Symmetric 𝔼ven Capacitive converter - Property of symmetry

The symmetry property is straightforward to grasp, as it directly reflects the elliptical shape of the EF locus in the design chart (see 'Class EF inverter design chart' tab): for any operating point 'A' located on the EF locus, with known reduced parameters \( r_A \), \( x_A \), \( p_A \), and \( D_A \), another operating point 'B' can be found on the EF locus whose reduced parameters satisfy:

\[ \left\{ \begin{aligned} &r_A = r_B \\ &x_A+x_B = 1 \\ &D_A + D_B =\frac{1}{2}\\ &p_A\cdot p_B=\left(\frac{2}{\pi}\right)^2 \end{aligned} \right. \]

The figure below provides a graphical overview of the symmetry property.

Note that an exception to this property can be found, namely the operating point whose reduced parameters verify:

\[ \left\{ \begin{aligned} &r_A = \frac{1}{\pi} \\ &x_A = \frac{1}{2} \\ &D_A = \frac{1}{4} \\ &p_A=\frac{2}{\pi} \end{aligned} \right. \]

This specific case can be seen either as an exception to the property of symmetry or as an operating point 'A' confused with its dual operating point 'B'.