Brush up on the theory before designing a high power Class‐E amplifier: Page 5 of 15

June 29, 2016 //By Alfio Scuto, Roberto Cammarata, ST Microelectronics
The most promising switched-mode PA for RF applications, among the several types available, is the Class-E for several reasons: high efficiency, simplicity of the load network, and a satisfying performance even with a non-optimal drive signal.

3.2. Device’s electrical stress

The output capacitance C1 reaches the max voltage when its current becomes zero (Figure 3):

iCm) = 0 → Equation 11

From Equation 3 follows:

IDC - I1sin(θm + φ) = 0 → Equation 12

Using the boundary conditions for class-E (Equation 6 and Equation 7) in Equation 5 (voltage across C1) we get:

IDC = (2/π)cosφI1 → Equation 13

IDC = sinφI1 → Equation 14

Comparing the two equations, for a duty cycle of 50%, we obtain:

φ = arctan(-2/π) = 0.563 rad → Equation 15

In Equation 12 replacing IDC with Equation 14, we get:

sin(θm + φ) + sin(φ) = 0 → Equation 16

 Using the Prosthaphaeresis identities, we get:

θm = -2φ → Equation 17

Finally, we obtained the popular equations for peak voltage and current for the active device:

Vpk = Vcm)= 2πφVDC = 3.562VDC → Equation 18

Ipk = IDC + I1 = IDC - IDC/sinφ = 2.862IDC → Equation 19

For a duty-cycle of 50%, the peak voltage at the drain terminal exceeds the supply voltage of the circuit by more than three times.

Dr. Raab in (2) has presented all the equations that govern an idealized Class-E RF power amplifier. In particular, he has proved that a duty-cycle of 50% represents an optimum in terms of output power capability. Moreover, the device’s breakdown voltage determines the maximum allowable supply voltage and it is in direct relation to the output power.

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