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    R. Ludwig and G. BogdanovRF Circuit Design: Theory and Applications

    2nd edition

    Figures for Chapter 1

    Figure 1-1 Block diagram of a generic RF system.

    DAC

    OSC.

    PA

    ADC LNA

    D i g i t a l

    C i r c u

    i t r y

    Analog-to-DigitalConverter

    Digital-to-AnalogConverter

    Local Oscillator

    TransmitterPower Amplifier

    Receiver LowNoise Amplifier

    Switch

    Low-PassFilter

    BandpassFilter

    Antenna

    Mixed Signal

    Circuits

    Analog Circuits

    Mixer

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    Figure 1-2(b) Printed circuit board layout of the power amplifier.

    BFG425

    B F G 2 1

    RF in RF out

    Input MatchingNetwork

    First StageTransistor

    Interstage MatchingNetwork

    OutputMatchingNetwork

    DC Bias Network

    Second StageTransistor

    Dual Transistor IC

    0.5 inch

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    Figure 1-3 Electromagnetic wave propagation in free space. The electric and mag-netic fields are shown at a fixed instance in time as a function of space ( are unitvectors in x - and y -direction).

    x

    y

    z

    H = H y y

    E = E x x

    x ,^

    y ^

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    .Table 1-1 Frequency bands and their applications

    Frequency Band Frequency Typical Application

    VHF (Very High Frequency) 88 108 MHz FM broadcasting

    UHF (Ultrahigh Frequency) 824 894 MHz810 956 MHz

    CDMA mobile phone serviceGSM mobile phone service

    UHF (Ultrahigh Frequency) 2,400 MHz WLAN

    SHF (Superhigh Frequency) 5,000 5,850 MHz Unlicensed NationalInformation Infrastructure

    SHF (Superhigh Frequency) 6,425 6,523 MHz Cable Television Relay

    SHF (Superhigh Frequency) 3,700 4,200 MHz Geostationary fixed satellite

    serviceX Band 8 12.5 GHz Marine and airborne radar

    Ku Band 12.5 18 GHz Remote sensing radar

    K Band 18 26.5 GHz Radar

    Ka Band 26.5 40 GHz Remote sensing radar

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    .

    Figure 1-4 Skin depth behavior of copper aluminumgold and typical solder

    104 105 106 107 108 1090

    0.5

    1

    1.5

    2

    f , Hz

    , m m

    Solder

    Al

    Au

    Cu

    Cu 64.5 106

    S/m,= Al 40.0 10

    6 S/m,= Au 48.5 10

    6 S/m,=

    solder 6.38 106

    S/m.=

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    Figure 1-5(a) Schematic cross-sectional AC current density representation

    normalized to DC current density.

    2a

    Current Flow

    | J z| /J z 0

    r a a

    Low currentdensity

    High currentdensity

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    Figure 1-5(b) Frequency behavior of normalized AC current density for a copperwire of radius a = 1 mm.

    r , mm

    0

    0.20.4

    0.6

    0.8

    1

    1.2

    1.4

    1.6

    1.8

    2

    1 kHz

    10 kHz

    100 kHz

    1 MHz 10 MHz

    100 MHz

    1 GHz

    0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

    | J z |

    / J

    z 0

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    Figure 1-6 The exact theoretical per-unit-length resistance as a function offrequency for round wires of varying materials and radii. The dashed lines representthe DC and skin depth based resistance approximations.

    100

    101

    102

    103

    104

    105

    106

    107

    108

    109

    102

    101

    100

    101

    f , Hz

    R ,

    / m

    Cu, 0.1 mm

    Cu, 1 mmAl, 1 mm

    Solder, 1 mm

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    Figure 1-7 One- and quarter-watt thin-film chip resistors in comparison with aconventional quarter-watt resistor.

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    Figure 1-8 Electric equivalent circuit representation of a high frequency resistor.

    R L L

    C a

    C b

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    Figure 1-9 Electric equivalent circuit representation of a wire-wound resistor at high frequency.

    R

    C 1

    L1

    C 2

    L2 L2

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    Figure 1-10 Absolute impedance value of a 2000 - thin-film resistor asa function of frequency.

    104 105 106 107 108 109 1010100

    101

    102

    103

    104

    f , Hz

    | Z |

    ,

    Ideal resistance

    Capacitive effect

    Inductive effect

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    Figure 1-11 Electric equivalent circuit of a capacitor at high frequency.

    L

    Re

    C

    Rs

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    Figure 1-12 Absolute value of the capacitor impedance as a func-tion of frequency.

    106 107 108 109 1010102

    101

    100

    101

    102

    103

    104

    f , Hz

    | Z | ,

    Real capacitor

    Ideal capacitor

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    Figure 1-13 Actual construction of a surface-mounted ceramic multilayer capacitor.

    Electrodes

    Ceramic material

    Terminations

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    Figure 1-14 Distributed capacitance and series resistance in the inductor coil.

    Rd Rd

    C d C d

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    Figure 1-15 Equivalent circuit of the high-frequency inductor.

    L Rs

    C s

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    Figure 1-16 Inductor dimensions of an air-core coil.

    l

    2a 2 r

    d

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    Figure 1-17 Frequency response of the impedance of an RFC.

    107 108 109 1010100

    101

    102

    103

    104

    105

    f , Hz

    | Z | ,

    Real inductor

    Ideal

    inductor

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    Table 1-2 Standard sizes of chip resistors

    Geometry Size Code Length L, mils Width W , mils

    0402 40 20

    0603 60 300805 80 50

    1206 120 60

    1812 120 180 L W

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    Figure 1-18 Cross-sectional view of a typical chip resistor.

    Protective coatResistive layer

    Marking

    Ceramic substrateInner electrodesEnd contact

    End contact

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    Figure 1-19 Cross section of a typical single-plate capacitor connected to theboard.

    Circuit traces

    Chip capacitor Ribbon lead or wire

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    Figure 1-20 Clusters of single-plate capacitors sharing a common dielectricmaterial.

    Dual capacitor Quadrupole capacitor

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    Figure 1-21 Typical size of an RF wire-wound air-core inductor (courtesy of Coil-craft, Inc.).

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    Figure 1-22 Flat coil configuration. An air bridge is made by using either a wire or aconductive ribbon.

    Air bridge

    Terminal Terminal

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    Figure 1-23 Construction of a three-dimensional LTCC/HTCC module made out ofindividual layers of ceramic tape that are collated, stacked, and fired (courtesy ofLamina Ceramics Inc.).

    BuriedResistor

    BuriedCapacitor

    Vias

    MetalCore

    Metalizationon

    Ceramic

    Surface-mountedactive devices

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    Figure 1-24 Impedance and quality factor behavior of a real, non-magnetic core in-ductor as measured by the HP 4192A LCR meter.

    103

    102

    101

    100

    101

    102

    Q

    101 102 103 104 105 106 107 101 102 103 104 105 106 107100

    101

    102

    103

    104

    105

    f , Hz f , Hz

    | Z | ,

    Resistancedominates

    Inductive behavior

    Self resonance

    Capacitivebehavior

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    Figure 1-25 LCR meter with a plastic core torroidal inductor con-nected to the test fixture and a measurement taken at 100 kHz .