A Appendix

Example to use Excel or Matlab calculate f_Zff

If Excel is used, first input parameters following below format.

Figure A-1 Use Excel to calculate f_Zff Step1

Change the variable name of values A2-D2 as the values of A1-D1.

Figure A-2 Use Excel to calculate f_Zff Step2

Input equation in E2. Input “=” first, then copy and paste below contents:

-(5.67e15*(sqrt(3)*sqrt(C_2^3*Cff^4*L_2^3*R_1^4*(4*Cff^2*R_1^2+27*C_2*L_2))-9*C_2^2*Cff^2*L_2^2*R_1^2)^(2/3)-1.3e16*C_2*Cff^2*L_2*R_1^2)/(1.49e16*C_2*Cff*L_2*R_1*(sqrt(3)*sqrt(C_2^3*Cff^4*L_2^3*R_1^4*(4*Cff^2*R_1^2+27*C_2*L_2))-9*C_2^2*Cff^2*L_2^2*R_1^2)^(1/3))/2/3.14

Then the f_Zff is calculated. And we can adjust C_ff to make f_Zff>f_cross.

Figure A-3 Use Excel to calculate f_Zff Step3

If Matlab is used, the following code can be used as an example:

clc

clear

R1=5e3;

C2=47e-6;

L2=15.3e-9;

Cff=620e-12;

fZff=-(5.67e15*(sqrt(3)*sqrt(C2^3*Cff^4*L2^3*R1^4*(4*Cff^2*R1^2+27*C2*L2))-9*C2^2*Cff^2*L2^2*R1^2)^(2/3)-1.3e16*C2*Cff^2*L2*R1^2)/(1.49e16*C2*Cff*L2*R1*(sqrt(3)*sqrt(C2^3*Cff^4*L2^3*R1^4*(4*Cff^2*R1^2+27*C2*L2))-9*C2^2*Cff^2*L2^2*R1^2)^(1/3))/2/3.14