happens inbetween, until the other port of the transmission line.  This is a good assumption when the line is well shielded, and does not couple into space, neighbors, or itself.

If not well shielded, we can express the coupling or isolation between transmission lines, calculated in standard ways.  Lines routed in parallel for some distance form a parallel-line directional coupler, and the magnitude can be calculated with quasi-static field methods (e.g., ATLC2), looked up in tables, or approximated with formulas (various calculators).  At worst, we can do a full wave simulation of the geometry, and extract parameters.  (Wave simulators provide ideal port connections, making this reasonable.)

The main difference to ideal transmission lines is, PCB lines are all with respect to ground, and a complete ground plane is required.  We do not have ideal ports (i.e., zero common mode current).  Although we can approximate them using free transmission line (e.g. twisted pair, coax) and transformer cores.

Holes in the ground plane are subject to coupling (and thus radiation) in the same way that transmission lines are subject to coupling between each other.  Holes and slots act like islands and wires -- the presence or absence of conductor is reciprocal, and equivalent to some extent.  Thus a trace crossing over a slot in the ground plane, couples into the slot (almost as strongly as being wired across it), and this is why slotted ground planes are generally frowned upon; when harnessed intentionally, it's a good mechanism to couple to slot lines, the Vivaldi antenna being a typical example.

Note that well-bypassed overlapping planes act together as one contiguous plane, so it's not an admonition to avoid signals crossing between power domains on a multilayer board.  The slotline mode is still activated, but the wave thus launched goes under and between the planes, where it spreads out into a very low impedance, quickly becoming negligible, or eventually finding its way into bypass capacitors.  Might still want to avoid crossing over sensitive analog planes, but fine for digital logic.

Tim