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    Lect 23

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    dvdiyen
    This document summarizes the T-junction power divider, resistive power divider, and Wilkinson power divider. 1) The T-junction power divider uses transmission line theory to divide power at a junction based on characteristic impedances with no isolation between output ports. 2) The resistive power divider connects transmission lines to a star circuit of resistors to provide a matched and reciprocal 3-way divider with 6dB loss and no isolation. 3) The Wilkinson power divider uses quarter-wave transmission lines and resistors to provide matched and isolated output ports with no loss when ports are matched.

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    Lect 23

    Uploaded by

    dvdiyen
    125 views14 pages
    This document summarizes the T-junction power divider, resistive power divider, and Wilkinson power divider. 1) The T-junction power divider uses transmission line theory to divide power at a junction based on characteristic impedances with no isolation between output ports. 2) The resistive power divider connects transmission lines to a star circuit of resistors to provide a matched and reciprocal 3-way divider with 6dB loss and no isolation. 3) The Wilkinson power divider uses quarter-wave transmission lines and resistors to provide matched and isolated output ports with no loss when ports are matched.

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    T- Junction, Magic Tee

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    lect23

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    This document summarizes the T-junction power divider, resistive power divider, and Wilkinson power divider. 1) The T-junction power divider uses transmission line theory to divide power at a junction based on characteristic impedances with no isolation between output ports. 2) The resistive power divider connects transmission lines to a star circuit of resistors to provide a matched and reciprocal 3-way divider with 6dB loss and no isolation. 3) The Wilkinson power divider uses quarter-wave transmission lines and resistors to provide matched and isolated output ports with no loss when ports are matched.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    125 views14 pages

    Lect 23

    Uploaded by

    dvdiyen
    This document summarizes the T-junction power divider, resistive power divider, and Wilkinson power divider. 1) The T-junction power divider uses transmission line theory to divide power at a junction based on characteristic impedances with no isolation between output ports. 2) The resistive power divider connects transmission lines to a star circuit of resistors to provide a matched and reciprocal 3-way divider with 6dB loss and no isolation. 3) The Wilkinson power divider uses quarter-wave transmission lines and resistors to provide matched and isolated output ports with no loss when ports are matched.

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    of 14

    Lecture 23: The (3-port) T-Junction Power Divider

    Lossless 3-port netowork


    The discontinuity at the
    junction create fringing
    fields and higher order
    modes, and leads to stored
    energy which can be
    accounted for by a lumped E plane waveguide T H plane waveguide T
    susceptance.

    Microstrip T-junction

    Transmission line model of a


    lossless T-junction.
    ELEC4630, Shu Yang, HKUST 1
    If we relax the requirement for matched ports, we can realize
    tee networks that divide power and provide a match at one
    port (typically chosen as the input port).

    1 1 1
    Yin jB
    Z1 Z 2 Z 0
    For a lossless network, all the characteristic impedances are
    real, and we can assume B = 0. Then Yo = Y1 + Y2 .
    The voltage V0 at the junction is the same for line 1 and line
    2, and the power in the lines is
    P1 = V02Y1/2 and P2 = V02Y2/2
    P2 Y2 Z1
    so the power division ratio r is r
    P1 Y1 Z 2
    ELEC4630, Shu Yang, HKUST 2
    Substituting Y2 = rY1 we have Yo = Y1(1+r), so Z1 = Zo(1+r)
    1+r
    and Z2 = Zo r

    The output line impedances Z1 and Z2 can be selected to provide


    various power division ratio. If we let r = 1, we get even power
    division (power split, -3 dB), and Z1 = 2 Z0, Z2 = 2 Z0 . If needed,
    the quarter-wave transformers can be used to bring the output line
    impedances back to the desired level.
    If B is not negligible, some type of tuning element can usually be
    added to the divider to cancel this susceptance.
    Output ports are not isolated.
    Example 7.1 of Pozar!

    ELEC4630, Shu Yang, HKUST 3


    Resistive Divider
    If we relax the requirement for zero loss,
    we can realize a matched, reciprocal
    power divider.

    Such a divider
    can be realized
    by connecting
    three Zo An equal-split three-port
    transmission resistive power divider.
    lines to a star
    circuit consisting
    The impedance looking into the resistor
    of three resistors
    followed by the output line, is
    R = Zo/3.
    Z0 4Z0
    Z Z0
    3 3
    ELEC4630, Shu Yang, HKUST 4
    The input impedance of the divider is
    Z0 2Z0
    Z in Z0 matched
    3 3
    Since the network is symmetric from all three ports, the
    output ports are also matched.

    Output Power
    V1
    The output voltage from port 2 and 3 are, V2 V3
    2
    Thus, S21 = S31 = S23 = 1/2, which indicates 6 dB below the
    input power level. We have
    0 1 1 1
    [S ] 1 0 1 Port 2 and 3 are
    1 P2 P3 Pin
    2 not isolated. 4
    1 1 0
    ELEC4630, Shu Yang, HKUST 5
    The Wilkinson Power Divider
    Motivation: to solve the problem of output isolation
    The Wilkinson power divider is a three-port that has all ports
    matched with isolation between the two output ports.

    An equal-split Microstrip Wilkinson Equivalent circuit


    power divider
    The Wilkinson power divider can be made to give arbitrary
    power division. But an equal-split one is used here for
    analysis. ELEC4630, Shu Yang, HKUST 6
    Features of the Wilkinson dividers
    1. By choosing the impedance of the /4 lines to be 2 Zo, the
    matched output loads ZL = Zo are transformed to 2Zo so they can
    be placed in parallel to equal 2Zo/2 = Zo creating a matched
    condition at the input port.
    2. Any mismatched power returned from a load at either output
    port is divided equally between the load on the input port (the
    generator source impedance, presumed to be Zg = Zo) and the
    resistor R.
    3. None of the reflected power from a mismatched load is
    dissipated in the other load, so the output ports are isolated (S23 =
    S32 = 0).

    ELEC4630, Shu Yang, HKUST 7


    Even-Odd Mode Analysis
    Preparing procedures:
    Step 1: Draw a
    symmetric equivalent
    circuit across the mid-
    plane.

    Step 2: Normalize all


    the impedances and
    resistance.
    Step 3: Define even
    Even mode: Vg 2 Vg 3 2V
    and odd modes
    Odd mode: Vg 2 Vg 3 2V

    ELEC4630, Shu Yang, HKUST 8


    Even mode: Vg 2 Vg 3 2V
    No current (o.c.) flows through the resistors between port 2 and 3
    or the short circuit at port 1.

    The
    impedance
    looking into
    port 2 is
    2
    Z
    Z in
    e x 0
    Bisection of the equivalent circuit for
    2 even mode excitation.
    Quarter-wave
    transformer For a matched port 2, we have Z 2
    so that V2e V and Z ine 1
    ELEC4630, Shu Yang, HKUST 9
    Setting up x coordinate as shown in the figure. Looking
    toward the left from port 1, the transmission line voltage can
    be written as
    V ( x ) V ( e j x e j x )
    Then, V2e V ( / 4) jV (1 ) V
    1
    V1 V (0) V (1 ) jV
    e

    1
    2 2
    We have therefore, V1 jV 2
    e
    2 2

    ELEC4630, Shu Yang, HKUST 10


    Odd mode: Vg 2 Vg 3 2V
    From symmetry point of view, the middle point
    of the equivalent circuit has zero potential.

    The
    impedance
    looking into
    port 2 is

    Z ino r / 2 Bisection of the equivalent circuit for


    A short- odd mode excitation.
    circuited For a matched port 2, we have r2
    quarter-wave
    line is open. so that V V
    2
    o

    ELEC4630, Shu Yang, HKUST 11


    Then port 2 and 3 are terminated in matched
    loads, so that we can find S11.

    1
    Z in ( 2 ) 2 1
    2
    Summary:
    S11 0
    symmetric
    S 22 S33 0
    V1e V1o
    S12 S 21 e
    V2 V2o
    j/ 2
    S13 S31 j / 2
    S 23 S32 0 ELEC4630, Shu Yang, HKUST 12
    When the Wilkinson power divider is driven at port 1 and the
    outputs are matched, no power is dissipated in the resistor.
    Thus the divider is lossless when the outputs are matched;
    only reflected power from ports 2 or 3 is dissipated in the
    resistor. Since S23 = S32 = 0, ports 2 and 3 are isolated.

    Example 7.2 of Pozar.


    Unequal Power Division and N-Way Wilkinson Dividers
    Design equations: K 2 P3 / P2
    1 K 2
    Z 03 Z 0
    K3
    Z 02 K 2 Z 03 Z 0 K (1 K 2 )
    1 Unequal division
    R Z0 K
    K ELEC4630, Shu Yang, HKUST 13
    An N-way, equal-split Wilkinson Power Divider
    All ports are matched,
    with isolation between all
    ports.

    Disadvantage: crossovers among the


    resistors, result in difficult fabrication
    process.
    Solution: using stepped multiple
    sections.

    ELEC4630, Shu Yang, HKUST 14

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