1. Introduction

Consider a simulation set-up of an electronic circuit and a given multisine excitation signal. The aim is to obtain the spectrum of the steady-state response of the circuit to the multisine excitation with commercial simulation tools.

The circuit under test assumed to be Period-In Same Period-Out (PISPO), which implies that it is a stable circuit that doesn’t generate sub-harmonics or quasi-periodic solutions. The PISPO circuits only generate harmonics and intermodulation tones of its input signal.

Most electronic circuits will generate a large number (theoretically an infinite amount) of harmonics and intermodulation products due to feedback around the non-linear circuits or due to the non-polynomial non-linearities in the devices [4]. Infinity is not really a useful number to work with, so we define the non-linear order of the circuit $\aleph$ as the order of non-linearity needed to explain all harmonics and intermodulation products that lie significantly above the numeric noise floor.

The definition of the non-linear order of the circuit is unconventional, as it depends on properties that are not related to the circuit itself such as the amplitude level of the input signal, the numerical precision of the simulator and the simulation options. It is therefore rarely the case that $\aleph$ is known a-priori and several simulations have to be run to properly determine $\aleph$. This leads to a chicken-or-egg problem where a correct simulation is needed to properly determine $\aleph$, but $\aleph$ is needed to set-up a proper simulation. After a few iterations and with some common sense, it is usually possible to obtain a reasonable guess for the order $\aleph$.