Course syllabus

FMCC003 Methods for Simulating Nonlinear Microwave Circuits

This PhD course is scheduled for study period four in the spring 2025 semester and will be offered every other year thereafter. Credit points: 7.5 higher education credit points.

Aim

After completing the course, participants will grasp the fundamental principles of nonlinear phenomena and computational steady-state methods for nonlinear microwave circuits. This includes the harmonic balance technique for highly nonlinear dynamic systems and Volterra techniques for computing the dynamic response of weakly nonlinear circuits. The aim is to comprehend the key properties of various numerical methods and assess their accuracy. After finishing the course, you will thoroughly understand how a modern nonlinear microwave simulator operates.

Learning objectives

Upon completing this course unit, you will be able to:

1. Explain nonlinear phenomena in microwave circuits and systems;
2. Evaluate device models for simulating nonlinear responses;
3. Analyse nonlinear circuits under large signal operation;
4. Analyse weakly nonlinear circuits with multitone excitation;
5. Assess and explain the limitations of various numerical methods;
6. Design code to simulate the response of nonlinear circuits.

Content

Linearity, nonlinearity, nonlinear dynamic systems and examples such as the Van der Pol and Duffing oscillators, phase-portrait, chaos, frequency generation, intermodulation distortion, saturation, cross modulation, AM/PM conversion, spurious response, adjacent channel interference, quasi-static models, empirical versus physical models, large-signal scattering parameters, frequency domain versus time domain techniques, large-signal/small-signal analysis (conversion matrices), harmonic balance technique, solution algorithms (Newton, optimisation, relaxation), selecting the number of harmonics and time samples (oversampling), power series, Volterra series, nonlinear reactive devices and Manley-Rowe relations, nonlinear resistive devices and Page-Pantell inequality, and some typical examples of nonlinear microwave circuits (mixers, multipliers, oscillators).

Literature

Nonlinear Microwave and RF circuits by Stephen A. Maas, Second Edition, Artech, 2003.

Steady-State Methods for Simulating Analog and Microwave Circuits by Kenneth S. Kundert, Jacob K. White, and Alberto Sangiovanni-Vincentelli. DOI: 10.1007/978-1-4757-2081-5.

Stability analysis of nonlinear microwave circuits by Almudena Suarez and Raymond Quéré, Artech 2002.

Nonlinear Dynamics and Chaos by Steven H Strogatz, 3rd edn. Chapman and Hall/CRC, 2024.

Technical papers

Prerequisites

Knowledge in circuit theory, analogue electronics, transmission line theory, linear algebra, multivariable calculus, Fourier analysis, complex variables and functions, numerical analysis, and programming.

Examination form

Successful completion of this course is based on the following assignments:

• Assignment 1 (TD): Develop a time-domain code to simulate a tunnel diode oscillator. Determine the transient response, present a phase portrait of the dynamic system, and employ shooting methods to find a steady-state solution.
• Assignment 2 (HB): Develop a harmonic balance programme to analyse a Schottky barrier diode under a large-signal operation. Compare Newton’s method with the relaxation method. Explore resistive and reactive harmonic generation and determine optimum embedding impedances for minimum conversion loss. Finally, the large-signal/small-signal analysis will be applied to predict the conversion loss for a diode frequency converter.
• Assignment 3 (Volterra): Develop a code to calculate the intermodulation distortion of a transistor amplifier using the Volterra series. Explore the influence of dc-bias and signal power.

Project assignments are designed to be solved and reported individually, but strongly encourage cooperation and discussions. It is recommended that you use an open-source programming language, such as Julia or Python, for your coding, as these are suitable for scientific computing and visualisation.

Organisation

The course is based on four lectures and three assignments (book course / PhD level). Before each lecture, participants should read the literature and participate in discussions.