Why transmission lines are key to truly understanding how real signals travel

Yes, the dreaded Transmission Line. It turns out that these mystical things are actually more than mildly useful in the real world! Surely you're joking Mr. TheEEView, but on this occasion I'm not. Tell us more...

Okay so before deep diving into the practical details of transmissions lines that are actually of critical importance, let's discuss why we should even bother learning more about them (because time is of the essence right?)

Why should we learn about Transmission Lines?

Simply put, every single interconnect is a transmission line.

That simple statement is in itself worth pondering further. Why is this so? Well let's take a look at a real interconnect broken down into it's fundamental components.

If we consider this dead simple circuit above, it is what we call ideal, how does it look under the microscope so to speak (let's just assume also for now the voltage source itself is ideal but the interconnect is practical)?

Okay that looks slightly more complex than the ideal version, nature doesn't make it easy for us :P In short, wires/interconnects have distributed inductance (L1 and L2 in the above) (every current carrying interconnect has inductance, fun fact) and every air gap has capacitance as the air functions as the dielectric between the signal path and its return path (ground) which is the distributed capacitance part (C1, C2) and distributed resistance R1 and R2 as all interconnects have non-zero resistance.

And what does the above look like? That horrid transmission line we all hoped/thought we could forget about! Okay so they are actually the reality and therefore important after all... Before we take a deep dive into how a signal travels through it, let's quickly review what an electromagnetic wave actually is.

An Electromagnetic Wave Primer

An open field

Not a bad photo huh? A random open field, cool. So what does that have to do with electromagnetic waves? Well the connection isn't immediately obvious but I will soon explain where it fits into the understanding puzzle.

You see the key to understanding electromagnetic waves is to be able to visualise them radiating outwards from a source in a spherical fashion traversing through space with the electrical and magnetic components as shown in the image below:

Electromagnetic wave

Try this thought experiment right now with the provided open field two images above to help your imagination. Imagine you are in the middle of the field and are a source of electromagnetic waves, from your perspective everywhere you look you see them radiating outwards in all directions in a sphere around you. Now if you were a charged particle in the sky what would you feel in terms of forces? You would feel an electric field component AND a magnetic field component. Which is changing in both space and time, space as the wave approaches you and with time you will feel the maximum's and minimum's of both components acting in perpendicular directions as shown above according to the direction and orientation of the wave front.

If we just consider the electric field component and say it operates in the y-axis then as a charged particle you would accelerate one way for half the period and then the other way for the other half noting of course that momentum will play a part in this in being able to actually eventually change direction once already moving one way. The magnetic field will similarly cause accelerations for the charged particle as a changing magnetic field induces an electric field, a little bit mind blowing to think about, but we will discuss this interplay more deeply in it's own article entirely, for now this is all the intuition we need to signals traversing through transmission lines.

How does a signal propagate along a transmission line?

So then, how does the signal actually travel along this thing? Glad you asked as this is an extremely important question and the answer will potentially blow your mind many times over so please stick with me here.

Voltage measured at node vs

Let's first look at what we would measure at the voltage source, we see a 5V pulse with a reasonably fast rise and fall times of 1ns. What happens is that this pulse begins travelling through the circuit from the positive terminal close to the speed of light (assuming conventional current of course) through each of the interconnects AND air. As we said above an electromagnetic wave radiates spherically, it does not care about the medium it will give it a crack and so any air gaps act as a capacitance which the wave goes through giving rise to what is known as a displacement current. In our transmission line model, we have modelled this capacitance as distributed capacitance C1 and C2. Let's now consider each of the loops in the circuit that the electromagnetic wave will traverse through.

Loop 1 of the transmission line

Let's consider the loop above first, as we mentioned we will see the electromagnetic wave travel from the positive terminal and then through R1 and L1 and then reach the plate of C1, we will then have the wave propagate through the capacitance and then continue along back to the negative terminal from the other plate of the capacitor. We have two components, the SIGNAL path and the RETURN path respectively as explained above, we will ALWAYS have both. In fact in many real world PCB layouts the fast majority of Electromagnetic Compatibility and Signal Integrity issues stem from the design, or lack thereof of the return path. Never forget that current always flows in loops.

So what would the voltage then look like at capacitor C1 with time if we only consider the circuit fragment above? (Assume the remainder is not connected for the moment).

Voltage measured across C1

Oh dear, that doesn't look particularly pretty does it, what happened to our beautiful pulse? It is now tarnished by these horrible ripple components. What has happened is the interplay between the inductance and capacitance is causing ringing. Recall that an inductance does not appreciate changing currents (due to changing magnetic flux) and will in response induce a voltage proportional to the rate of change of current which opposes the change and also that a capacitor has a current flowing onto/off the plate proportional to its rate of change of voltage and so you have waves bouncing back and forward and it is this action which results in the ringing you see. There are of course methods to reduce this ringing but that deserves treatment in its own right. Note that there is also ringing when the voltage settles back to 0V, this is known as ground bounce. It goes negative because the voltage on the upper plate measured relative to the negative plate (where we have placed ground) is lower. More on this in another article too, both are very important concepts!!!

Now let's measure the voltage across our load resistance Rl considering the entire circuit:

Voltage measured across Rl

Alright so we also get some rippling action but notice that it also eventually settles to 5V and 0V. Once again we see the electromagnetic wave propagate from the source voltage, through R1 L1 and then R2 L2 before finally traversing through Rl. Now, something different happens here, because the resistance of Rl is radically different to the interconnect resistance (500m vs 1000) the wave see's 500m happily until it hits the source of a very different value and due to this we will observe reflections from Rl back towards the source which then bounces back in a loop, it's like a brick wall almost but eventually with time the reflections will settle down resulting in the clean 5V you eventually see, similar action happens when the pulse returns back to 0V.

So to answer the original question posed of why transmission lines are key to understanding how real signals travels is that it is what we observe in nature, we cannot avoid the scenarios we have seen above, we need to work with them. Having a deep understanding of how a wave travels along a transmission line helps us develop intuition through mental models to then design circuits and PCB's in a way which allows us to achieve the signals we would ideally like to see arrive at destinations which  not considered will almost certainly lead to Electromagnetic Compatibility and Signal Integrity issues which can be incredibly costly to organizations and in the worst case cause bankruptcy!

I really hope this article helps give you at least an initial feel for how this all actually works in the real world, it will be the first of many so don't worry if there are still many open/confusing points as there is a lot to unpack on this deep topic which will all be unpacked in good time :)