First up, I would like to share my recent experience with ground plane tweak, and its variants.
This tweak was discovered by BudP over at diyaudio. Link
here. This thread is long and it can sometimes be tough to glean the gist of the tweak. In short, if an audio equipment does NOT have a good ground plane, it can benefit from having a loop of conducting multistranded wire, hung from the negative terminal of source output, or the amplifier's negative terminals, or speaker's negative terminals, or all of them.
BudP's recipe is to have 140 strands of 40 gauge transformer wire, 26 inches long, made into a loop and the ends soldered together after removing the insulation of the transformer wires at both ends where they have to be soldered together. The insulation on the rest of the loop remains as it is to maximise surface area of the loop. The loop has to be connected to your audio equipment as mentioned above after covering in something like a cotton tubing. By the time it is inserted into a cotton tube, it is no longer a loop but more of a 12 inch pigtail (1 + 1 inch gone for soldering). He also recommends further tweaks to the loop by placing three pieces of dielectric like heat shrink at equal distance around the loop. Typical length of the dielectric is 0.6 inches. Reducing the length can change the nature of the sound. The use of transformer wire is recommended because each wire is insulated, and therefore the combined surface area is 140 times that of an individual strand. I have tried this tweak long ago, but got both the length of the loop (I used a 12 inch instead of the recommended 26) and the material wrong (I had used multistranded wires from a speaker cable). I also got the number of wire run wrong - I didn't count how many strands my loop had. I used the two loops I made in the speakers, but honestly didn't hear any difference, good or bad. In hindsight and with more reading, it is now clear that my version didn't work because non-insulated conducting strands bunched together didn't give a particularly large surface area, and the loop length was too short. Further info
here.
I have been meaning to re-do this tweak, though the thought of stripping the insulation from 140 strands (x4 ends) didn't sound appealing at all. Besides, I didn't have enough length of 40 gauge transformer wire without another trip to the market.
BudP's explanation of the working of the tweak is that the loop creates a "reservoir" of electrons which can be called upon when current requirement goes up. If seen from an electrical point of view, it does exactly nothing. In fact circuit theory tells us that there won't be any electrical current flowing through this loop, as electricity flows through the shortest path. The ends are tied and soldered together, so current would cross over at that point and does not need to flow via the longer loop path. Be that as it may, many have reported both positive and negative effects of having the loop, so it is known to work, whether or not his explanation of the phenomena is right or wrong. Those inclined to know more may please read the above diyaudio link where the inventor himself has given detailed explanations.
Variation 1:
It was then I read about the first variation of this idea. What if one uses a strip/ribbon of copper instead of many runs of transformer wire? The copper strip can be such that it has equal, if not much more, surface area than the transformer wire pigtail. So was born this variation of the ground plane tweak. People have used anything from half inch to 8 inch wide copper ribbon, running almost the length of the speaker cable. The "recommended" recipe for this variation is to have a copper ribbon running parallel to the speaker cable at a distance of about 4 inch. Again like the pigtail, it is connected to the negative terminal of source or amp or speaker. The explanation given for this tweak is that the ribbon creates a field that counteracts the field created by the speaker cable itself. More info
here.
A further "tweak" to this tweak was born at my place. For proof of concept I used kitchen aluminium foil since I couldn't easily source copper ribbon. The aluminium foil was cut into a strip of 1 inch width. Initially I tried five feet of it, which is about midway the length of my 3m speaker cable. The immediate effect was a lowered noise floor. Encouraged, I extended the ribbon to 10 feet and there was some further audible improvement. I didn't hear any change in the bass but the midrange and highs cleaned up. Big time. This led to improved resolution of lower level musical cues. The lowered noise floor allows me to turn up the volume from my regular 12 o'clock position to 1 o'clock, without listener fatigue. This is a good thing because louder volume allows one hear more into the details of the music. This sounds cliched, but I did hear lots of new details in music which I regularly listen to for evaluating changes after swapping out some component or making tweaks. There was also a sense of relaxation in the music, and the midrange got more spotlighted. There is also a substantial improvement in the "specificity" of the sound stage, with instruments and voices occupying much more focused places in the depth and width sound fields. One minor downside I hear in my setup is the soundstage is brought slightly forward but the advantages over rule this quibble.
To make things manageable, I hung the ribbons (one ribbon each of ten feet connected to each negative binding post terminal) to the speaker cables using thin solid core wires (CAT5/6 cables work just fine as the foil is very, very light). The one disadvantage of this tweak is your audio area starts looking like leftover from a Christmas decoration

, what with a long silver coloured streamer gently swaying

But the effect it brings about makes you forgive its sins in the aesthetics department.
Variation 2:
A similar tweak called Battery Ground Tweak (BGT) was invented by unclestu over at audioasylum. It works on a similar principle. For analog audio, the recipe is to have a capacitor bank of about 40000 uF powered by a 9V battery. The negative terminal of this contraption is connected to negative terminal of source or amp or speaker (but the inventor said that it works best on the source). The positive terminal of the circuit is not connected to anything. A bypass capacitor of about 0.1 uF is recommended to bypass the capacitor bank. I have been using this circuit on my source and the effect is same as the alumimium foil, just more. More info
here, including circuit diagram.
I have been running together the BGT (at source) and aluminium foil (on the power amp) and enjoying much better sounding music.
I recently made another BGT and connected it to the amp too. I can say that it is better than using the foil. Using foil + BGT on the amp doesn't seem to improve the sound any more than what the BGT alone on the amp had already achieved, so effectively the alumimium ribbon is now redundant.
My implementation: ten 4700 uF, 35V Rubycon electrolytic capacitors are paralleled for a combined capacitance of 47000 uF. One 0.1 uF and two lower value polystyrene caps are used as bypass. I tried powering the circuit with two 9V batteries in series but I find the sound too bright. 9V works better. I will try with slightly lower capacitance (say around 37600 uF) as I find the sound even with only a single 9V battery a wee bit bright for my taste.
If you want to try this for video or SPDIF, use about 100,000 uF and 18V.
The above tweaks are easily do-able even by the beginner tweaker. Especially the aluminium foil tweak, since most of us already have the raw material in our kitchens. It has effect even if the aluminium foil is used rolled up, but the effect is likely lesser than having it run along the speaker cable. Further, most likely there will be improvement with copper ribbon as it is a better conductor than aluminium. Copper personally not yet tried.
Even the BGT costs very less. I would encourage you to try these tweaks at home. The results are stunning. I am certain I won't be able to go back to no BGT in my setup.