Symmetric 𝔼ven Capacitive converter - Property of symmetry

Here, we aim to present an experiment that highlights the symmetry property of the class-EF inverter. To this end, we implement a class-EF inverter, as shown below, operating at 15 MHz with a DC input voltage of \(V_{DC}=25\) V using the following components:

Name	Value	Reference
\(L+L_1\)	??	homemade, AWG16 wire
\(R\)	5 \(\Omega\)	MP9100-5.00-1%
\(C_1\)	470 pF	100B471JT200XT
Switch		GS61008B
\(C_s\)	385 pF	Parasitic capacitance of the switch

Two photos of the converter are shown below. It is worth noting that the setup presented here is exactly the same as the one used during the experiment and shown in the video below.

The inductor \(L+L_1\) consists of a single coil made from AWG16 wire. By compressing or stretching this coil, the inductance value \(L+L_1\) can be modified:

• Stretching the inductor decreases its value
• Compressing it increases its value

Assuming that the value of the downstream resistor \(R\) is independent of the inductance \(L+L_1\), compressing or stretching the inductor effectively shifts the operating point vertically along the chart. This allows for a direct observation of the symmetry property in action. The video below provides a detailed overview of the experiment.

Below are two annotated photos from our experiment, corresponding to operating points A and B:

Using the information from these two images, we can illustrate three of the four equations related to the symmetry property. First, as clearly shown in the video, the load resistance \(R\), the circuit switching frequency \(F=15\) MHz, and the capacitance \(C_s=385\) pF remain unchanged. Therefore, the reduced resistance value is identical for operating points A and B, validating a first equation of our property of symmetry:

\[ r_A=r_B=R\cdot\omega\cdot C_s \]

Secondly, the duty cycles for operating points A and B, determined by measuring the transistor conduction time, are 35.5 % and 16 %, respectively. This approximately validates a second equation of the property of symmetry:

\[ D_A+D_B=51.5\ \%\ \approx \frac{1}{2} \]

Finally, the product of the two reduced powers \(p_a\) and \(p_B\) measured at operating points A and B is approximately equal to \((2/\pi)^2\), which roughly illustrates a third equation of our property of symmetry:

\[ p_A\cdot p_B=\left(\frac{P_A}{\omega\cdot C_s\cdot V_{DC}^2}\right)\cdot\left(\frac{P_B}{\omega\cdot C_s\cdot V_{DC}^2}\right)=0.63\approx\left(\frac{2}{\pi}\right)^2\ (=0.41) \]

Why this discrepancy?

• The analytical developments related to the property of symmetry were carried out assuming unity efficiency.
• The equipment used to measure the power absorbed by the inverter is not highly precise.
• In practice, the resistance \(R\) of our circuit varies slightly when the geometry of the inductor is modified.

It should be noted, however, that the equations of this property have been validated through circuit simulations.