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    Insertion Loss and Transmission Co-Efficient: V Z I e e V Z V

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    Aurongo Nasir
    Here are the key steps to solve this problem: (i) The impedance of two dipoles in parallel is 75/2 = 37.5 Ω. (ii) Using the transmission line equation for a load impedance in parallel with the characteristic impedance, the input impedance at the parallel juncture is Zin = (Z0ZL)/(Z0 + ZL) = (50 * 37.5)/(50 + 37.5) = 25 Ω. (iii) This 25 Ω impedance is now the load on the feed line. Using the transmission line equation again, the input impedance of the feed line is Zin = (Z0ZL)/(Z0 + ZL

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    Insertion Loss and Transmission Co-Efficient: V Z I e e V Z V

    Uploaded by

    Aurongo Nasir
    43 views15 pages
    Here are the key steps to solve this problem: (i) The impedance of two dipoles in parallel is 75/2 = 37.5 Ω. (ii) Using the transmission line equation for a load impedance in parallel with the characteristic impedance, the input impedance at the parallel juncture is Zin = (Z0ZL)/(Z0 + ZL) = (50 * 37.5)/(50 + 37.5) = 25 Ω. (iii) This 25 Ω impedance is now the load on the feed line. Using the transmission line equation again, the input impedance of the feed line is Zin = (Z0ZL)/(Z0 + ZL

    Original Description:

    Lecture

    Original Title

    L4_eee433

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    Here are the key steps to solve this problem: (i) The impedance of two dipoles in parallel is 75/2 = 37.5 Ω. (ii) Using the transmission line equation for a load impedance in parallel with the characteristic impedance, the input impedance at the parallel juncture is Zin = (Z0ZL)/(Z0 + ZL) = (50 * 37.5)/(50 + 37.5) = 25 Ω. (iii) This 25 Ω impedance is now the load on the feed line. Using the transmission line equation again, the input impedance of the feed line is Zin = (Z0ZL)/(Z0 + ZL

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    43 views15 pages

    Insertion Loss and Transmission Co-Efficient: V Z I e e V Z V

    Uploaded by

    Aurongo Nasir
    Here are the key steps to solve this problem: (i) The impedance of two dipoles in parallel is 75/2 = 37.5 Ω. (ii) Using the transmission line equation for a load impedance in parallel with the characteristic impedance, the input impedance at the parallel juncture is Zin = (Z0ZL)/(Z0 + ZL) = (50 * 37.5)/(50 + 37.5) = 25 Ω. (iii) This 25 Ω impedance is now the load on the feed line. Using the transmission line equation again, the input impedance of the feed line is Zin = (Z0ZL)/(Z0 + ZL

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 15

    Insertion loss and Transmission co-efficient

    [
    V ( z ) = V0+ e − jβz + ΓL e + jβz ] (1)
    V0+
    I ( z) =
    Z0
    [e − jβ z
    − ΓL e + jβz ] (2)

    (3)
    (4)
    TRANSMISSION CO-efficient

    (5)

    Equ. 5 can be written as

    (6)
    Equating equ 3 and 6 at Z=0 gives
    T=1+Γ (7)

    (8)

    Substituting (8) in (7)


    (9)
    INSERTION LOSS

    (10)
    VOLTAGE STANDING WAVE RATIO (VSWR(ρ))

    ρ= (11)

    (12)
    VSWR
    Substituting 12 in 11 gives

    ρ= (13)
    ISWR
    We can express the current standing wave ratio as

    I ( z ) max 1 + ΓL
    ρ = ISWR = = (14)
    I ( z ) min 1 − ΓL
    where
    I max ( z ) = I 0+ (1 + ΓL )
    (15)
    I min ( z ) = I (1 − ΓL )
    +
    0

    INPUT IMPEDANCE OF TL

    Zin Z=0
    Z=-l
    Voltage and current on any point in LOSSLESS TL
    (1)

    (2)
    INPUT IMPEDANCE OF TL

    (5)

    (6)
    (6)

    (7)

    (6)

    (8)

    (6)

    (7 )and (8)
    Maximum Impedance, Minimum Impedance and Normalized Impedance

    Vmax V0 (1 + ΓL ) (1 + ΓL )
    +

    Z max = = + = Z0
    I min V0 (1 − ΓL ) (1 − ΓL )
    Z0
    Vmin V0+ (1 − ΓL )
    (1 − ΓL )
    Z min = = + = Z0
    I max V0 (1 + ΓL ) (1 + ΓL )
    Z0

    Normalized zmax and zmin are obtained by dividing


    the Zmax and Zmin by Z0
    (1 − ΓL ) = 1
    (1 + ΓL ) = ρ z min( norm ) =
    z max( norm ) = (1 + ΓL ) ρ
    (1 − ΓL )
    We can conclude that Vmax,Imin, Zmax and
    VSWR(ρ) points in Transmission line are
    same. Similarly Vmin,Imax, Zmin and
    1/VSWR(1/ρ) are same point
    Determination of Z0
    Measure the sending end impedance with
    receiving end short-circuited (ZL=0)
    Z sc = jZ 0 tan βl

    Measure the sending end impedance with


    receiving end open-circuited (ZL=α)
    Z oc = − jZ 0 cot βl

    Thus
    Z 0 = Z sc Z oc
    General Form of input impedance
    For lossless line
    γ=jβ

    We know
    tanh(jβl)=jtan βl
    Short circuited line
    Z L + Z 0 tanh( jβl ) Z sc = Z 0 tanh γl
    Z in = Z 0
    Z 0 + Z L tanh( jβl )
    Z + Z 0 tanh(γl )
    Open circuited line
    Z in = Z 0 L
    Z 0 + Z L tanh(γl ) Z oc = Z 0 coth γl

    We can find the propagation constant


    1 Z sc
    γ = tanh −1
    l Z oc
    P-1
    The open circuit and short impedances measured at the input
    terminals of a lossless transmission line of length 1.5 (m), which is
    less than a quarter wavelength are –j54.6 (Ω) and j103 (Ω)
    respectively. Find (i) Z0 and γ of the line. (ii) Without changing the
    operating frequency find the input impedance of a short-circuited line
    that is twice the given length and (iii) How long should the short-
    circuited line be on order for it to appear as an open circuit at the
    input terminals
    P-2
    Two half-wave dipole antenna each with an impedance of 75
    Ω are connected in parallel through a pair of
    transmission lines and the combination is connected to a
    feed transmission line. All lines are 50 Ω and lossless.
    (i) Calculate the input impedance of the antenna-terminated
    line at the parallel juncture.
    (ii) Calculate the input impedance of the feed line.

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