Transmission Lines Input Impedance

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    Input ImpedanceJesi V. Delos Santos

    Tobi Roque B. Santamaria

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    What is Input Impedance

    or Z(input)

    Impedance presented to the transmitter tothe transmission line and its load antenna

    Or simply the line impedance seen at thebeginning of the transmission line

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    What is Input Impedance

    The input impedance of any length of a

    uniform transmission line terminated in its

    characteristic impedance (non reflectively)is equal to the characteristic impedance of

    the line.

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    Recall

    What is a Matched Line? r = 0

    A transmission line whose characteristic

    impedance is the same as its terminations.

    In this manner, there is complete

    absorption of the incident power, and there

    are no wave reflections back to the

    source.

    Also called matched transmission line, or

    matching line.

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    Recall

    What is a Mismatched Line?

    Simply not a Matched Line

    Its impedances are not equal

    There is a reflection

    If open( r = 1) if shorted( r = -1)

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    Lossy

    LosslessLossless case (=0, =j, tanh(l) = jtanl)

    Input Impedance Formula

    tanh

    tanh

    0

    0

    0

    L

    Lin

    ZZ

    ZZZZ

    tan

    tan

    0

    0

    0

    L

    Lin

    jZZ

    jZZZZ

    Recall:

    tanh(jA) = jtanA

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    Short-Circuit/Open-Circuit

    Short Circuit Line

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    Open Circuited Line

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    Short-Circuit/Open-Circuit

    For a line of known length l, measurements of its input impedance,

    one when terminated in a short circuit and another when terminated

    in an open circuit, can be used to find its characteristic impedance

    Z0 and electrical length

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    Special Line Cases

    Recall for Lossless

    Half-wave section in a lossless case(l=/2, l=):

    Quarter-wave section in a lossless case(l=/4, l=/2):

    tan

    tan

    0

    0

    0

    L

    Lin

    jZZ

    jZZZZ

    Lin ZZ

    L

    in

    Z

    ZZ

    2

    0

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    Problems(lots of problems)

    1. A 50- lossless transmission line is

    terminated with a load impedance of

    25+75. What is the input impedance at a

    distance of 5 from the load?

    Ans: 25 + j75

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    Problems(lots of problems)

    2. Find the input impedance in ohms for a

    50 lossless transmission line, 3.5 long, if

    the load is 20 +j75.

    Ans: 20 + j75

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    Problems(lots of problems)

    3. A radio transmission line of 300

    impedance is to be connected to an antenna

    having an input impedance of 150 . What

    is the impedance of a quarter-wavematching line?

    Ans: 212

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    Problems(lots of problems)

    4. A section of low-loss transmission line is

    0.40 wavelengths long and is terminated in a

    short circuit. Its characteristic impedance is

    73 + j0 . The frequency of operation is 200Mhz. Determine the input reactance of the

    line section, and the value of inductance or

    capacitance to which it is equivalent.Ans: ZinSC = -j53.4, C = 14.9pF

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    Problems(lots of problems)

    5. A 6-m section 150- lossless

    transmission line is terminated in a load ZL =

    (150 j50) , determine its input impedance

    if = 0.4/m.

    Ans: 115.70 + j27.42

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    Problems(lots of problems)

    6. A 50- lossless line is terminated in a

    load impedance ZL = (30 j20) . Find the

    input impedance if it is .33 long.

    Ans: 102 + j2.54

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    Problems(lots of problems)

    7. A 75- resistive load is preceded by a /4

    section of a 50- lossless line, which itself is

    preceded by another /4 section of a 100-

    line. What is the input impedance?

    Ans: 300

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    Problems(lots of problems)

    8. A lossless transmission line of electrical

    length l= 0.35 is terminated in a load

    impedance as shown in Fig. Find Zin.

    Ans: 64.8 + j38.3