Due to the large reactance of the RF choke at the frequency of operation, we can consider that only DC current IDC flows from the power supply. Moreover with the assumption of QL = ∞ for the series resonator, L2-C2, only the fundamental frequency current can flow through the load.
The current delivered to the load R is:
iR(θ) = I1sin(θ + φ) → Equation 1.
Where I1 denotes the amplitude of the load current and φ is the initial phase.
At OFF state, the currents flowing through switch and shunt capacitor C1 are:
isw(θ) = 0 → Equation 2,
iC(θ) = IDC - I1sin(θ + φ) → Equation 3.
The current iC(θ) is charging / discharging the shunt capacitor C1 (see Figure 2). Since we assume that during the ON state the voltage across switch/shunt capacitor is equal to zero, the capacitor voltage in the OFF state can be found as:
→ Equation 4
If we substitute Equation 3 into Equation 4 and perform the integration in the given boundaries, we will find that the capacitor voltage at any instant in the OFF state is given by:
→ Equation 5