PWM Signal Dithering for Harmonic Distortion and Phase Accuracy
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Solution Overview
Problem
Phased array systems face errors due to frequency shifts when the phase angle of elements changes, violating time-invariance requirements, leading to errors in digital signal output as the base frequency is assumed equal to the carrier frequency.
Innovation Solution
A hardware-efficient method using high-order polynomial interpolation to generate pulse-width modulated (PWM) signals that preserve amplitude and phase relative to a constant base frequency, allowing the carrier frequency to vary, by interpolating phase offsets and duty cycles to maintain continuity and accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If the phase angle of phased array elements is changed to simplify system operation, then the ease of operation is improved, but frequency shifts occur that violate time-invariance requirements and cause errors in digital signal output
Solution Approach 1:
The patent changes the parameter representation from direct phase angles to polynomial coefficients that describe phase evolution over time. By representing phase as a polynomial function of time rather than fixed values, the system can dynamically adjust phase while maintaining mathematical continuity and avoiding frequency shifts that would otherwise occur during phase transitions.
Solution Approach 2:
The patent transforms the static phase angle concept into a dynamic polynomial representation where phase evolves continuously over time according to polynomial equations. This dynamic approach allows the system to adapt phase settings while maintaining the mathematical properties needed for time-invariant signal processing, resolving the contradiction between operational flexibility and signal accuracy.
2Manufacturing precision
If high-order polynomial interpolation is used to preserve phase and frequency accuracy, then the manufacturing precision is improved, but the device complexity increases
Solution Approach 1:
The patent segments the continuous phase adjustment problem into discrete polynomial order selections (first-order, second-order, etc.). Each polynomial order represents a different level of precision that can be independently chosen based on system requirements. This segmentation allows the system to achieve high precision when needed while avoiding unnecessary computational complexity for less demanding applications.
Solution Approach 2:
The patent implements a hierarchical approach where the system can use minimal polynomial computation (first-order) for routine operations and escalate to higher-order polynomials only when maximum precision is required. This partial action strategy ensures that the full computational complexity of high-order polynomial interpolation is applied only when necessary, rather than always incurring the maximum computational burden.
Data Source
AI summary
A digital signal generation assumes that a base frequency (the frequency with which the primitive phase angles are specified relative to) is equal to the carrier frequency for all relevant times. But this causes errors in the digital signals output to each array element transducer. Thus, it is necessary for the development of a signal generation system that is capable of producing a digital signal using the free selection of amplitude and phase. This is used to produce a substantially error-free signal that preserves the amplitude and phase relative to a constant base frequency while allowing the carrier frequency to vary.