Electronic – How to minimize impedance from capacitor to Gnd and Power planes

There isn't one.

That said, there are some thing I've gathered over time. What you do with the ground planes depends heavily on what you're trying to do. You could be trying to provide low impedance paths, or you could be trying to isolate one area from another, or you could be trying to deal with EMI.

There certainly is a performance penalty for doing it wrong, but you may not really care unless you're dealing either with high frequency circuits or precision analog work. The number of fluctuating bits of the ADC reading with inputs grounded, or the spectral purity of an RF signal as measured by a spectrum analyzer will tell you how wrong you are with any design. It's generally impossible to get it 100% right (datasheet spec) unless you've a system as simple as their test circuits.

The most complicated ground connection problems have to do with RF frequencies, and with signals that are either weak or are passing through traces which are susceptible to EMI coupling in that frequency. At microwave frequencies, a centimeter is enough to make a very effective antenna and mess with things. I remember a professor of mine once told me that when he was working in the industry, they'd leave plenty of points where two grounds could be shorted together, and then an engineer would test each of them one by one to see which gave the best performance. They were working with high frequency (microwave) circuits.

Typically, there's three kinds of 'ground plane' like elements you'd be wanting to short.

1. Real ground planes. For some reason or the other you've got many of them, and you want to connect them together. This is probably the most common occurrence of the problem in the run of the mill circuits.

2. Ground / guard traces that are running along with signal lines which may be providing a return path, guarding a high frequency signal or one bound to/from a high impedance source or sink. This could either be to prevent signal leakage or to prevent EMI coupling.

3. Multiple ground planes which are actually the same ground.

To begin with, you should understand that there isn't really a universal ground, and also that different grounds in the same circuit arent necessarily the same ground. A typical example you'd come across is a datasheet for an ADC that talks about analog and digital grounds. This is to make sure that the oh so noisy digital circuitry doesn't mess with the high resolution ADC you've paid extra for. Different kinds of circuits have different characteristics when it comes to their interaction with the ground. Since digital circuits are characterized by a sudden spike in current at each clock, they tend to be particularly noisy at the clock frequency, and subsequently at harmonics and sub harmonics. Bypassing capacitors are supposed to deal with this, but they rarely do a thorough enough job to get milli or microvolt resolution possible from the ADC using a relatively quieter analog ground with much less switching going on.

Similarly, power grounds tend to be noisy because loads like motors and solenoids tend to be noisy, either because of effects of commutation or things like PWM. The high currents involved and the finite ground resistance (even a chunk of copper has some resistance) means that the transients showing up on the power ground tend to be higher. Sometimes high enough to completely screw up your encoder measurements while controlling a motor for instance.

The goal, then, is to isolate these grounds best you can. That means that they dont overlap, at all. You don't put analog ground on the top and digital ground at the bottom. Everything to do with analog goes with the analog ground, and everything to do with the digital goes with the digital ground in separate areas of the pcb. When the goal is isolation, you connect the planes together at a single point. More than one point can be disasterous since it leads to current loops and hence EMI problems and unintended antennae. The point where the grounds are all shorted is usually referred to as the star ground point of the circuit and is as close as you're going to get to a circuit wide ground. Generally, these should be shorted as close and centrally as possible to a place where the two circuits interact, usually an ADC or DAC. In truely haphazard designs, you'd short them near the supply and pray for the best. This is type 1.

In type 2, you have some sort of a guard trace. If the trace is at ground, then you're probably worried about EMI and not leakage. In the case of leakage, you'd want to drive the guard at close to the signal level. In both these cases, you want the guard to be as low impedance to the source as possible. This means multiple vias dropping down to the ground plane at regular intervals, if the trace is to be grounded.

The third and somewhat less exotic variety, and really is sort of just stating the obvious. This has to do with the vias taking decoupling caps to ground or the random vias shorting top and bottom ground planes. Once you've created a star ground and isolated the different areas, you want each ground to be as uniform as possible. For example, you don't want there to be a measurable potential difference between two corners of analog ground plane. You do this by providing a low impedance path to the star ground - each pin or pad that needs to be grounded goes to the plane which provides it a straight shot to the star ground point. Having the plane has the added advantage of providing a return path under each signal trace, which avoids current loops forming which may act as antennae. In cases where the ground plane must be broken, but you need to have a return path, you would provide an alternate route through another layer. If you have multiple planes with ground in the same area (note:these must be the same ground), periodic vias can help reduce impedance slightly.

I'm not sure that I know the best way to build the board, but I know what I would do.

1. The location of the 12V-to-5V regulator, whether linear or switching, will not matter. The corner of the board is fine.
2. I would not bother with filling either top or bottom of the board with ground planes. The impedance of the signal traces is defined by the internal planes, not the extra copper you pour on the outside. The extra coper isn't shielding internal signals, all that is underneath are power and ground planes. Instead, connect ground and power pins of components directly, as close as possible to the pin, to the planes.
3. Don't share power and ground vias between different devices. One via per pin minimises noise on the pin and routing distance to the ground plane. If you are so worried about the manufacturing price that a few vias are going to be significant, you must be shipping in very high volume, so you can prototype a dozen different layouts to optimise it. If this is a one-off, the biggest cost risk is that you don't get it right first time, so be conservative and use lots of vias.
4. Put a via by every component ground pin (not necessarily every component signal pin that happens to need routing to ground). Minimum noise on power and ground planes comes from effective decoupling. High frequency noise is minimised by using physically small ceramic capacitors and keeping the power and ground vias close together - underneath the capacitor, if possible. The cross sectional area of the loop from power plane up through via to capacitor, along capacitor and down through via to ground plane, places the lower limit on how effective the decoupling is.
5. I would definitely not put any splits in the ground plane. Instead, if there are analog signals sensitive to noise, I would not route digital signals close to them. I would try and keep those sensitive analog signals just on the top layer if possible, no vias to the bottom at all. If I can isolate an area of sensitive connections all together on the top layer, I would route a single loop of trace all round there on the top layer, and connect that loop at one point with a via to the ground plane. That approach has worked well for me in the past with very sensitive signals.

And finally: it is conceivable that some clever technique of sharing ground connections might help noise in the analog wiring, but you'd need to know the exact circuit and think very hard about it to be confident. These rules of thumb have worked pretty well for me.

Good Luck!