example 3.1.2

z=[0:.0001:10];f2=10*log10((exp(z)+1)./z);

figure(20);plot(z,f2);

nzmin=find(f2==min(f2))

f2(nzmin)

z(nzmin)

b_over_a_optim=exp(z(nzmin))

hold on;plot(z(nzmin),f2(nzmin),'ro')

text(z(nzmin),20+f2(nzmin),['optim b/a =...

       exp(zmin) =' num2str(b_over_a_optim)])

etha0=377;

mur=1;er=1             % no filling material

mu0=4*pi*10^-7;    % H/m

e0=8.853*10^-12;  % F/m

 

no fill-up or fill-up with materials that have er close to 1,

that tend to be cheaper than those with er>>1 when fillip

up transmission lines

 

 

 

Z0=1/( 2*pi)*(mu0*mur/(e0*er))^.5*z(nzmin)

 

if coaxial fill-up were PTFE (Teflon)

er=2.2

Z0=1/( 2*pi)*(mu0*mur/(e0*er))^.5*z(nzmin)

 

But for the mass production of cheap coaxial might be too expensive, even with Teflon.

 

Let's have a look at a common 75 ohm coaxial   

​

​

a=1.016;b=4.512;  % both mm

since specs read 'foam PE' what relative permittivity has the filling material?

Z0=75;

er=(etha0/Z0*1/(2*pi)*log(b/a))^2

 

matching the relative permittivity of Foam Polyethylene in table

[PRAD] www.pulsedpower.net/Info/common_dielectrics.htm

 

Yet one has to be aware of the wide frequency span that supplier claims the coaxial is operative because the attenuation varies widely depending upon what frequencies used.

 

sigma_Cu=5.183e7 % S/m

etha0=377;

f1=5e6;f2=1.8e9;f0=(f1+f2)/2; % chosen centre band in specs

df=(f2-f1)/25;f=[f1:df:f2];

 

Rs=(pi*f/sigma_Cu).^.5

a=1.016;b=4.512;  % both mm, Commscope F677TSW EXPRESS

mur=1;er=1.2 % cheap coax

alpha_c=Rs./(2*etha0*(mur/er)^.5)*(1/a+1/b)*1/log(b/a);

Np2dB=10*log10(exp(1)^2); 

alpha_c_dB=alpha_c*Np2dB;

alpha_c_dB_100m=alpha_c_dB*100;

 

 

directly from the manufacturer's datasheet:

Lcoax75=...

[1.9 5.25 6.4 6.46 9.35 9.84 10 10.82 11.64 12.63 13.61 14.43 15.29 16.08

16.73 18.54 20.01 21.49 23.66 24.71 25.71 26.68 27.63 28.54 29.39 29.44];

figure;semilogx(f,alpha_c_dB_100m);

hold on;

semilogx(f,Lcoax75);grid on

legend('theoretical','real measurements')

 

We can start feeling the need to test, if not all, at least all the critical components of any expensive system. Theoretical models? datasheets?

Test the one you buy. when systems are really expensive one of the strategies is to send someone to factory to test what you buy, and then test again in your facility before assembly, with heavy penalties agreed in advance for specs deviations.