## Appendix B: X-parameters and Volterra theory

### B.1 Introduction

This appendix describes the theoretical derivation of the properties of the X-parameter functions for a small A_{1,1} amplitude. The theory is based on the assumption that the modeled behavior can be described by the Volterra theory in the limit for the amplitude of A_{1,1} going to zero. The theory shows that the frequency-domain version of the Volterra theory can be considered as a McLaurin series polynomial approximation of the X-parameters.

### B.2 Mathematical notation and problem definition

For clarity, the mathematical notation that is used is recalled in the following:

A_{p}_{,h} the spectral component with harmonic index “h” of the incident wave at port “p”

B_{p}_{,h} the spectral component with ...