Module – 1
TWO PORT NETWORK THEORY
                     20EC024 - RF AND MICROWAVE COMMUNICATION
SRIT – ECE / R2020   VII SEM ECE
         Unit 1 – TWO PORT NETWORK THEORY
2
       Review of Low frequency parameters: Impedance, Admittance, Hybrid
        and ABCD parameters
       Different types of interconnection of Two port networks
       High Frequency parameters
       Formulation of S parameters, Properties of S parameters
       Reciprocal and lossless Network
       RF behavior of Resistors, Capacitors and Inductors.
2                         Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
      Two Port Network
3
   A two-port network (a kind of four-terminal network or quadripole) is an electrical
    network (circuit) or device with two pairs of terminals to connect to the external circuits.
   Two terminals constitute a port if the currents applied to them satisfy the essential
    requirement known as the port condition: the electric current entering one terminal must
    equal the current emerging from the other terminal on the same port.
   The ports constitute interfaces where the network connects to other networks, the points
    where signals are applied or outputs are taken.
   In a two-port network, often port 1 is considered the input port and port 2 is considered
    the output port.
                                        Figure: Example two-port network with symbol
                                        definitions. Notice the port condition is satisfied: the
                                        same current flows into each por t as leaves
                                        that port.
3                         Unit - 1: 20EC024
                                    UECC015 -- RF
                                               RF AND MICROWAVE COMMUNICATION
                                                                COMMUNICATION   7/28/2020
    Two Port Network - Basic Definitions:
4
4              Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
    Unit 1 – TWO PORT NETWORK THEORY
5
       Review of Low frequency parameters: Impedance, Admittance,
        Hybrid and ABCD parameters
       Different types of interconnection of Two port networks
       High Frequency parameters
       Formulation of S parameters, Properties of S parameters
       Reciprocal and lossless Network
       RF behavior of Resistors, Capacitors and Inductors.
5                     Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
    Two Port Network
6
    Low frequency network :
       Port - definitions
           Electrical Terms        : pair of terminal
           In Microwave network : Reference plane transverse to the length of the microwave
            transmission line or waveguide.
     Physical length of the network is smaller than the wavelength of the signal
      transmitted
    Generalities: The standard configuration of a two port:
                             I1                                              I2
                   +                                                                      +
                         Input               The Network                Output
                  V1                                                                     V2
                   _     Port                  / Device                  Port             _
6                            Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
2 port Microwave Devices – Matrix representation
7
                 (a) 2 port network, (b) z- Matrix representation, (c) Y- Matrix representation
  A Microwave network is formed when several microwave devices and components such as
  Sources, Attenuators, Resonators, Filters, Amplifiers., etc., are coupled together by a
  transmission line or wave guide.
  The point of interaction of two or more devices is called as Junction.
  At low frequencies since the physical length of the network is very small the measurable
  input and output variables are Voltage and Current which can be related interms of Z, Y, H
7
  or ABCD Parameters. Unit - 1: UECC015
                                20EC024 - RF AND MICROWAVE COMMUNICATION
                                                 MICROWAVE COMMUNICATION 7/28/2020
    Network Equations:
8
    For a two port network, the relationship of V & I with respect to the Z, Y, H
    and ABCD parameters can be given as:
        Impedance     V1 = Z11I1 + Z12I2                   Transmission          V1 = AV2 - BI2
       Z parameters                                          A, B, C, D
                      V2 = Z21I1 + Z22I2                    parameters            I1 = CV2 - DI2
                      I1 = Y11V1 + Y12V2                                       V1 = h11I1 + h12V2
        Admittance                                            Hybrid
                                                           H parameters         I2 = h21I1 + h22V2
       Y parameters   I2 = Y21V1 + Y22V2
8                      Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
       Impedance (Z Parameter)
9
   Z is the impedance, measured in ohms. (Z=R+jX)
   Resistance is a measure of the opposition of a circuit to the flow of a steady current.
   Impedance includes the dynamic effect known as reactance(X) along with the
    resistance.
      Reactance(X) is the opposition of a circuit element to a change in current or
       voltage, due to that element's inductance or capacitance. A built-up electric field
       resists the change of voltage on the element, while a magnetic field resists the
       change of current.
   Z-parameters are also known as open-circuit impedance parameters as they
    are calculated under open circuit conditions.
9                        Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Impedance (Z Parameter)
10
                                                                Contd.,
 A Z-parameter matrix describes the electrical behavior of any linear
  network that can be regarded as a black box with a number of ports.
 A port is a pair of terminals carrying equal and opposite currents into
  and out-of the network, and having a particular voltage between them.
 The voltages(V) may be defined in terms of the Z-parameter matrix and
  the currents(I) by the following matrix equation:
                                    V=ZI
 Where Z is an N × N matrix
10                 Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
         Impedance (Z Parameter)
                                                                       Contd.,
11
        The Z-parameter matrix for the two-port network is probably the most common.
        The relationship between the port currents, port voltages and the Z-
         parameter matrix is given by:
11                        Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Z parameters:
12
           V                            Z11 is the impedance seen looking into port 1 when
       Z = 1
        11 I
             1       I       =0
                                        port 2 is open.
                         2
             V                          Z12 is a transfer impedance. It is the ratio of the
       Z    = 1                         voltage at port 1 to the current at port 2 when port
         12   I2     I =0
                      1                 1 is open.
       Z
             V
            = 2
                                        Z21 is a transfer impedance. It is the ratio of the
         21   I
                1    I2 = 0             voltage at por t 2 to the current at por t 1 when por t
                                        2
             V                          is open.
       Z
         22
            = 2
              I2     I =0
                                        Z22 is the impedance seen looking into port 2 when
                      1                 por t 1 is open.
12                            Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Impedance Relations
13
        The input impedance of a two-port network is given by:
                                              Z 21Z
                    Z in = Z 11−                      12
                                       Z 22 + Z L
        where ZL is the impedance of the load connected to port 2.
        The output impedance is given by:
                                                      Z      Z 21
                  Z           = Z            −            1 2
                                                            + Z S
                      o u t            2 2
                                                  Z   11
     Where ZS is the impedance of the source connected to port 1.
13                            Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
      Admittance (Y Parameter)
14
    Admittance is a measure of how easily a circuit or device will allow a current to
     flow.
    It is defined as the inverse of impedance.
    The SI unit of admittance is Siemens (Symbol S).
    Oliver Heaviside coined the term admittance in December 1887.
    Admittance is defined as
                                                       1
                                        Y       =
                                                       Z
14                       Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
      Admittance (Y Parameter)
                                                                    Contd.,
15
    The currents may be defined in terms of the Y-parameter matrix and the
     voltages by the following matrix equation:
                                             I = VY
    The Y-parameter matrix for the two-port network is probably the most
     common.
    In this case, the relationship between the port voltages, por t currents and
     the Y-parameter matrix is given by:
15                     Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
      Y parameters:
16
         I                     Y11 is the admittance seen looking into port 1when port 2 is
     Y = 1                     shorted.
      11 V       V       =0
           1         2
         I                     Y12 is a transfer admittance. It is the ratio of the current at port 1
     Y = 1                     to the voltage at port 2 when port 1 is shorted.
      12 V       V       =0
           2         1
          I
                               Y21 is a transfer impedance. It is the ratio of the current at port 2
     Y = 2
      21 V                     to the voltage at port 1 when port 2 is shorted.
            1    V       =0
                     2
           I
     Y = 2                      Y22 is the admittance seen looking into port 2 when port 1 is
      22 V                      shorted.
             2   V       =0
                     1
16                            Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
         Admittance relations
17
        The input admittance of a two-port network is given by
                                                       Y12Y 21
                                Y in = Y 1 1        −
                                                      Y 22 + Y L
       Where YL is the admittance of the load connected to port 2.
      The output admittance is given by
                                                         Y12Y 21
                              Y out = Y             −
                                                        Y11 + Y S
                                               22
        Where YS is the admittance of the source connected to port 1.
17                       Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Transmission parameters (A,B,C,D)
18
      ABCD Parameters, When Receiving End is Open Circuited
      The defining equations are:
         1   2
18                Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
      Transmission parameters (A,B,C,D)
                                                                     Contd.,
19
    The ABCD-parameters are known variously as chain, cascade, or transmission
     line parameters.
    A,B,C,D are the constants that characterizes the junctions.
    ABCD parameters – convenient to represent when number of circuits are
     connected in Cascade.
    Unlike in the definition used for Z and Y parameters, notice that I2 is directed
     away from the port.
19                      Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Properties of ABCD parameters
20
        ABCD parameters can be expressed in terms of the Z parameters.
        For a lossless network:
        The usefulness of the ABCD matrix is that cascaded two-port networks can
         be characterized by simply multiplying their ABCD matrices
20                      Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Hybrid Parameters
21
      Every linear circuit having input and output terminals can be
       analyzed by four parameters.
      One is measured in ohm, one in mho and two dimensionless
       quantities.
      These four parameters are called hybrid or h Parameters.
      Hybrid means “mixed”.
21                 Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Hybrid Parameters
                                                                    Contd.,
22
        The equations for the hybrid parameters are:
22                     Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Measurement Difficulties
23
        Measurement of Z, Y, H and ABCD Parameters is difficult at Microwave
         Frequencies.
        Reasons:
            Non- availability of terminal voltage and current measuring equipment.
            Short circuit and especially open circuit are not easily achieved for a wide
             range of frequencies.
            Presence of active devices makes the circuit unstable for short or open circuit.
        S-Parameters relates the reflected waves amplitude.
        For Circuit analysis S-parameters are related to Z or Y or ABCD
         parameters.
23                         Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Routines
24
      Z parameters are useful for analyzing series connected
       networks.
      Y Parameters are useful for analyzing parallel connected
       networks.
      ABCD Parameters are used for analyzing cascaded two-port
       networks.
      S parameters are useful for describing interactions of voltage
       and current waves with a network.
24                  Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Unit 1 – TWO PORT NETWORK THEORY
25
        Review of Low frequency parameters: Impedance, Admittance,
         Hybrid and ABCD parameters
        Different types of interconnection of Two port networks
        High Frequency parameters
        Formulation of S parameters, Properties of S parameters
        Reciprocal and lossless Network
        RF behavior of Resistors, Capacitors and Inductors.
25                     Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Different types of interconnection of Two port networks
Three ways that two ports are interconnected:
26                      Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
                   Interconnection Of Two Port Networks
     Cascade Connection
27
27                  Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
                   Interconnection Of Two Port Networks
     Cascade Connection
28
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                     Interconnection Of Two Port Networks
     Parallel Connection
29
29                  Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
                     Interconnection Of Two Port Networks
     Parallel Connection
30
                       Interconnection Of Two Port Networks
       Series Connection
31
     For Network Na   V1a = z11a I 1a + z1 2 a I 2 a
                      V 2 a = z 21a I 1a + z 22 a I2a
                      V1b = z11b I 1b + z1 2 b I 2 b
     For Network Nb
                      V 2 b = z 2 1b I 1b + z 2 2 b I 2 b
                        I 1 = I 1 a = I 1b
     We notice that
                        I 2 = I 2a = I 2b
31                       Unit - 1: UECC015
                                   20EC024 - RF AND MICROWAVE
                                                    MICROWAVE COMMUNICATION
                                                              COMMUNICATION   7/28/2020
                      Interconnection Of Two Port Networks
      Series Connection
32
     We notice that
                      V1 = V1 a + V1b = (z 11 a + z 11b )I 1 + (z 1 2 a + z 1 2 b )I 2
                      V 2 = V 2 a + V 2 b = (z 2 1 a + z 2 1b )I 1 + (z 2 2 a + z 2 2 b )I 2
32
     Unit 1 – TWO PORT NETWORK THEORY
33
        Review of Low frequency parameters: Impedance, Admittance,
         Hybrid and ABCD parameters
        Different types of interconnection of Two port networks
        High Frequency parameters
        Formulation of S parameters, Properties of S parameters
        Reciprocal and lossless Network
        RF behavior of Resistors, Capacitors and Inductors.
33                     Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     High Frequency parameters
34
     Scattering Parameters:
      Scattering Parameters (S-Parameters) plays a major role is network
       analysis.
      This importance is derived from the fact that practical          system
       characterizations can no longer be accomplished through simple open-
       or short-circuit customarily in low-frequency measurements, as is
       applications.
      In the case of a short circuit with a wire; the wire itself possesses
       an inductance that can be of substantial magnitude at high frequency.
      Also open circuit leads to capacitive       loading at the terminal.
34                    Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
         High Frequency parameters
                                                                         Contd.,
35
        In either case, the open/short-circuit conditions needed to determine Z-
         , Y-, h- andABCD-parameters can no longer be guaranteed.
        When dealing with wave propagation phenomena, it is not desirable to
         introduce a reflection coefficient whose magnitude is unity.
        For instance, the terminal discontinuity will cause undesirable voltage
         and/or current wave reflections leading to oscillation that can result in the
         destruction of the device.
        With       S-parameters,     one     has     proper      tool    to characterize
         the      two-port     network      Description practically all RF devices
         without harm to DUT(Device Under Test).
35                          Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Definition of Scattering Parameters
36
        S-parameters are power wave descriptors that permit us to
         define the input-output relations of a network in terms of incident
         and reflected power waves.
                                                              
                      
                                               [S]             
             b1                                                                        b2
         an – normalized incident power waves
         bn – normalized reflected power waves
36                    Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Definition of Scattering Parameters
37
                                     Contd.,
                 1
37               Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Unit 1 – TWO PORT NETWORK THEORY
38
        Review of Low frequency parameters: Impedance, Admittance,
         Hybrid and ABCD parameters
        Different types of interconnection of Two port networks
        High Frequency parameters
        Formulation of S parameters, Properties of S parameters
        Reciprocal and lossless Network
        Transmission matrix
        RF behavior of Resistors, Capacitors and Inductors.
38                    Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
      Formulation of S parameters
39
    An n-port microwave network has n arms into which power can be fed
     and from which power can be taken.
    There are thus n incoming waves and n outgoing waves.
    Power can be reflected by a port, so the input power to a single port can
     partition between all the ports of the network to form outgoing waves.
    Associated with each port is the notion of a "reference plane" at which
     the wave amplitude and phase is defined.
    The reference plane associated with a certain port is at the same place
     with respect to incoming and outgoing waves
39                    Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
      Formulation of S parameters
                                                                        Contd.,
40
    “n” incoming wave complex amplitudes are usually designated by the n
     complex quantities “an”.
    “n” outgoing wave complex quantities are designated by the n complex
     quantities “bn”.
    The incoming wave quantities are assembled into an n-vector A and the
     outgoing wave quantities into an n-vector B.
    The outgoing waves are expressed in terms of the incoming waves by the
     matrix equation B = SA where S is an n by n square matrix of complex
     numbers called the "Scattering Matrix”.
    It completely determines the behavior of the Network.
    The elements of this matrix are termed as "s-parameters”, are all frequency-
     dependent.
40                     Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Definition of S parameters
41              Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Matrix equations for a 2 & 3-port Network
42
      b1 = s11 a1 + s12 a2
      b2 = s21 a1 + s22 a2
      b1 = s11 a1 + s12 a2 + s13 a3
      b2 = s21 a1 + s22 a2 + s23 a3
      b3 = s31 a1 + s32 a2 + s33 a3
     an and bn are obtained from the port current and voltages by the
     relations
      an = (V + ZoI)/(2 sqrt(2Zo))
      bn = (V - ZoI)/(2 sqrt(2Zo))
42                  Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     PROPERTIES OF S-PARAMETER
43
     1. Zero diagonal elements for perfect matched network
     For an ideal network with matched termination
                      Sii=0
     since
      there is no reflection from any port.
      Under perfect matched condition the diagonal element of [s]
        are zero
43                 Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     PROPERTIES OF S-PARAMETER
                                                                   Contd.,
44
     2. Symmetry of [s] for a reciprocal network
        The reciprocal device has a same transmission characteristics
         in either direction of a pair of ports and is characterized by
         a symmetric scattering matrix
                          Sij = Sji ; for i≠j
     Which results               [S] t = [S]
44                    Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     PROPERTIES OF S-PARAMETER
45
                                                                    Contd.,
     3. Unitary property of lossless network
        For any loss less network the sum of product of each term of any one
         row or any one column of s matrix multiplied by its complex
         conjugate is unity.
        For a lossless N port devices the total power leaving N ports must be
         equal to total input to the ports.
45                     Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     PROPERTIES OF S-PARAMETER
46
                                                                 Contd.,
     4. Zero property
     It states that the sum of the product of any/each term of
     any one row or any one column of a s matrix is multiplied by
     the complex conjugate of corresponding terms of any other
     row is zero
46                  Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     PROPERTIES OF S-PARAMETER
47
                                                                 Contd.,
     5. Phase shift property
     If any of the terminal or reference plane are mover away from
     the junction by an electric distance βk, lk. each of the coefficient
     Sij involving K will be multiplied by the factor (e –jβk/k)
                                 0                          e−    jφ1 2
                                                                           
                         [S ] =  − jφ 2 1                                 
                                e                               0         
47                  Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION     7/28/2020
     Unit 1 – TWO PORT NETWORK THEORY
48
        Review of Low frequency parameters: Impedance, Admittance,
         Hybrid and ABCD parameters
        Different types of interconnection of Two port networks
        High Frequency parameters
        Formulation of S parameters, Properties of S parameters
        Reciprocal and lossless Network
        RF behavior of Resistors, Capacitors and Inductors.
48                     Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Reciprocal and lossless Network
49
        Reciprocal Networks:
            Has identical transmission characteristics from port one to port two or from
             port two to port one
            circuit behavior independent of directions of waves and currents.
            Some Characteristics of Impedance and Admittance Matrices
            Both Z and Y matrices are symmetric
        Lossless Networks
            All the Z and Y elements are imaginary.
            To determine Z and Y elements, both voltage and current values need to be
             measured.
            This is difficult at microwave frequencies.
49                        Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Symmetry of [s] for a reciprocal network
50
        The reciprocal device has a same transmission characteristics in either direction of a pair
         of ports and is characterized by a symmetric scattering matrix
            Sij = Sji ; i≠j Which results [S] t = [S]
        For a reciprocal network with assumed normalized the impedance matrix equation is
            [b] = ( [z] + [u] )-1 ([z] – [u]) [a] -----------(1)
     Where u is the unit matrix, S matrix equation of network is
            [b] = [s] [a] ------------(2)
     Compare equ (1) & (2)
             [S] =([Z]+[u])-1 ([Z] – U]) [R] = [Z] – [U]
             [Q] = [Z] + [U]
     For a reciprocal network Z matrix Symmetric
             [R] [Q] = [Q] [R]
             [Q] -1[R][Q][Q]-1 = [Q]-1[Q][R][Q]-1 [Q] -1[R] = [R][Q]-1
             [Q] -1[R] [ S ] = [R][Q]-1
50                               Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Unit 1 – TWO PORT NETWORK THEORY
51
        Review of Low frequency parameters: Impedance, Admittance,
         Hybrid and ABCD parameters
        Different types of interconnection of Two port networks
        High Frequency parameters
        Formulation of S parameters, Properties of S parameters
        Reciprocal and lossless Network
        RF behavior of Resistors, Capacitors and Inductors.
51                     Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Unit 1 – TWO PORT NETWORK THEORY
57
        Review of Low frequency parameters: Impedance, Admittance,
         Hybrid and ABCD parameters
        Different types of interconnection of Two port networks
        High Frequency parameters
        Formulation of S parameters, Properties of S parameters
        Reciprocal and lossless Network
        RF behavior of Resistors, Capacitors and Inductors.
52                     Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
          RF behavior of Resistors, Capacitors and Inductors
58
               Frequency Spectrum
                                    300 MHz – 3 GHz
                  100 Hz
     ELF
     VLF
                  10 kHZ                                                                Radio Frequency
                  100 kHz                                                               • TV
     LF
                  1 MHz                                                                 • Wireless Phones
     MF (MW)                                                                            • GPS
                  3 MHz
     HF (SW)
                  30 MHz
     VHF
                  300 MHz
     UHF                                                                              Microwave Frequency
                  1 GHz
     SHF                                      8 GHz to 40 GHz                    • Radar
                  30 GHz                                                         • Remote Sensing
     EHF
                  300 GHz
     IR
53                          Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
      RF behavior of Resistors, Capacitors and Inductors
                                                  Contd.,
59
• Lumped components (wires, resistors,         capacitors, inductors connectors
  etc.,) behave differently at low and high frequencies.
• Why?
     • current and voltage vary spatially over the component size
     • Leads to the concept of distributed components!
        The KCL and KVL are no more applicable
54                        Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     RF behavior of Resistors, Capacitors and Inductors
60
     •   What do we mean by distributed?
              •   Example – Inductor
         Low Frequency (Lumped)                                    High Frequency (Distributed)
              Z = R + jωL                                                           Z =?
55                        Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     RF Behavior of Passive Components
61
     RF Behavior of Passive Components
      Why do inductors, capacitors, and resistors behave differently at
        Radio Frequency?
      What is skin effect?
      Equivalent Circuit Model?
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     RF Behavior of Passive Components
62
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     RF Behavior of Resistors
63
58              Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     RF Behavior of Resistors
64
                                Contd.,
     RF Behavior of Resistors
65
                                Contd.,
     RF Behavior of Resistors
66
                                                             Contd.,
61              Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
Resistors at High Frequencies
68
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     Resistors at High Frequencies Contd.,
69
     Resistors at High Frequencies
70
                                                           Contd.,
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     Resistors at High Frequencies
71
                                                           Contd.,
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     Capacitors at High Frequencies
72
     Capacitors at High Frequencies
73
                                 Contd.,
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     Capacitors at High Frequencies
74
                                 Contd.,
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                Unit - 1: UECC015 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Inductors at High Frequencies
75
70             Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
               Unit - 1: UECC015 - RF AND MICROWAVE COMMUNICATION   7/28/2020
     Inductors at High Frequencies
76
                                                                                Contd.,
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     Inductors at High Frequencies
77
                                  Contd.,
72             Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
                         Summary
     UNIT 1 – TWO PORT NETWORK THEORY
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        Review of Low frequency parameters: Impedance, Admittance,
         Hybrid and ABCD parameters
        Different types of interconnection of Two port networks
        High Frequency parameters
        Formulation of S parameters, Properties of S parameters
        Reciprocal and lossless Network
        Transmission matrix
        RF behavior of Resistors, Capacitors and Inductors.
73                    Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020
79
     End of unit – I
         Thank you
74   Unit - 1: 20EC024 - RF AND MICROWAVE COMMUNICATION   7/28/2020