If we connect the top and ground metal layers with a lot of Via, will the parasitic capacitance increase or decrease? As far as I know, it will reduce resistance.
I think the main purpose of the vias is to stop propagation away from the track through the board between the top and bottom grounds. Having the vias closer together reduces this, but once the level is very low there is no need for more vias.
Having too many Via in PCB can introduce significant parasitic capacitance. If it is known that the diameter of the solder mask on the ground layer of the via is D2, the diameter of the via pad is D1, the thickness of the PCB is T, and the dielectric constant of the PCB board substrate is ε, the parasitic capacitance of the via is approximately C=1.41εTD1/(D2-D1)
The main effect of the parasitic capacitance of the via hole on the circuit is to extend the rise time of the signal and reduce the speed of the circuit. In addition, the smaller the via, its own parasitic capacitance. The smaller, the more suitable for high-speed circuits.
The answer given by Mahboubeh - Safari dehnavi seems to be about low frequency circuits, where the track is not a transmission line. For microwave circuits, where the track is a transmission line, the vias do not increase the capacitance of the line.
Malcolm White I think that your answer regarding the transmission line is reasonable. Let's discuss another thing "via placement" and whether or not it has any effect on signal transmission. (like it is very close from the center or very far from the center)
I depends on what form of transmission line you want. The line shown is not pure microstrip - it is a mixture of microstrip and coplanar transmission line. The top ground increases the capacitance of the line, reduces its impedance, and probably changes the effective dielectric constant and velocity. If the vias were very close to the edge they would also increase the capacitance and affect the other things. They would introduce a periodic perturbation to the capacitance that might lower the highest operating frequency. This won't happen if the vias are far enough from the edge.