Born Approximation for Intermodulation Product Calculation
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Solution Overview
Problem
Current methods for calculating intermodulation intercept points (IP2 and IP3) in RF and analog circuits are inefficient due to the need for high accuracy at low RF power levels and the requirement for high-order device derivatives, which are often not available in device models, leading to complex simulations and large dynamic ranges.
Innovation Solution
The method employs a perturbative approach based on the Born approximation, which treats RF inputs as perturbations to the operating point, allowing for the calculation of IP2 and IP3 without requiring explicit high-order derivatives, using second and third-order solutions to estimate intermodulation products and intercept points, and reduces the dynamic range to cover only RF excitations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If multi-tone simulation is used to measure IP2/IP3, then measurement accuracy is improved, but computational efficiency deteriorates due to resolving all nonlinear orders and large dynamic range requirements
Solution Approach 1:
The patent extracts only the relevant intermodulation products (IP2/IP3) from the circuit response by selectively computing second and third order solutions, rather than resolving all nonlinear orders as in conventional multi-tone simulations. This extraction approach eliminates computational overhead from irrelevant frequencies while maintaining measurement accuracy.
Solution Approach 2:
The patent changes the simulation approach by using perturbative methods with small signal assumptions, transforming the problem from requiring large dynamic range accommodation to working with reduced dynamic range parameters. This allows efficient computation of intermodulation products without the computational burden of full multi-tone convergence.
2Measurement precision
If Volterra series is used for distortion analysis, then intermodulation products can be calculated, but device complexity increases due to requiring second and higher order derivatives
Solution Approach 1:
The patent uses readily available first-order device derivatives from standard device models, avoiding the need for expensive or unavailable second and third order derivatives. By using perturbative approaches that rely on first-order derivatives and computing higher order effects through iterative solutions, the method makes distortion analysis accessible with conventional device models.
Solution Approach 2:
The patent introduces an intermediary perturbative approach that bridges the gap between simple linear analysis and complex Volterra series. By using small signal perturbations and iterative solutions, it computes intermodulation products without directly requiring high-order derivatives, making the analysis feasible with standard device models.
3Reliability
If three-tone simulation is performed at low RF power, then intermodulation results reliability is improved, but dynamic range requirements increase to accommodate large LO signal and small RF signals
Solution Approach 1:
The patent extracts only the essential RF signal components and their nonlinear interactions, excluding the large LO signal from the dynamic range calculations. By focusing computation on the RF tones and their intermodulation products rather than the full three-tone spectrum including LO, the method reduces dynamic range requirements while maintaining result reliability.
Solution Approach 2:
The patent applies partial action by computing only the necessary second and third order solutions for intermodulation products, rather than fully converging all nonlinear orders. This partial computation approach maintains reliability for IP2/IP3 measurement while reducing the computational dynamic range burden.
Data Source
AI summary
A pertubative approach based on the Born approximation resolves weakly nonlinear circuit models without requiring explicit high-order device derivatives. Convergence properties and the relation to Volterra series are discussed. According to the disclosed methods, second and third order intermodulation products (IM2, IM3) and intercept points (IP2, IP3) can be calculated by second and third order Born approximations under weakly nonlinear conditions. A diagrammatic representation of nonlinear interactions is presented. Using this diagrammatic technique, both Volterra series and Born approximations can be constructed in a systematic way. The method is generalized to calculate other high-order nonlinear effects such as IMn (nth order intermodulation product) and IPn (nth order intermodulation intercept point). In general, the equations are developed in harmonic form and can be implemented in both time and frequency domains for analog and RF circuits.