# Phase Coefficient versus frequency plot

I have been asked to confirm that the propagation characteristics of a transmission line, with the given parameters

R= 2.2 Ohm, L = 105nH, C = 69pF, G = 14 nS.

Along with these two equations, I have been able to confirm all except the phase coefficient (Beta) against frequency. The given characteristic plot being: However when running my MATLAB Code:

% Constants
R = [2.2];         % ohm m^-1
L = *1e-9;        % H m^-1
C = *1e-12;         % F m^-1
G = *1e-9;         % S m^-1

% Frequency range
f = logspace(0,30);     % Hz
y=sqrt(R+(1i.*w.*L)).*(G+(1i.*w.*C));
alpha = real(y);
beta = imag(y);

% Characteristic impedance
Zo = sqrt((R + 1i*2*pi*f.*L)./(G + 1i*2*pi*f.*C));

% Plot results
loglog(f, 2*pi*f*sqrt(L*C));
xlabel('Frequency (Hz)');
ylabel('Phase Coefficient');
title('Phase Coefficient vs Freq');

hold on
loglog(f, beta);
grid on;


I get this plot; I am confused as to why at higher frequencies the two lines don't merge like in the characteristic plot

In place of "phase coefficient", plot "group speed" (which seems "weird" ... $$\ vph = 3.71*10^8 m/s\$$). 