charge logic for switching circuit

[yefj]

Hello,bellow we have a switch capactor circuit ,What is the charge expression for phase 2
on
Q_C1= Vres*C1
Q_C2= Vmux1*C2
Q_C3= Vmux2*C3
Q_C4= Vmux3*C4

What can we say about the total charge of phase 2? is it a sum of all 4 elements?
Thanks

 

[sutapanaki]

The total charge at the (-) input of the amplifier upon opening of Phi1e is -Vin(C1+C2+C3+C4). It stays unchanged during phase2. Charge there just redistributes across caps depending on the voltages.

 

[yefj]

Hello Sutapanaki, my gowl is to build a transfer function from the switching
where we making Q_ph1=Q_ph2
regarding Q_ph1= Vin(C1+C2+C3+C4 i agree.

but grarding Q_phi2 we have expressions of Vmux.
Q_C1= Vres*C1
Q_C2= Vmux1*C2
Q_C3= Vmux2*C3
Q_C4= Vmux3*C4
I am having trouble to see the intuition on how all this charges play together and why?(for deremining Q_ph2)
Thanks.

 

[sutapanaki]

When you open the Phi1_e switch you freeze the charge at the (-) input of the amplifier. This node doesn't have a resistive path to anywhere so whatever charge is trapped there, stays there when you open Phi1 and also during Phi2. You can apply your Mux voltages but the only thing it will do is redistribute charge across the capacitors. The total charge, however remains the same.