# CIRCUIT THEORY

ING-IND/31 - 9 CFU - 2° Semester

GIACOMO CAPIZZI

## Learning Objectives

Knowledge of the main methods of synthesis for passive and active lumped networks and of the main approximation's methods for lumped filters. Knowledge of the Basics of High performance computing (HPC) and Trasmission line analysis.

## Course Structure

The course includes both lectures and numerical exercitations aimed to clarify and consolidating the theoretical contents presented in the lectures.

## Detailed Course Content

Frequency response of one port passive lumped networks: Resonant circuits: series resonance, parallel resonance; determination of the resonant frequency of a network; one port series LC circuits: frequency response, resonance; one port parallel LC circuits: frequency response, resonance; one port series RLC circuits: frequency response, cutoff frequencies, bandwidth, conditions for resonance occurrence, Q factor (quality factor), normalized frequency response; one port parallel RLC circuits.

Network functions: Types of Network functions: driving-point functions and transfer network functions, examples of network functions; general properties of network functions; poles and zeros and frequency response; impulse response and network functions; symmetry property of network function; relationship between a network function and its frequency response.

Synthesis of passive lumped networks: General properties of immittances functions of LLFPB one port networks; positive real functions; necessary and sufficient conditions for positive real functions; elementary synthesis procedures; properties and synthesis of LC immittances: Foster’s canonic forms and Cauer’s canonic forms; properties and Synthesis of RC immittances; the Foster preamble; properties and Synthesis of RLC immittances: Brune synthesis, Bott and Duffin synthesis; fundamental properties of passive two ports networks: the impedences, admittance and transmission matrices; Synthesis of lossless two-ports networks; examples of RC network Synthesis.

Sensitivity: Definition of sensitivity; Function sensitivity; multiparameter sensitivity; sensitivity of lossless ladder filters; coefficient sensitivities ; roots sensitivity; sensitivity for parasitic elements; adjoint method for sensitivity computation.

Approximation methods for lumped filters: Amplitude approximation: format of specificatons; group delay; approximation by real rational function: Butterworth approximation, Chebychev approximation, inverse Chebychev approximation; frequency transformation: low-pass to high-pass, low-pass to band-pass, low-pass to band-elimination; phase approximation; Bessel-Thompson approximation; all-pass filter.

Trasmission line analysis: Lossless transmission line: theoretical foundation, equivalent circuit representation, wave equations and their solutions, transmission line equations in the frequency domain; examples of transmission lines: coaxial line, two-wire lines, shielded two-wire line, stripline, microstrip; electric circuit with transmission line: definition of local impedance, reflection coefficients, line voltage, current and impedance diagrams; the Smith chart; analysis of simple circuits; energy dissipation in transmission lines: conductor losses, dielectric losses, loss parameters of some transmission lines; lossy transmission lines whit small losses: approximate expressions of the complex propagation constant and characteristic impedence; solution of lossy transmission line equations lines whit small losses; matching circuits; types of impedance matching: L cells with lumped reactive elements, single stub matching network, double stub matching network, 4 matching networks.

The Scattering matrix: The Scattering matrix: scattering parameters definition; Properties of the scattering matrix [S] of a device; Relationship between [S], [Z] and [Y]; Change of reference impedances; Change of reference planes; connection of structures.

Basics of High performance computing (HPC): High performance computing (HPC): computing architectures, high performance hardware, Moore's law, multiple processing, threading, memory stacks, SISD, SIMD, MISD, MIMD, MPI, OpenMP, grid, shared memory, computational paradigms; general pourpose computing on GPU (GPGPU): graphic cards and GPUs, NAND, ADD, adder, GPU devices, GPU schematics, CUDA - STREAM; Compute Unified Device Architecture (CUDA): host and device, memory, data passage, threading, GPU threading, parallel computing, barriers, deadlocks, cuda instructions, functions, kernels, memory copy, array, indexing, allocations; Cuda by example: Cuda toolkit, debugger, profilers, compilers, process flow, vector addition, threads and blocks, CUFFT, multi-GPU programming, running examples.

Basics of Pspice: Start the project; construct the circuit: use “Pspice” devices, picking and placing components; use appropriate signal sources for: transient analysis (time domain response), AC analysis (frequency response), DC analysis; selecting and placing markers; “simulate” the performance of the circuit: transient analysis (time domain response), AC analysis (frequency response), DC analysis, run the simulation, edit the “simulation profile”, save the project, recall and restart.

## Textbook Information

1. S. P. Ghosh, A.K. Chakraborty, “Network Analysis and Synthesis”, Tata McGraw Hill.

2. G. Hager and G. Wellein, “Introduction to High Perfomance Computing for Scientist and Engineering”, CRC Press.

3. Rob Faber, “CUDA Application Design and Development”, Morgan Kaufmann.

4. Steve Winder, “Analog and Digital Filter Design”, Newnes Elsevier Science.

5. Omar Wing, “Classical Circuit Theory”, Springer.

Open in PDF format Versione in italiano