1. Microwave Basics
Anurag Nigam

2. NatTel Microsystems Pvt. Ltd.
Introductions
Anurag holds Master of Technology Degree in Satellite Technology and Applications from Indian Institute of Science, Bangalore. He has 12 years of design experience in RFIC/MMIC Designs in various companies. Currently, Anurag is a Senior Designer with NatTel Microsystems. His main area of interest is High Speed Mixed Signal IC Design & RADAR Designs.
Contacts: Ph. No ,
Name of Instructor:…Anurag Nigam……………………………
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Theme
Day 1- Background Preparation
Maxwell Equations-Physical Interpretation & Application
Interconnects- Design, Mismatch, & Insertion Losses
GaAs Process- Pseudomorphic HEMTs, Inductors, & MIM Capacitors
Process Introduction
Day 2- Power Amplifier, MMIC Design Example
DC Characterization- Biasing Decoupling, Biasing Techniques, Thermal Stability
Small Signal Characterization- Matching & Stability
Large Signal Characterization- Single Tone Analysis, Matching across Power
Load Pull
Day 3- Design Refining, Layout & Design Post Processing
Modulated Signal- QAM16 Input, Ptolemy & Circuit Co-simulations
Linearity- Two Tone Analysis, IP3, ACPR, & EVM
On-chip Power Combiners & Dividers
Layout & Tiling
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Tutorial 1
Right Hand Thumb Rule
Qm =0
Right Hand Screw System
90°
Poynting Vector
Day1
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What is Microwave?
Microwave refers to alternating Electric Field and Magnetic Field intensities with frequencies ranging between 300 MHz and 300 GHz. Same can be viewed in terms of voltages and currents in circuits. For easy of communication frequencies can be grouped into bands with labels. Light has electromagnetic nature as well. All Electromagnetic Waves (EM Waves) in free space have velocity that is universal constant. Special EM Waves with Electric and Magnetic Fields orthogonal to each other and to the direction of propagation with no field component in the direction of Propagation are call Transverse Electromagnetic Waves.
Right Hand Screw System
90°
Poynting Vector
Phase Velocity
90°
Phase Velocity -velocity with which constant phase point moves in space
Frequency-number of cycles of E or H per second
Wavelength –smallest distance between two equiphase points in space
Poynting Vector –vector quantity referring to direction of propagation of energy
300 MHz
300 GHz
1 Meter
1 mm
1GHz
2 GHz
4 GHz
8 GHz
12 GHz
18 GHz
26 GHz
40 GHz L S C X Ku K Ka
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6. Applications of Microwave
RADAR
Communications
Imagery & Global Positioning
Personal
Communications
Heating
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7. Merits and Demerits of Microwaves
At Microwave Frequencies dimensions of components become comparable to wavelength. For example a Capacitor causes current to lead in phase compared to voltage across it. At microwave frequencies there is additional phase variation across length of the component. Same is true for inductors as well. There are parasitic associated with components. This makes modeling of components at microwave frequencies more complex and computation size bigger.
EM solution using Numerical Techniques like Method of Moment, Finite Element Method and Finite Difference Time Domain Methods are used for modeling at Microwave Frequencies.
At much higher frequencies Geometric Optics, Physical Optics, Universal Theory of Diffraction & Physical Theory of Diffraction are used. W L
SMD Capacitor
SMD Inductor
At microwave frequencies, Antennas and Arrays are small for same Directional Gain.
Most of the systems have typically 15% to 20% Bandwidth of the band centre frequency. At Microwave Frequencies larger Bandwidth is available.
Microwave frequencies do not get reflected by Ionosphere. Microwave frequencies can be used for remote sensing, communication using satellites and imagery of terrains and water bodies.
Polar Molecules like water can be oscillated using Microwave frequencies. Damping of these molecules causes heating. This phenomenon is used for cooking food and heating in medical procedures.
For RADAR Applications, small targets can be detected using Microwave frequencies. Automotive RADAR uses Microwave Frequencies.
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8. Important Variables Electric Field Intensity Magnetic Field Intensity
Electric Flux Density
Magnetic Flux Density
Electric Current Density
Magnetic Current Density
Electric Charge Density
Magnetic Charge Density
Electrical Conductivity
Units

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Electromagnetism
James Clerk Maxwell mathematically hypothesized mechanism of propagation of EM Waves (Light)
Point Form of Maxwell’s Equations
James Clerk Maxwell
Oliver Heaviside formalized vector notation of Maxwell’s Equations
Oliver Heaviside
Heinrich Rudolf Hertz experimentally validated Maxwell’s Equations
Heinrich Rudolf Hertz
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10. Integral Form of Maxwell’s Equations
George Gabriel Stokes
Special Case of Ostrogradsky’s Theorem in Two Dimensions
Mikhail Ostrogradsky
General Theorem of reduction of problem dimension by one using Integrals
George Green
Special Case of Ostrogradsky’s Theorem in Three Dimensions
Karl Friedrich Gauss
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11. Maxwell’s Curl Equation1
Right Hand Thumb Rule H
Time Varying Electric Flux Density
Surface Electric Current Density
Electric Current Density Due to Medium Conductivity and Electric Field
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12. Maxwell’s Curl Equation2
Right Hand Thumb Rule E
Time Varying Magnetic Flux Density
Surface Magnetic Current Density
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13. Maxwell’s Divergence Equation1
Surface Integral of Normal Component of Electric Flux Density over closed surface
Electric Charge enclosed by the surface
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14. Maxwell’s Divergence Equation2
Magnetic Charge enclosed by the surface is Zero
Qm =0
Surface Integral of Normal Component of Magnetic Flux Density over closed surface
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15. Constitutive Relations
Metal 1- Copper plated with gold
Metal 2- Copper plated with gold
Dielectric (Laminate/Substrate) W L d
Electric and Magnetic Flux Density are related to Electric and Magnetic Field Intensity through material dependent constants. These relations are called Constitutive Relations.
Polar & Anisotropic
Anisotropic
Isotropic
Magnetic
Material
Dielectric
Insulators &
Semiconductors
Direction Dependent Constants
Direction Independent Constants
Constant of proportionality relating Electric Flux Density and Electric Field Intensity is Constant of Permittivity and that relating Magnetic Flux Density and Magnetic Field Intensity is Constant of Permeability.
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16. Constitutive Relations
For medium with conductivity (Electric Charge Mobility), Electric Current Density is related to Electric Field Intensity described by Ohm’s Law.
Permittivity
frequency
Conductors
As there are no free magnetic charges there is no Magnetic Current Density.
Linear & Non-Linear Substrates
In case constant of permittivity, permeability or conductivity vary with Field intensity, material is Non-Linear otherwise it is linear. Commonly used substrates in microwave circuits are linear.
Dispersive & Non-Dispersive Substrates
In case constant of permittivity or permeability vary with frequency, material is dispersive. Non-dispersive substrates are preferable for broadband applications.
Dispersive
Substrate
Input Pulse
Output Pulse
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Dielectric Material
Electric Polarization
Normal Component of applied E causes electric dipoles to align
Polarization Flux Density P is introduced for continuity to account for charges at the interface P + + + + + + + - + - + D E - - - - - - -
Normal Component of D is continuous in both media
Dipoles align resulting in lower Electric Field Intensity in medium
where
Is the dielectric constant of free-space (8.854e-12 F/m)
Is the relative dielectric constant. It is a complex number
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Dielectric Loss
Alternating Electric Field Intensity causes electric dipoles to oscillate. Damping of these dipoles causes loss known as Dielectric Loss. Dielectric loss is represented by imaginary part of complex dielectric constant.
Phasor Form of Maxwell’s Equation
Field Vectors can vary in time with periodic nature that can be decomposed into sinusoidal basis functions. Thus field vectors in Maxwell’s Equations can be assumed to be sinusoidal and Maxwell’s Equations can be represented in Phasor Form as follows
Electric Dipoles when Time Varying E is applied
Ratio of real to imaginary part of Curl of H is measure of dielectric and conductor loss to reactive energy stored in substrate. This ratio is known as Loss Tangent.
Loss Tangent
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