COMSOL Circuit Simulation

COMSOL Circuit simulation

Physics world Manohar Kumar Aalto University COMSOL: Multiphysics

Multiphysics: Systems involving more than one simultaneously occurring physical field and the studies of and knowledge about these processes and systems (def: Wikipedia). Aerodynamics Structural integrity + streamline flow of COMSOL: the air stream and whirlpool formation+ Multiphysics cooling via air jet stream+ heating

Earlier approach: Different domains and their aspects of a structure are studied individually.

Multiphysics simulation: It Wire bonding of chips could be done simultaneously

System requirement • At least 1 GB memory, but 4 GB or more per processor core is recommended. • 1-5 GB of disk space, depending on your licensed products and Current distribution installation options. Wire bonding of a chip Temperature distribution

COMSOL Multiphysics Sept 2015 COMSOL: Multiphysics

Three facets of Multiphysics problems • Mathematics • Physics • Applications

Top-down approach Define the problem first, then physics and then use mathematics to solve it

Multiphysics Rubik COMSOL: Electrical Applications ▪ Joule heating Multiphysics ▪ Induction heating ▪ Microwave heating ▪ Electromagnetic waves Air cooled DC choke Applications in physics: ▪ Piezoelectric heating • Electrical ▪ Piezoresistive effect • Mechanical ▪ Electrochemical effect • Fluid • Chemical

Magnetic flux density in toroidal choke

See Physics sections COMSOL Multiphysics Sept 2015 Partial differential equations (depends upon more than one COMSOL: variable, different than ordinary • Laplace Equation differential equations) Multiphysics • Poisson’s Equation • Wave Equation • Stabilized Convention-Diffusion Equation Mathematics module: • Helmholtz equation • Partial differential equations • Heat Equation • Ordinary differential equations • Convention-Diffusion Equation • Optimization and sensitivity • Interface and boundary value • Coordinates Solution of 2D Poisson’s Equation

휌 ∇2 휑 = − 휀0

The voltage potential and Electric field distribution in parallel plate capacitor COMSOL Multiphysics Sept 2015 Partial differential equations

For second-order PDE for the function 푢 푥1, 푥2, … . 푥푛 휕2푢 휕2푢 휕푢 휕푢 COMSOL: 퐹 … . . , , , … . . , 푥1, 푥2 … . . 푥푛 = 0 Multiphysics 휕푥1휕푥1 휕푥푛휕푥푛 휕푥1 휕푥푛 푥푖’s general co-ordinates: Spatial coordinates (Physics) In spatial 2-D space co-ordinates Mathematics module: 휕2푢 휕2푢 휕2푢 휕2푢 휕푢 휕푢 • Partial differential equations 퐹 , , , , , , … . . , 푥, 푦 = 0 • Ordinary differential equations 휕푥2 휕푥휕푦 휕푥휕푦 휕푦2 휕푥 휕푦 • Optimization and sensitivity 휕2푢 휕2푢 For symmetric conditions = • Interface and boundary value 휕푥휕푦 휕푥휕푦 • Coordinates 퐴푢푥푥 + 2퐵푢푥푦 + 퐶푈푦푦 + … . 푙표푤푒푟 표푟푑푒푟 푡푒푟푚푠 = 0

Quadratic equation: Discriminant: 퐵2 − 퐴퐶 Elliptic PDE 휕2푢 휕2푢 2 + 2 = 0 퐵2 − 4퐴퐶 < 0 휕푥 휕푦

Parabolic PDE 휕푢 휕2푢 - = 0 퐵2 − 4퐴퐶 = 0 휕푡 휕푦2

휕2푢 휕2푢 Hyperbolic PDE - = 0 퐵2 − 4퐴퐶 > 0 휕푡2 휕푦2 Partial differential equations

퐴푢푥푥 + 2퐵푢푥푦 + 퐶푈푦푦 + … . 푙표푤푒푟 표푟푑푒푟 푡푒푟푚푠 = 0

COMSOL: 2 휕2 Quadratic equation: Discriminant: 퐵 − 퐴퐶 ∆ = ෍ 휕푥푖 Multiphysics Elliptic PDE 휕2푢 휕2푢 푖=푛 + = 0 퐵2 − 4퐴퐶 < 0 휕푥2 휕푦2 푥 휖 ℝ푛 Mathematics module: ∆푢 = 0 Laplace equations Electric field, gravitational • Partial differential equations field, fluid potentials • Ordinary differential equations Equilibrium state ∆푢 = −휅휌 Poisson’s equations • Optimization and sensitivity (No temporal/time dependent ) • Interface and boundary value • Coordinates Partial differential equations

퐴푢푥푥 + 2퐵푢푥푦 + 퐶푈푦푦 + … . 푙표푤푒푟 표푟푑푒푟 푡푒푟푚푠 = 0

COMSOL: 2 휕2 Quadratic equation: Discriminant: 퐵 − 퐴퐶 ∆ = ෍ 휕푥푖 Multiphysics Parabolic PDE 휕푢 휕2푢 푖=푛 - = 0 퐵2 − 4퐴퐶 = 0 휕푡 휕푦2 푥 휖 ℝ푛 Helmholtz’s Mathematics module: −∆푢 = 휆푢 • Partial differential equations equations Electromagnetic radiation, • Ordinary differential equations Heat and acoustic, thermal/heat • Optimization and sensitivity 푢푡 − ∆푢 = 0 diffusion transport, fluid transport • Interface and boundary value equation • Coordinates Time dependent equations 푖푢 + ∆푢 = 0 Schrodinger's 푡 equation

Effect of heat sink for chip cooling Partial differential equations

퐴푢푥푥 + 2퐵푢푥푦 + 퐶푈푦푦 + … . 푙표푤푒푟 표푟푑푒푟 푡푒푟푚푠 = 0

COMSOL: 2 휕2 Quadratic equation: Discriminant: 퐵 − 퐴퐶 ∆ = ෍ 휕푥푖 Multiphysics Hyperbolic PDE 휕2푢 휕2푢 푖=푛 - = 0 퐵2 − 4퐴퐶 > 0 휕푡2 휕푦2 푥 휖 ℝ푛 Mathematics module: 2 푢푡푡 − 푐 ∆푢 = 0 Wave equations • Partial differential equations Electro-mechanical wave • Ordinary differential equations Current/voltage Transmission line • Optimization and sensitivity 푢푡푡 + 푢푡 − 푢푥푥 = 0 distribution over Time dependent equations • Interface and boundary value transmission line • Coordinates Short Open

50 ohm E (V/m) E

t (s)

Transient model of a coaxial cable Interface and boundary value

COMSOL: Ordinary differential equation Partial differential equation Multiphysics Initial value problem Boundary value problem

Mathematics module: • Partial differential equations Value of function and The value of function defined at the • Ordinary differential equations its derivative at t = 0 boundary of the domain, where • Optimization and sensitivity solution is supposed to be defined • Interface and boundary value • Coordinates 휕2푢 휕2푢 = 휕푡2 휕푥2

Domains 푡 휖 0, ∞ , 푥 휖 0, 푎 (x = a) 푢 0, 푡 = 푢 푎, 푡 = 0 ∀ 푡 휖 0, ∞

Vibrating string 푢 푥, 0 = 푢 푎, 0 = 0

Any suggestion for the solution? 휕푢(푥, 0) 휕푢(푎, 0) = = 0 휕푡 휕푡 Interface and boundary value (RF Module) 풏. 훁푉 푉 Terminating + = 0 Only at external boundary COMSOL: impedance 푅 + 푗휔퐿 푍퐿 Type equation Multiphysics Open circuit here.풏. 훁푉 = 0 Infinite impedance and zero current Type equation Mathematics module: Short circuit here.푉 = 0 Zero impedance and zero voltage • Partial differential equations • Ordinary differential equations • Optimization and sensitivity Matched port 푍 = 푍 Default value of 푍퐿 = 50 Ω • Interface and boundary value 0 퐿 • Coordinates

Scattering 풏 × 푬 = 푍 푯 boundary condition 0

High impedance at the boundary, meaning current Perfect Magnetic conductor 풏 × 푯 = 0 density = 0

Zero charge 풏. 푫 = 0 Exterior boundary and edges with charge conservation Coordinate systems

COMSOL: Geometry Default coordinates Additional geometry 2D x y 1D, axial symmetry 1D and 0 D Multiphysics 3D x y z Axial symmetry 2D r 휑 z Mathematics module: • Partial differential equations • Ordinary differential equations • Optimization and sensitivity 3D Geometry • Interface and boundary value • Coordinates • Spherical • Cylindrical • Cartesian

Example: Axial symmetry 2D Norm of the electric field for the m=1 mode at 2.122 GHz Physics module (Electrical mainly)

COMSOL: • Electrical Fields and currents • Magnetic Fields, No currents Multiphysics • Electromagnetic fields AC/DC • Electromagnetic heating • Application (Physics) module: Electromagnetic and mechanics • Particle tracing • AC/DC • Electrical circuits • RF • Electromagnetic waves and scattering • Semiconductor • Electromagnetic waves, frequency domains • Mathematics RF • Electromagnetic waves, Time explicit • Acoustic • Electromagnetic waves, Transient • Chemical species transport • Transmission line • Electrochemistry • Semiconductor • Fluid flow • Schrodinger equation • Heat Transport • Schrodinger-Poisson equation Semiconductor • Optics • Semiconductor Optoelectronics Beam envelopes • Plasma • Semiconductor Optoelectronics Frequency domains • Structural Mechanics • . • . • Mathematics (PDE, ODE, etc.) Physics studies module (Electrical mainly)

It compute the response of a linear (linearized) model for COMSOL: harmonic excitations via one or several frequencies. Its output Frequency domain is typically displayed as a transfer function, for example, 퐸 = sin(휔푡 + 휑) magnitude or phase of deformation, sound pressure, Multiphysics 푬 = 푬ퟎ sin(휔푡 + 휑) impedance, or scattering parameters versus frequency. 푩 = 푩ퟎ sin(휔푡 + 휑) Study module: It is used for field variables which doesn’t change over time. • Frequency Domain Stationary studies Examples: In electromagnetics, it is used to compute static electric or magnetic fields, as well as direct currents. In heat • Stationary 휕푬 휕푩 transfer, it is used to compute the temperature field at thermal • Time domain = 0, = 0 휕푡 휕푡 equilibrium. • Eigen Frequency • Custom studies This study is used when field variables change over time. Examples: In electromagnetics, it is used to compute transient Time domain electromagnetic fields, including electromagnetic wave 푬 풕 , 푩(풕) propagation in the time domain. In heat transfer, it is used to Short compute temperature changes over time Open 50 ohm It is used for computing eigenmodes and eigenfrequencies of a linear (linearized) model. Examples: In electromagnetics, the eigenfrequencies correspond to the resonant frequencies

E (V/m) E Eigen Frequency and the eigenmodes correspond to the normalized electromagnetic field at the eigenfrequencies. t (s) Physics studies module (Summary) COMSOL: Multiphysics

Study module: AC/DC • Frequency Domain • Stationary • Time domain • Eigen Frequency • Custom studies Physics studies module (Summary) COMSOL: Multiphysics

Study module: RF • Frequency Domain • Stationary • Time domain • Eigen Frequency • Custom studies Modelling: Low pass filter

2 1 COMSOL: Circuit simulation Multiphysics Surprisingly, you could do this here in COMSOL but waste of time, unless until Modelling: RF/AC-DC you would like to couple it • Understand the problem to the some 3D model • Space dimension • Use boundary condition to 0 reduced the space dimension Dimension: Anyone could be used but 1 D will be most appropriate • Source for excitations Boundary condition: Vs = V at 2 and ground node at 1 • Study module: time domain, frequency domain, etc. Source of excitations: Vs = V sin 휔푡 + 휑 + 퐴 • Variables to study: Eigen function, Study module: time domain then V = 0 and if frequency domain A = 0 voltage, electric field, etc. • Materials: Conductive, insulating Output: Current or Voltage etc. Components: Resistors and capacitors • Meshing • Solve Modeling: Parallel plate capacitors COMSOL: Multiphysics Geometry? PDE? Boundary condition? Modelling: RF/AC-DC • Understand the problem • Space dimension • Use boundary condition to reduced the space dimension • Source for excitations • Study module: time domain, frequency domain, etc. • Variables to study: Eigen function, voltage, electric field, etc. • Materials: Conductive, insulating etc. • Meshing The voltage potential and Electric field distribution • Solve Modeling: Heat Sink COMSOL: Multiphysics Geometry? PDE? Boundary condition? Modelling: RF/AC-DC • Understand the problem • Space dimension • Use boundary condition to reduced the space dimension • Source for excitations • Study module: time domain, frequency domain, etc. • Variables to study: Eigen function, voltage, electric field, etc. • Materials: Conductive, insulating etc. • Meshing • Solve Temperature of the PCB in absence and presence of heat sink Modeling: Mesh structure (3 D/2-D solid construction) COMSOL: Finite element method • Geometry divided in smaller pieces Multiphysics • Solution piece wise continuous function

Discretization of the geometry Geometry Modelling: RF/AC-DC • Sequence of the division • Meshing • Geometry use for the division • Element order: Interpolation between the nodes

Two option for meshing in COMSOL Controlled by physics 1. Physics controlled mesh: Fully automatic Common meshing element available 2. User controlled mesh

Triangle Tetrahedron Tetrahedron Hexahedron Triangular Prism Prism Default element is triangle for 2D and tetrahedron for 3 D Modeling: Mesh structure (3 D/2-D solid construction) COMSOL: Multiphysics

Modelling: RF/AC-DC • Meshing

Is this optimized mesh structure?

Focus on key part of structure COMSOL Multiphysics Desktop Impedance of a coaxial cable Electromagnetic wave model to an electrical circuit

2 1

0 COMSOL: Things to do for the next class

Multiphysics Please download the software: download.aalto.fi

Please go through COMSOL desktop COMSOL simulation Enough text and videos available online COMSOL Documentation Assignment and tutorial on Wednesday Brush up partial differential equation and Electromagnetism