example 6.3

c0=2.998e8;

f0=5e9;

 

a=47.55;b=22.15                                        % mm

er=2.25;tand=.0004;                                 % teflon fill-up

 

k=2*pi*f0*(er)^.5/c0

 

% L is z dimension wave mode numeral

% k=((m*pi/a)^2+n*pi/b()^2+(L*pi/d)^2)^.5

% a>b and constraining d>a

 

L=1                                             % resonant cavity half-wave deep.

 

m=1;n=0;syms d

eq1=(m*pi/a)^2+(n*pi/b)^2+(L*pi/d)^2==k^2

d_L1=double(solve(eq1,d))

 

 

d_L1=d_L1(find(d_L1>0))                     % instead of d_L1=d_L1(2)

 

 

% d_L1 matches the resulting value of reverted expression (6.39) 285pg

L*pi/(k^2-(pi/a)^2)^.5                       

 

L=2                                                    % resonant cavity full-wave 1 cycle deep.

 

eq2=(m*pi/a)^2+(n*pi/b)^2+(L*pi/d)^2==k^2

 

d_L2=double(solve(eq2,d))

 

 

 

d_L2=d_L2(find(d_L2>0))                     % instead of d_L2=d_L2(2)

 

etha0=120*pi;etha=etha0/(er)^.5      % intrinsic impedance

Rs=1.84e-2;                                             % Cu at 5GHz

d=d_L1;L=1;

Qc_L1_teflon=(k*a*d)^3*b*etha/(2*pi^2*Rs)*1/... (2*L^2*a^3*b+2*b*d^3+L^2*a^3*d+a*d^3)

 

d=d_L2;L=2;

Qc_L2_teflon=(k*a*d)^3*b*etha/(2*pi^2*Rs)*1/... (2*L^2*a^3*b+2*b*d^3+L^2*a^3*d+a*d^3)

 

Qd_L1_teflon=1/tand

Qd_L2_teflon=1/tand

 

Qd_L1_teflon=1/tand

Qd_L2_teflon=1/tand

 

Q0_L1_teflon=(1/Qc_L1_teflon+1/Qd_L1_teflon)^-1

 

Q0_L2_teflon=(1/Qc_L2_teflon+1/Qd_L2_teflon)^-1