• Bernard Cooper

Student thesis: Master of Science by Research


This thesis will detail the application simulation of techniques to model superconductivity for microwave waveguide and planar transmission lines. The overarching aim is to streamline the design of a parametric amplifier based on the kinetic inductance of a superconducting transmission line. Such an amplifier has the potential to produce high gain, low noise and operate over a large bandwidth making it ideal for a radio astronomy receiver set up. To optimize the design process the interaction between the pump and input signal must be simulated to characterise the gain. Furthermore, to improve the overall performance of such an amplifier it is necessary to accurately simulate superconductivity in a commercial electromagnetic simulator software. The former was performed by numerical simulations developed in Python. Analytical expressions of coupled mode equations were used to simulate the potential gain over an octave of bandwidth. A finite time domain difference(FDTD) approach was then successfully implemented for linear transmission lines. The details of how to implement the same procedure for the non-linear transmission line is also included. The later was achieved by applying Mattis-Bardeen theory of superconductivity to produce a frequency and temperature dependent surface impedance that can 9 then be utilised in EM software packages to simulate superconductivity. The simulations were compared against vector network analyser (V.N.A) measurements took for a bulk niobium single port cylindrical cavity resonator. This analysis was extended to produce an analytical expression for surface resistance at critical coupling for both TE and TM modes. The work concludes with a Ku-band meandered co-planar waveguide resonator design. A power dependence was applied to the superconducting surface impedance to simulate the onset of dissipation in this design.
Date of Award1 Aug 2020
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorMichael Garrett (Supervisor) & Lucio Piccirillo (Supervisor)


  • Critical Coupling
  • Kinetic Inductance
  • Surface Impedance
  • Parametric Amplifier
  • Cavity Resonator
  • Microwave
  • Resonator
  • Superconductors

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