RF and Microwave Circuit Design
Description
Provides up-to-date coverage of the fundamentals of high-frequency microwave technology, written by two leading voices in the field
RF and Microwave Circuit Design: Theory and Applications is an authoritative, highly practical introduction to basic RF and microwave circuits. With an emphasis on real-world examples, the text explains how distributed circuits using microstrip and other planar transmission lines can be designed and fabricated for use in modern high-frequency passive and active circuits and sub-systems. The authors provide clear and accurate guidance on each essential aspect of circuit design, from the theory of transmission lines to the passive and active circuits that form the basis of modern high-frequency circuits and sub-systems.
Assuming a basic grasp of electronic concepts, the book is organized around first principles and includes an extensive set of worked examples to guide student readers with no prior grounding in the subject of high-frequency microwave technology. Throughout the text, detailed coverage of practical design using distributed circuits demonstrates the influence of modern fabrication processes. Filling a significant gap in literature by addressing RF and microwave circuit design with a central theme of planar distributed circuits, this textbook:
* Provides comprehensive discussion of the foundational concepts of RF and microwave transmission lines introduced through an exploration of wave propagation along a typical transmission line
* Describes fabrication processes for RF and microwave circuits, including etched, thick-film, and thin-film RF circuits
* Covers the Smith Chart and its application in circuit design, S-parameters, Mason???s non-touching loop rule, transducer power gain, and stability
* Discusses the influence of noise in high-frequency circuits and low-noise amplifier design
* Features an introduction to the design of high-frequency planar antennas
* Contains supporting chapters on fabrication, circuit parameters, and measurements
* Includes access to a companion website with PowerPoint slides for instructors, as well as supplementary resources
Perfect for senior undergraduate students and first-year graduate students in electrical engineering courses, RF and Microwave Circuit Design: Theory and Applications will also earn a place in the libraries of RF and microwave professionals looking for a useful reference to refresh their understanding of fundamental concepts in the field.
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Persons
Dr. Charles E. Free was formerly a Reader in Microwave Technology at the University of Surrey, United Kingdom. He specializes in RF electronics and microwave engineering and has contributed to approximately 150 scholarly publications.
Professor Colin S. Aitchison was previously Chair of the European Microwave Conference and has contributed to approximately 185 scholarly publications. He was formerly Dean of the Technology faculty at Brunel University, United Kingdom.
Content
Preface
1. RF Transmission lines
1.0 Introduction
1.1 Voltage, current and impedance relationships on a transmission line
1.2 Propagation constant
1.2.1 Dispersion
1.2.2 Amplitude distortion
1.3 Lossless transmission lines
1.4 Matched and mismatched transmission lines
1.5 Waves on a transmission line
1.6 The Smith chart
1.6.1 Derivation of the chart
1.6.2 Properties of the chart
1.7 Stubs
1.8 Distributed matching circuits
1.9 Manipulation of lumped impedance using the Smith chart
1.10 Lumped impedance matching
1.10.1 Matching a complex load impedance to a real source impedance
1.10.2 Matching a complex load impedance to a complex source impedance
1.11 Equivalent lumped circuit of a lossless transmission line
1.12 Supplementary problems
1.13 Appendices
Appendix A1.1 Coaxial cable
A1.1.1 Electromagnetic field patterns in coaxial cable
A1.1.2 Essential properties of coaxial cables
Appendix A1.2 Coplanar waveguide
A1.2.1 Structure of coplanar waveguide (CPW)
A1.2.2 Electromagnetic field distribution on a CPW line
A1.2.3 Essential properties of coplanar (CPW) lines
A1.2.4 Summary of key points relating to CPW lines
Appendix A1.3 Metal waveguide
A1.3.1 Waveguide principles
A1.3.2 Waveguide propagation
A1.3.3 Rectangular waveguide modes
A1.3.4 The waveguide equation
A1.3.5 Phase and group velocities
A1.3.6 Field theory analysis of rectangular waveguides
A1.3.7 Waveguide impedance
A1.3.8 Higher-order rectangular waveguide modes
A1.3.9 Waveguide attenuation
A1.3.10 Sizes of rectangular waveguide, and waveguide designation
A1.3.11 Circular waveguide
Appendix A1.4 Microstrip
Appendix A1.5 Equivalent lumped circuit representation of a transmission line
References
2. Planar Circuit Design I: Designing using Microstrip
2.0 Introduction
2.1 Electromagnetic field distribution across a microstrip line
2.2 Effective relative permittivity,
2.3 Microstrip design graphs and CAD software
2.4 Operating frequency limitations
2.5 Skin depth
2.6 Examples of microstrip components
2.6.1 Branch-line coupler
2.6.2 Quarter-wave transformer
2.6.3 Wilkinson power divider
2.7 Microstrip coupled-line structures
2.7.1 Analysis of microstrip coupled lines
2.7.2 Microstrip directional couplers
2.7.2.1 Design of microstrip directional couplers
2.7.2.2 Directivity of microstrip directional couplers
2.7.2.3 Improvements to microstrip directional couplers
2.7.3 Examples of other common microstrip coupled-line structures
2.7.3.1 Microstrip DC break
2.7.3.2 Edge-coupled microstrip band-pass filter
2.7.3.3 Lange coupler
2.8 Summary
2.9 Supplementary problems
2.10 Appendix A2.1: Microstrip design graphs
References
3. Fabrication processes for RF and microwave circuits
3.1 Introduction
3.2 Review of essential materials parameters
3.2.1 Dielectrics
3.2.2 Conductors
3.3 Requirements for RF circuit materials
3.4 Fabrication of planar high-frequency circuits
3.4.1 Etched circuits
3.4.2 Thick-film circuits (direct screen printed)
3.4.3 Thick-film circuits (using photoimageable materials)
3.4.4 LTCC (low temperature co-fired ceramic) circuits
3.4.5 Use of ink jet technology
3.5 Characterization of materials for RF and microwave circuits
3.5.1 Measurement of dielectric loss and dielectric constant
3.5.1.1 Cavity resonators
3.5.1.2 Dielectric characterization by cavity perturbation
3.5.1.3 Use of the split post dielectric resonator (SPDR)
3.5.1.4 Open-resonator
3.5.1.5 Free-space transmission measurements
3.5.2 Measurement of planar line properties
3.5.2.1 The microstrip resonant ring
3.5.2.2 Non-resonant lines
3.5.3 Physical properties of microstrip lines
3.6 Supplementary problems
references
4. Planar Circuit Design II: Refinements to basic designs
4.1 Introduction
4.2 Discontinuities in microstrip
4.2.1 Open-end effect
4.2.2 Step width
4.2.3 Corners
4.2.4 Gaps
4.2.5 T-junctions
4.3 Microstrip enclosures
4.4 Packaged lumped-element passive components
4.4.1 Typical packages for RF passive components
4.4.2 Lumped-element resistors
4.4.3 Lumped-element capacitors
4.4.4 Lumped-element inductors
4.5 Miniature planar components
4.5.1 Spiral inductors
4.5.2 Loop inductors
4.5.3 Interdigitated capacitors
4.5.4 MIM (metal-insulator-metal) capacitors
4.6 Appendix 4.1: Insertion loss due to a microstrip gap
References
5. S-parameters
5.1 Introduction
5.2 S-parameter definitions
5.3 Signal flow graphs
5.4 Mason's non-touching loop rule
5.5 Reflection coefficient of a 2-port network
5.6 Power gains of two-port networks
5.7 Stability
5.8 Supplementary Problems
5.9 Appendix A5.1 Relationships between network parameters
A5.1.1 Transmission parameters (ABCD parameters)
A5.1.2 Admittance parameters (Y-parameters)
A5.1.3 Impedance parameters (Z-parameters)
References
6. Microwave Ferrites
6.1 Introduction
6.2 Basic properties of ferrite materials
6.2.1 Ferrite materials
6.2.2 Precession in ferrite materials
6.2.3 Permeability tensor
6.2.4 Faraday rotation
6.3 Ferrites in metallic waveguide
6.3.1 Resonance isolator
6.3.2 Field displacement isolator
6.3.3 Waveguide circulator
6.4 Ferrites in planar circuits
6.4.1 Planar circulators
6.4.2 Edge-guided-mode propagation
6.4.3 Edge-guided-mode isolator
6.4.4 Phase shifters
6.5 Self-biased ferrites
6.6 Supplementary problems
References
7. Measurements
7.1 Introduction
7.2 RF and Microwave connectors
7.2.1 Maintenance of connectors
7.2.2 Connecting to planar circuits
7.3 Microwave vector network analyzers
7.3.1 Description and configuration
7.3.2 Error models representing a VNA
7.3.3 Calibration of a VNA
7.4 On-wafer measurements
7.5 Summary
References
8. RF Filters
8.1 Introduction
8.2 Review of filter responses
8.3 Filter parameters
8.4 Design strategy for RF and microwave filters
8.5 Multi-element low-pass filter
8.6 Practical filter responses
8.7 Butterworth (or maximally-flat) response
8.7.1 Butterworth low-pass filter
8.7.3 Butterworth band-pass filter
8.7.3 Butterworth band-pass filter
8.8 Chebyshev (equal ripple) response
8.9 Microstrip low-pass filter, using stepped impedances
8.10 Microstrip low-pass filter, using stubs
8.11 Microstrip edge-coupled band-pass filters
8.12 Microstrip end-coupled band-pass filters
8.13 Practical points associated with filter design
8.14 Summary
8.15 Supplementary problems
8.16 Appendix A8.1 Equivalent lumped T-network representation of a transmission line
References
9. Microwave Small-Signal Amplifiers
9.1 Introduction
9.2 Conditions for matching
9.3 Distributed (microstrip) matching networks
9.4 DC biasing circuits
9.5 Microwave transistor packages
9.6 Typical hybrid amplifier
9.7 DC finger breaks
9.8 Constant gain circles
9.9 Stability circles
9.10 Noise circles
9.11 Low-noise amplifier design
9.12 Simultaneous conjugate match
9.13 Broadband matching
9.14 Summary
9.15 Supplementary problems
References
10. Switches and Phase Shifters
10.1 Introduction
10.2 Switches
10.2.1 PIN diodes
10.2.2 FETs (Field Effect Transistors)
10.2.3 MEMS (Microelectromechanical Systems)
10.2.4 IPCS (Inline Phase Change Switch) devices
10.3 Digital phase shifters
10.3.1 Switched-path phase shifter
10.3.2 Loaded-line phase shifter
10.3.3 Reflection-type phase shifter
10.3.4 Schiffman 90 phase shifter
10.3.5 Single switch phase shifter
10.4 Supplementary problems
References
11. Oscillators
11.1 Introduction
11.2 Criteria for oscillation in a feedback circuit
11.3 RF (transistor) oscillators
11.3.1 Colpitts oscillator
11.3.2 Hartley Oscillator
11.3.3 Clapp-Gouriet Oscillator
11.4 Voltage controlled oscillator (VCO)
11.5 Crystal-controlled oscillators
11.5.1 Crystals
11.5.2 Crystal-controlled oscillators
11.6 Frequency synthesizers
11.6.1 The phase-locked loop
11.6.1.1 Principle of a phase-locked loop
11.6.1.2 Main components of a phase-locked loop
11.6.1.3 Gain of a phase-locked loop
11.6.1.4 Transient analysis of a phase-locked loop
11.6.2 Indirect frequency synthesizer circuits
11.7 Microwave oscillators
11.7.1 Dielectric resonator oscillator
11.7.2 Delay line stabilized oscillator
11.7.3 Diode oscillators
11.7.3.1 Gunn diode oscillator
11.7.3.2 IMPATT diode oscillator
11.8 Oscillator noise
11.9 Measurement of oscillator noise
11.10 Supplementary problems
References
12. RF and Microwave Antennas
12.1 Introduction
12.2 Antenna parameters
12.3 Spherical polar coordinates
12.4 Radiation from a Hertzian dipole
12.4.1 Basic principles
12.4.2 Gain of a Hertzian dipole
12.5 Radiation from a half-wave dipole
12.5.1 Basic principles
12.5.2 Gain of a half-wave dipole
12.5.3 Summary of the properties of a half-wave dipole
12.6 Antenna arrays
12.7 Mutual impedance
12.8 Arrays containing parasitic elements
12.9 Yagi-Uda array
12.10 Log-periodic array
12.11 Loop antenna
12.12 Planar antennas
12.12.1 Linearly polarized patch antennas
12.12.2 Circularly polarized planar antennas
12.13 Horn antennas
12.14 Parabolic reflector antennas
12.15 Slot radiators
12.16 Supplementary problems
12.17 Appendix: Microstrip design graphs for substrates with r = 2.3
References
13. Power Amplifiers and Distributed Amplifiers
13.1 Introduction
13.2 Power amplifiers
13.2.1 Overview of power amplifier parameters
13.2.1.1 Power gain
13.2.1.2 Power added efficiency (PAE)
13.2.1.3 Input and output impedances
13.2.2 Distortion
13.2.2.1 Gain compression
13.2.2.2 Third-order intercept point
13.2.3 Linearization
13.2.3.1 Pre-distortion
13.2.3.2 Negative feedback
13.2.3.3 Feedforward
13.2.4 Power combining
13.2.5 Doherty amplifier
13.3 Load matching of power amplifiers
13.4 Distributed amplifiers
13.4.1 Description and principle of operation
13.4.2 Analysis
13.5 Developments in materials and packaging for power amplifiers
References
14. Receivers and Sub-Systems
14.1 Introduction
14.2 Receiver noise sources
14.2.1 Thermal noise
14.2.2 Semiconductor noise
14.3 Noise measures
14.3.1 Noise figure (F)
14.3.2 Noise temperature (Te)
14.4 Noise figure of cascaded networks
14.5 Antenna noise temperature
14.6 System noise temperature
14.7 Noise figure of a matched attenuator
14.8 Superhet receiver
14.8.1 Single-conversion superhet receiver
14.8.2 Image frequency
14.8.3 Key figures-of-merit for a superhet receiver
14.8.4 Double-conversion superhet receiver
14.8.5 Noise budget graph for a superhet receiver
14.9 Mixers
14.9.1 Basic mixer principles
14.9.2 Mixer parameters
14.9.3 Active and passive mixers
14.9.4 Single-ended diode mixer
14.9.5 Single balanced mixer
14.9.6 Double balanced mixer
14.9.7 Active FET mixers
14.10 Supplementary problems
14.11 Appendices
Appendix A14.1 Error function table
Appendix A14.2 Measurement of noise figure
References Answers to selected supplementary problems
1
RF Transmission Lines
1.1 Introduction
Transmission lines, in the form of cable and circuit interconnects, are essential components in RF and microwave systems. Furthermore, many distributed planar components rely on transmission line principles for their operation. This chapter will introduce the concepts of RF transmission along guided structures, and provide the foundations for the development of distributed components in subsequent chapters.
Four of the most common forms of RF and microwave transmission line are shown in Figure 1.1.
- Coaxial cable is an example of a shielded transmission line, in which the signal conductor is at the centre of a cylindrical conducting tube, with the intervening space filled with lossless dielectric. The dielectric is normally solid, although for higher-frequency applications it is often in the form of dielectric vanes so as to create a semi-air-spaced medium with lower transmission losses. A typical coaxial cable is flexible with an outer diameter around 5 mm, although much smaller diameters are available with 1 mm diameter cable being used for interconnections within millimetre-wave equipment. Also, for very high-frequency applications, the cable may have a rigid or semi-rigid construction. Further data on coaxial cables are provided in Appendix 1.A.
- Coplanar waveguide (CPW), in which all the conductors are on the same side of the substrate, is also shown in Figure 1.1. This type of structure is very convenient for the mounting of active components, and also for providing isolation between signal tracks. Coplanar lines are widely used in compact integrated circuits for high-frequency applications. Further data on coplanar lines are given in Appendix 1.B.
- Waveguide, formed from hollow metal tubes of rectangular or circular cross-section, is a traditional form of transmission line used for microwave frequencies above 1 GHz. For many circuit and interconnection applications, waveguide has been superseded by planar structures, and its use in modern RF and microwave systems is restricted to rather specialized applications. It is the only transmission line that can support the very high powers required in some transmitter applications. Another advantage of an air-filled metal waveguide is that it is a very low loss medium and therefore can be used to make very high-Q cavities, and this application is discussed in more detail in Chapter 3 in relation to dielectric measurements. A more recent application of traditional waveguides is in substrate integrated waveguide (SIW) structures for millimetre-wave applications, and this is explained in more detail in Chapter 4 in the context of emerging technologies. Further data on the theory of waveguides are given in Appendix 1.C.
- Microstrip is the most common form of interconnection used in planar circuits for RF and microwave applications. As shown in Figure 1.1, it consists of a low-loss insulating substrate, with one side completely covered with a conductor to form a ground plane, and a signal track on the other side. Further data on microstrip are given in Appendix 1.D. This is a particularly important medium for high-frequency circuit design and so Chapter 2 is devoted to an in-depth discussion of microstrip and the associated design techniques.
1.2 Voltage, Current, and Impedance Relationships on a Transmission Line
In its simplest form, a transmission line can be viewed as a two-conductor structure with a go and return path for the current. For the purpose of analysis we may regard any transmission line as made up of a large number of very short lengths (dz), each of which can be represented by a lumped equivalent circuit, as shown in Figure 1.2. In the equivalent circuits, R and L represent the series resistance and inductance per unit length of the conductors, respectively, C represents the capacitance between the lines per unit length, and G is the parallel conductance per unit length, and represents the very high resistance of the insulating medium between the conductors.
Figure 1.1 Common types of high-frequency transmission line.
Figure 1.2 Representation of a transmission line in terms of lumped components.
It should be noted that it is legitimate to represent a continuous transmission line by the lumped equivalent circuit shown in Figure 1.2 providing that dz is small compared to a wavelength. R, L, G, and C are normally referred to as the primary line constants, and have the units of O/m, H/m, S/m, and F/m, respectively.
In order to establish relationships between the voltage and current on a transmission line we need first to specify a line excited by a sinusoidal voltage at the sending end whose angular frequency is ?. If we then let the voltage and current at some arbitrary point on the line be V and I, respectively, we can consider the effect on an elemental length at this point. The voltage drop across the elemental length will be dV and the parallel current will be dI, as shown in Figure 1.3.
Using standard AC circuit theory, we can relate the change in voltage, dV, to the components of the equivalent circuit as
i.e.
Considering the limit, as dz 0, giving
(1.1)Figure 1.3 Equivalent circuit of an elemental length, dz, of a transmission line.
Considering the parallel current, dI, we have
i.e.
As dz 0, giving
(1.2)Differentiating Eq. (1.1) with respect to time gives
Substituting for from Eq. (1.2) gives
which can be written as
(1.3)where
(1.4)Similarly
(1.5)To determine the variation of V along the line, we have to solve the differential Eq. (1.3) for V. This is a second-order differential equation with a standard solution in the form
(1.6)The two terms on the right-hand side of Eq. (1.6) show how the peak amplitudes and phases of waves travelling in the forward and reverse directions vary with distance. The values of the amplitudes and phases of these waves are determined by the value of ?, which is defined as the propagation constant (this is considered in more detail in Section 1.3).
Differentiating the expression in Eq. (1.6) gives
(1.7)Combining Eqs. (1.7) and (1.1) gives
i.e.
(1.8)Remembering that we can rewrite Eq. (1.8) as
or
(1.9)where
(1.10)The impedance, ZO, is termed the characteristic impedance of the transmission line. Characteristic impedance is an important property of any transmission line and it is useful to have an appreciation of its physical significance. Theoretically, it is the ratio of the voltage to current at an arbitrary position on an infinitely long transmission line that supports a wave travelling in one direction. If the line is lossless, i.e. R = 0 and G = 0, then we see from Eq. (1.10) that and has a constant value that is independent of frequency. It follows that if such a line is terminated by an impedance equal to the characteristic impedance, there will be no reflections from the termination. Moreover, if a transmission line is terminated with its characteristic impedance, then the impedance at the input of the line will be equal to the characteristic impedance; under these conditions the line is said to be matched.
Considering the sending end of the line, i.e. z = 0, then from Eqs. (1.6) and (1.9) we obtain
(1.11)where VS and IS are the voltage and current at the sending end of the line, respectively.
Rearranging Eq. (1.11) to obtain V1 and V2 gives:
(1.12)The voltage, V, and current, I, at any distance, z, along the transmission line can now be found in terms of the voltage and current at the sending end by substituting V1 and V2 from Eq. (1.12) into Eqs. (1.6) and (1.9) giving
(1.13)Equation (1.13) may be written in terms of hyperbolic functions as
(1.14)Similarly,
(1.15)The impedance, Zz, at any distance z from the sending end of the line can now be found by dividing Eq. (1.14) by Eq. (1.15) giving
(1.16)where is the impedance at the sending end of the line.
If we now consider a transmission line of finite length, l, terminated by an arbitrary impedance, ZL, then Zz = ZL when...
