The ground plane is ubiquitous in modern high frequency circuits and it does much to help form circuit elements, isolate components, and keep signals clean. While there is always some debate about things like separating analog and digital grounds, everyone agrees the ground plane is critical. Almost every aspect of modern circuit design is based on having a healthy ground plane.
So how would high-frequency circuit designs need to change if a ground plane could not be used? What problems would arise? What solutions can we think of, other than adding a ground plane?
I think that there may be heating problems in the circuit without ground plane.
As https://www.researchgate.net/profile/Thomas_Scheller says, the alternative is to use a matched pair transmission line type circuit.
What is your definition of high fpequency? For me it is about 1MHz, but even that is just a vague rule of thumb. I.e. for audio or a switching power supply 1 MHz is a high frequency, for modern digital stuff it is not.
A circuit has to have by definition a circit of current, or provision therof, and that is either from direct wire/trace connection or via a plane. Add here that just because there is a plane, the electron flow will always take the shortest "as the crow flies" path betweed points, it will not spread out (terms and conditions apply) although the plane will be at the nominal potential of that part of the circuit at that point.
Rember though, at some point there will always be a ground plane of some type, unless one is in space, since the original specification of ground is the ground itself.
By high-frequency, I guess I mean above 2 GHz. In other words, the circuit is doing more than just blinking LEDs.
I would suggest that high-frequency is anywhere where local "environmental" impedances become significant in effect to the circuit operation.
Noting that for RF this becomes significant even at a few MHz; and for digital it is all about the edge rates and amplitudes of the transition between states, not just how often they occur (a fact that is often missed).
All components have complex terms as soon as one has connections between parts; some of which can be very small, others which can change dramatically with frequency.
Even in nominally AF design there can be active parts that have multi MHz bandwidth, e.g. When using a DN2535 (a low threshold depletion mode. (normally-on) transistor) as a DC biasing current source, it can take off and oscillate at c. 200MHz (needn’t ask how I know this).
So basically I am saying don’t put arbitrary decision points on what may or may not constitute things like HF, and always use a high as possible bandwidth ‘scope even if one is supposedly doing DC or “LF” work. In my example that 200 MHz oscillation would not show on a low bandwidth scope, but would seriously impact on the circuit’s operation.
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