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Comment by kuon | Hacker News Reader

What is "cool", (or a challenge if you design PCB like I do), is that this is not true for alternating current.

For example, if you have a track that does a L on top side, and copper plane on bottom side, with an alternating signal, the return path will follow the L and not go back in a straight line.

Those links have some explanations:

https://resources.altium.com/p/what-return-current-path-pcb

https://www.nwengineeringllc.com/article/how-to-design-your-...

https://electronics.stackexchange.com/questions/360472/real-...

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My understanding about electronics basics is taking a hit, after reading this piece of info.

> With time-varying signals, the return current follows the path of least reactance, which is also the path of least impedance. This means the return current path in your PCB is determined entirely by the impedance of the circuit that carries the return current.

I was also a bit surprised by this. But I do recall doing equations regarding capacitive and inductive reactance. In both cases there is a frequency-dependent effect which alters the shape of the waveform. It being frequency dependent, it disappears in the presence of DC (inductors becoming irrelevant and capacitors becoming nonconductive).

So I can kind of see it. But not enough to turn it into a return-path-is-suprising type example.

There's electric field created by the L-shaped conductor a millimeter away. No wonder that it affects electrons in the larger conductor.

School physics teaches us that metals are perfect conductors of electric field, so the field in the large conductor should be the same across it, and not follow the L shape.

But it's only true for a stationary situation, basically DC. At higher frequencies the fact that the conductor (every part if it!) has some capacitance and inductance starts to play a major role in how a fast-changing signal propagates over it. Both the capacitance and the inductance of the part of the large conductor under the L-shaped conductor on the other side are affected by the L-shaped conductor.

These considerations could help see the result as "more intuitive".

Add "when you have a ground plane" into the GP's fact. When you don't, it isn't true, but most circuits do have one.

Basically, capacitance and inductance are important for oscillating signals. And that plane has a huge capacitance.

All the basic electric circuit theory is just based on a bunch of simplifications that only apply under certain conditions. You get anywhere outside of assumptions for those simplifications, and all kinds of "weird" things start happening. And they're weird just because you're failing to abandon the simplifications, and start looking at Maxwell equations which are a bit more fundamental.

A popular video explaining some of the practical aspects of this phenomenon: https://www.youtube.com/live/ySuUZEjARPY?feature=share

It can be explained using the language of basic circuit theory. DC current prefers the path of the least resistance, but AC / RF current (1 MHz and above [0]) prefers the path of the least impedance, which is the combination of resistance and reactance. The main source of reactance in practical circuits is parasitic inductances - all real-world components, like wires, have unwanted parasitic inductance at AC, in the same way that all conductors have unwanted parasitic resistance at DC. The farther two conductors in a loop are located apart, the greater the parasitic inductance. Thus, when you have a big loop and a small loop, current prefers to flow via the smaller loop with lower parasitic inductance - even if the end points of the big loop have a shorter "straight line" distance with a smaller DC resistance. When you have two inductors in parallel, current prefers the smaller one - just like when you have two resistors in parallel, current prefers the smaller one.

Now going from circuit theory to physics, we would see that inductance is not the property of an individual component called the "inductor", but it's the result of the magnetic field of the current around a closed loop of a circuit. Thus, every circuit must have a parasitic inductance. To a first approximation, this inductance is proportional to the loop area enclosed by the circuit. Thus, for high-speed digital / RF signal transmission, we often want to make the return conductor be as close to the signal conductor as possible [1]. This is why ground planes are often used in circuit boards, and why twisted pairs are often used in cables.

[0] The point of transition depends on many factors, including the physical size of the circuit. Sometimes it can be as low in the 100 kHz range.

[1] I ignored the issue of characteristic impedance

Thanks a lot for the info. Am an electronics hobbyist and still trying to understand this better. Lot of new terms in your explanation. :)

Don't think of the path of least resistance (this is the limit case for f = 0 Hz), but about the path of least impedance and a lot of your intuition will translate. Also remember: 50/60Hz is almost zero on a pcb board and you can basically think of it as DC.

To be correct for ac and dc, the title should say “… find the path of least impedance”. Which is resistance and reactance combined (capacitance or inductance). Also to be clear: they are not talking about 50/60 hz ac signal which will follow a path basically exactly like dc on a pcb, but much higher frequencies.

Interesting what are you doing with ac circuits?

I design sensors, currently for medical applications where I use varying signal to measure properties of a medium. Tiny electrodes in an array that are excited with AC, through different effects (capacitive...), things like density, conductivity... can be deduced from the measure.

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