Computing DC operating points of non-linear circuits using homotopy methods:

Presentation slides and final report (PDF files).

Aim of this project is to calculate the dc operating points of different nonlinear circuits using homotopy methods.Different homotopy algorithms will be implemented using software package MATLAB and the circuits will be simulated using the SPICE software.

Investigating synthesis of resistive networks:

Presentation slides and final report (PDF files).

I want to start with two terminal elements as the building block for resistive networks. I shall try to find various matrix structures extracted from these networks. The next step is to find some rules for connecting two terminal networks in different configurations, and their effect on producing higher order networks. Using the above rules and building blocks, I shall be able to transform a given matrix to a combination of the building block matrices, and try to work back the network.

Study on the stability of nonlinear circuits:

Presentation slides and final report (PDF files).

I decided to do a survey on the stable and unstable dc operating points of nonlinear circuits.

Firstly, some basic definitions of stable operating points are introduced. Then, some theorems on how to identify stable and unstable operating points of nonlinear circuits with resistors, capacitors, inductors and transistors

are concluded. After that, some nonlinear circuits are analyzed and some simulations are conducted by using SPICE. Finally, some conclusions are given.

One small step for the undergrads, one quantum leap forward for the grads:

Presentation slides (not available) and final report (PDF files).

We propose to derive a model for the single electron transistor based on first and second order quantum effects. Using this model, we will construct and analyse compatible Spice implementation and compare that to our theoretical models analysed in MATLAB. We will compare our results with published results in the field. Time permitting, we will implement our model for the single electron transistor into a transistor amplifier and analyse the circuit.

SPICE and MATLAB simulation on nonlinear transistor circuits:

Presentation slides and final report (PDF files).

The goal of this project is to use SPICE and MATLAB as our tools to simulate and observe circuit behaviors and interesting characteristics, and to use the theorems and properties we have learned as a reference tool.

We will use SPICE to construct the circuits using existing library, simulate, and observe circuit behaviors. In particular, we are interested in the I-versus-V curve of the circuits and how the choices of external biasing affect the existence/uniqueness of solutions.

We will also use MATLAB to solve the equation for each circuit, which is written based on Ebers-Moll model, to contrast the results from SPICE. In this part, we are interested in how the values of the transistor current gains and resistors affect the structure and properties of the matrices, thereby having a direct impact on the existence/uniqueness of solutions.