Theoretical analysis of frequency variation tolerance between elements of RTD-THz oscillator arrays for mutual locking

TL;DR

This paper provides a theoretical analysis of how frequency variation tolerance affects mutual locking in RTD-THz oscillator arrays, revealing how array configuration influences the maximum allowable frequency variation for coherent operation.

Contribution

It derives an approximate expression for frequency variation tolerance in arbitrary array configurations and analyzes how this tolerance depends on the number of elements in 1D and 2D arrays.

Findings

Tolerance decreases with more elements in 1D arrays.

Tolerance varies with array shape in 2D arrays, peaking at square configurations.

2D arrays have smaller element-number dependence than 1D arrays.

Abstract

Array configuration is one of the effective ways to increase the output power of terahertz oscillators using resonant tunneling diodes. Mutual locking between the array elements results in coherent single-spectrum oscillation and a narrow radiation beam. However, frequency variation between elements disturbs the mutual locking. In this paper, the frequency variation that can be tolerated for mutual locking is approximately derived for an array with arbitrary coupling configuration. Using this result, the element-number dependence of the frequency variation tolerance for 1D and 2D arrays is calculated. In 1D arrays, the frequency variation tolerance decreases inversely proportional to the square root of the element number. In 2D arrays, as the number of columns is increased while keeping the number of elements per column constant, the frequency variation tolerance increases for small number of columns, reaches a maximum at square configuration, and then decreases with increasing number of columns. The element-number dependence in 2D arrays is smaller than that in 1D arrays.