Pade Approximation Convert Circuit for DDS Sinusoidal Wave Generation

Resolve Bottlenecks,
Find Innovative SolutionsGenerate Solutions

Solution Overview

Problem

Existing direct digital frequency synthesizers using Taylor polynomial and CORDIC algorithms for sinusoidal wave generation are time-consuming and require large circuit areas, especially for calculating a quarter period of a sine wave, leading to high calculation time and circuit costs.

Innovation Solution

The implementation of a Pade approximation convert circuit using a multiplier, divider, and adder, along with multiplexers, to efficiently generate a quarter period of a sinusoidal wave signal through the Pade approximation algorithm, reducing the need for extensive multiplication and iterative calculations.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If Taylor polynomial or CORDIC algorithm is used for sinusoidal wave generation, then the sinusoidal wave can be generated with continuous linear variation of phase, but the calculation time increases and circuit area becomes large

Engineering Contradiction:

Improvesinusoidal wave generation accuracyVSAvoidcalculation time

Core Design Contradiction:

ReliabilityVSLoss of time

Solution Approach 1:

The patent changes the mathematical approach from Taylor polynomial expansion or CORDIC iterative calculation to Pade approximation using continued fractions. This parameter change in the calculation methodology reduces the number of operations required while maintaining sinusoidal wave generation accuracy, thereby decreasing calculation time without sacrificing reliability

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent replaces complex iterative mechanical-like calculation processes (CORDIC algorithm with multiple rotation iterations) with a direct mathematical approximation method (Pade approximation). This substitution eliminates the need for repeated iterative operations, significantly reducing calculation time while preserving the ability to generate accurate sinusoidal waves

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

2Measurement precision

If Taylor polynomial or CORDIC algorithm is used for sinusoidal wave generation, then the sinusoidal wave can be generated with high resolution, but the circuit area required increases

Engineering Contradiction:

Improvefrequency resolutionVSAvoidcircuit area

Core Design Contradiction:

Measurement precisionVSArea of stationary object

Solution Approach 1:

The patent changes the computational methodology to Pade approximation, which requires fewer computational resources. This parameter change in the mathematical approach allows high-resolution frequency synthesis to be achieved with a smaller circuit implementation, as the Pade approximation method is more resource-efficient than Taylor polynomial expansion or CORDIC algorithm

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent extracts and eliminates redundant calculation steps from the traditional methods. By using Pade approximation with continued fractions, the circuit only needs to perform essential operations without the excessive multiplication and iterative calculations required by Taylor or CORDIC methods, thereby reducing circuit area while maintaining frequency resolution

Inventive Principle:

Principle #2Taking out (Extraction)

3Productivity

If CORDIC algorithm with high rotation frequency is used, then the sinusoidal wave calculation can be performed, but the calculation time increases due to too high rotation frequency

Engineering Contradiction:

Improvecalculation speedVSAvoidtotal calculation time

Core Design Contradiction:

ProductivityVSLoss of time

Solution Approach 1:

The patent replaces the iterative rotational calculation mechanism of CORDIC algorithm with a direct Pade approximation method. This substitution eliminates the need for high-frequency rotation iterations, allowing the circuit to achieve fast calculation speeds without incurring the time penalty of excessive iterative operations

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent skips the intermediate iterative steps of CORDIC rotation calculations by directly applying Pade approximation. This allows the system to rush through the calculation process in fewer steps, achieving high productivity without the time loss associated with high-frequency iterative rotations

Inventive Principle:

Principle #21Skipping (Rushing through)

Data Source

PatentUS8060547B2Pade approximation convert circuit of direct digital frequency synthesizer

Publication Date: 2011.11.15 NAT CHUNG SHAN INST SCI & TECH

AI summary

This invention relates to Pade approximation convert circuit of the direct digital frequency synthesizer in which a multiplier receives and multiplies a first input signal and a variable signal so as to produce a multiplication signal; a divider receives and divides a second input signal and a variable signal so as to produce a division signal; an adder receives and adds the multiplication signal and the division signal so as to generate an output signal, that is then returned back to the divider. A quarter period of a sinusoidal wave signal is completed by the proceeding of direct calculation two times such that the time for the calculation of a complete sinusoidal wave can be saved and the area of the calculation circuit can be reduced.