# Distortion Analysis for the Assessment of LTI and non-LTI Transmitters

## TL;DR

This paper develops bounds on the time domain distortion of small antennas and transmitters, comparing LTI and non-LTI systems, to evaluate their fidelity and performance limits.

## Contribution

It introduces a method to assess time domain distortion for small antennas, including non-LTI transmitters, using frequency domain bounds and Q-factor analysis.

## Key findings

- Derived expressions for spherical shell antennas match narrowband approximations.
- Boundaries enable analysis of small dipole-like structures' performance.
- Non-LTI transmitters can be evaluated directly in the time domain for distortion.

## Abstract

Bounds on the frequency domain behavior of electrically small antennas are adapted to assess the time domain distortion or fidelity achievable by simple linear time-invariant (LTI) systems. Rigorous expressions for a TM$_{01}$ spherical shell are used as a direct analog to the well known Chu limit on an antenna's bandwidth-efficiency product. These expressions are shown to agree with results obtained using narrowband single resonance approximations, allowing for the analysis of arbitrary small dipole-like structures through bounds on their single frequency Q-factor and efficiency. The resulting expressions are used as a basis for assessing the performance gains of electrically small non-LTI (e.g., direct antenna modulation) transmitters for which Q-factor and impedance bandwidth are not defined but which can be analyzed directly in the time domain via distortion.