These equations are based on slides 15 & 16 of 05-877v1.

S21(f,L) = exp(-L*(k_0+k_sm*sqrt(f)+k_dm*f))*exp(-i*L*(k_sv*sqrt(f)+k_dv*2*pi*f))

where f in is Hz, L is in inches, and i = sqrt(-1). S21(f,L) is linear (not log). It is complex.

S12 is assumed to be identical to S21.


S11_near = (pcb_Z-100)/(100+pcb_Z);
S11_far = (100-pcb_Z)/(100+pcb_Z);
S11 = (1+S11_near)*S11_far*(abs(S21)^2*exp(i*2*angle(S21)));

where 100 is the assumed differential impedance of the measurement equipment. Since S21 is a function of frequency and L, S11 is a function of frequency and L. S11(f,L) is also linear (not log). It is complex. S22 is assumed to be identical to S11. S11 is commonly identified as rho.


The values for the equations can be found in 'FR4 equation fitting values.txt'.


Tom Lindsay, ClariPhy