25/09/15  

1  

0 5 10 15 20 25 30 35 40−180

−160

−140

−120

−100

−80

−60

−40

−20

0

Freq [MHz]

unwrapped phase of S21

Coaxial Cable

S21(ω) = exp(-γL) = exp(-αL –jβL)= exp (-α’sqrt(ω)L – j ω τ)

τ = √εr L/c =electrical delay βL = (ω/c) √εr L = ω τ

|S21|dB \S21

Open Coaxial Cable

Coax.  Cable  

� = S11

open    end  

Ideal    Case  

0  

|�|dB

Frequency  

0   Frequency  

\�

Radia.on  +  Losses   0  

|�|dB

pf

� ⇡ e�↵0p!2Le�j2⇡f2⌧

� =b1a1

= e�j2⇡f2⌧

τ = √εr L/c

25/09/15  

2  

Coaxial cable: reflection and transmission

0 500 1000 1500 2000 2500 3000−3

−2.5

−2

−1.5

−1

−0.5

0

Freq [MHz]

Module of S11

0 500 1000 1500 2000 2500 3000

−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

Freq [MHz]

Module of S21

Coax.  Cable  

� = S11

open    end  

|�|dB

|S21|dB

Coax.  Cable  

Port  1   Port  2  

/ �p!

/ �2p!

Open Coaxial Cable: resonance

L = m λ/2 λm = 2L/m fm = m (c/n)/ 2L

Δf = (c/n)/2L

n = c/(Δf 2 L)

n = refraction index n= √εr

best matching