COMMS 4 Flashcards
R (Parallel)
R= 1/(πaδσ_c )
L (Parallel)
L= μ/π ln〖d/a〗
C (Parallel)
C=πϵ/ln〖d/a〗
G (Parallel)
G= σ/cosh^(-1)〖d/2a〗
σ
σ=1/ρ
δ
δ=1/√πfμσ
R (Coaxial)
R= 1/(2πδσ_c ) (1/a+1/b)
L (Coaxial)
L= μ/2π ln〖b/a〗
C (Coaxial)
C=2πϵ/ln〖b/a〗
G (Coaxial)
G= (2σ_c)/cosh^(-1)〖b/a〗
G= 2σ/ln〖b/a〗
CHARACTERISTICS IMPENDENCE (Z_O)
Z_(O=) √(((R+jωL))/((G+jωC) ))
lossy line
Z_(O=) √(R/G)
lossless line
Z_(O=) √(L/C)
CHARACTERISTICS IMPENDENCE (Z_O) (PARALLEL LINE)
Z_(O=) 276/√k log 2S/d
CHARACTERISTICS IMPENDENCE (Z_O) (COAXIAL CABLE)
Z_(O=) 138/√k log D/d
Attenuation Constant (α)
α=R/(2Z_o ),Neper/m or dB/m
Phase Shift Constant (β)
β=ω√LC,Rad/m or Deg/m
β=2π/λ,Rad/m or Deg/m
Attenuation and Phase Constant
γ=α+jβ=√((R+jωL)+(G+jωC) )
where: α is in Neper/Km,β is in Rad/Km
Velocity Propagation (V_p)
V_p=λf
V_p=ω/β=2πf/β
V_p=V_C/√k
V_p=V_c*Vf in or medium
Velocity Factor
Vf=V_P/V_C ;Vf=1/√k
REFLECTION COEFFICIENTS
Γ=e_reflected/e_incident ; Γ=e^-/e^+
Load &Characteristic Impedance (RC)
Γ=(Z_L-Z_O)/(Z_L+Z_O )
Reflected & Incident Power (RC)
Γ=√(P_ref/P_inc )
Reflected & Incident Signal (RC)
Γ=e_ref/e_inc =Γ=I_ref/I_inc
Reflected & Incident Signal (SWR)
SWR=(V_inc+V_ref)/(V_inc-V_ref ) = (I_inc+I_ref)/(I_inc-I_ref )
Transmission Line Voltage Measurement (SWR)
SWR=V_max/V_min =e_max/e_min =I_max/I_min
Load &Characteristic Impedance (sWR)
SWR=Z_L/Z_O ifZ_L>Z_0
SWR=Z_O/Z_L ifZ_O>Z_L
Reflected & Incident Power (SWR)
SWR =(1+√(P_ref/P_inc ))/(1-√(P_ref/P_inc ))
RELATIONSHIP BETWEEN SWR AND Γ (SWR)
SWR =(1+Γ)/(1-Γ)
RELATIONSHIP BETWEEN SWR AND Γ (Γ )
Γ =(SWR-1)/(SWR+ 1)
RETURN LOSS/ REFLECTION LOSS
R_L=1/Γ;R_(L (dB))=-20logΓ
TRANSMISSION LOSS (SWR)
T_LdB=-10log[1-(SWR-1)/(SWR+1)]^2
TRANSMISSION LOSS (Γ)
T_LdB=-10log[1-Γ]^2
TRANSMITTTED POWER
P_abs=P_inc-P_ref
P_abs=P_inc (1-Γ^2 )
TIME DELAY
t_d=√LC
t_d=1.016√k
PHASE SHIFT
θ=(360t_d)/T
T=1/f
CABLE ATTENUATION
attenuation= dB/100ft
INPUT IMPEDANCE
Z_in=Z_o [(Z_L+jZ_o tanβl)/(Z_o+jZ_L tanβl)]
ELECTRICAL LENGTH
βl°=(360°l)/λ;βl_rad=ωl/λ
l=λ/4
Z_in=(Z_o^2)/Z_L ;Z_o=√(Z_in ) Z_L
l=λ/2
Z_in=Z_L
Z_L=∞
Z_in=-jZ_o cotβl
Z_L=0
Z_in=jZ_o tanβl
Z_L=Z_O
Z_in=Z_o