Microwave Basics Anurag Nigam

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. +91 9158580922, E-mail: nigam_anurag2011@nattelmicro.com Name of Instructor:…Anurag Nigam……………………………..................... Participant’s Name:…………………………………………………………….... Nature of Job:……………………………………………………....................... Area of Focus:……………………………………………………………………. NatTel Microsystems Pvt. Ltd.

NatTel Microsystems Pvt. Ltd. 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 NatTel Microsystems Pvt. Ltd.

NatTel Microsystems Pvt. Ltd. Tutorial 1 Right Hand Thumb Rule Qm =0 Right Hand Screw System 90° Poynting Vector Day1 NatTel Microsystems Pvt. Ltd.

NatTel Microsystems Pvt. Ltd. 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 NatTel Microsystems Pvt. Ltd.

Applications of Microwave RADAR Communications Imagery & Global Positioning Personal Communications Heating NatTel Microsystems Pvt. Ltd.

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. NatTel Microsystems Pvt. Ltd.

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

NatTel Microsystems Pvt. Ltd. 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 NatTel Microsystems Pvt. Ltd.

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 NatTel Microsystems Pvt. Ltd.

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 NatTel Microsystems Pvt. Ltd.

Maxwell’s Curl Equation2 Right Hand Thumb Rule E Time Varying Magnetic Flux Density Surface Magnetic Current Density NatTel Microsystems Pvt. Ltd.

Maxwell’s Divergence Equation1 Surface Integral of Normal Component of Electric Flux Density over closed surface Electric Charge enclosed by the surface NatTel Microsystems Pvt. Ltd.

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 NatTel Microsystems Pvt. Ltd.

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. NatTel Microsystems Pvt. Ltd.

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 NatTel Microsystems Pvt. Ltd.

NatTel Microsystems Pvt. Ltd. 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 NatTel Microsystems Pvt. Ltd.

NatTel Microsystems Pvt. Ltd. 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 NatTel Microsystems Pvt. Ltd.