Series connection of capacitors

Question

I have some questions for the series connection of capacitors. It would be great if someone could help me get these.

What will happen for the below cases when you have 2 capacitors in series and 2 supplies connected to the extreme ends-

^{simulate this circuit – Schematic created using CircuitLab}

1. When the supply V1 is a fixed voltage V1 and supply V2 is a fixed voltage V2. What will be the charge and the intermediate node voltage Vb?

2. When the supply V1 is ramping from 0 to a voltage Vs and supply V2 is a fixed voltage Vs. What will be the charge and the intermediate node voltage Vb here?

3. For case 2, When there is some initial charge on any capacitor , say C1 has Q_ini charge, how will the individual charge and intermediate voltage Vb get affected?

Answer 1

This C divider ratio will have an intermediate V depending on the ratio of C1/(C1+C2) across C2 of the difference V.

So the smallest C value has the highest V and then leakage R ratio’s will affect the steady state V after some time constant T=(Rp1+Rp2)*C1//C2 to 64% Delta V @ 1T

This “Capacitive Transformer” method is a common method for sampling a single phase HVAC , not shown here, to a safe LV for sensing using Vb with V2 =0V or grounded.

e.g. a bushing 100 pF 100kV cap (arc protected) integrated in porcelain, to a 10uF cap to get 1V , used by ABB.

Can you think of any practical use for this in a switching S&H circuit? For DC and small signals? Can you imagine any effects in switching cascaded FET’s at high speed with a large Ciss load from a smaller Coss driver with higher RdsOn?