R. Hu is with Asuka Microelectronics Inc., Hsinchu, Taiwan, R.O.C.

1. Phase-Adjustable Pipelining ROM-Less Direct Digital Frequency Synthesizer With a 41.66-MHz Output Frequency Chua-Chin Wang, Senior Member, IEEE, Jian-Ming Huang, Yih-Long Tseng, Wun-Ji Lin, and Ron Hu R. Hu is with Asuka Microelectronics Inc., Hsinchu, Taiwan, R.O.C. Digital Object Identifier 10.1109/TCSII.2006.882236 Rostrum：De-Ji Liu Date：04/07/2008

2. OUTLINE • Abstract • Introduction • High speed ROM-LESS DDFS • Trigonometric First-Order Quadruple Angle Approximation • Second-Order Approximation • System Design by Ten-Stage Pipelining • Comparison

3. ABSTRACT • A high-speed phase-adjustable read-only-memory less direct digital frequency synthesizer employing trigonometric quadruple angle formula. • A ten-stage pipelining architecture is employed based upon decomposition of phase operands.

4. INTRODUCTION • All of the ROM-based solutions suffer from ROM’s, low speed, large area, and high power consumption. • However, to reduce the error, a scaling table and an error correction table are needed in their design. • We propose a novel pipelining ROM-less design for DDFS that employed a trigonometric quadruple angle formula to attain a smaller error range.

5. Trigonometric First-Order Quadruple Angle Approximation The quadruple angle formula can be rearranged as follows: We redefine our first-order approximation method, which is called TA1(X) ,as follows:

6. Fig. 1 illustrates the actual cosine function and TA1(x) , whereas the difference of these two functions. TA1(x) - cos4x, is given in Fig. 2.

7. Second-Order Approximation A simple thought to further reduce the amount of error between the cosine function and the approximation equation is to employed a second-order difference method, which is given as follows:

8. Err2(x)

9. System Design by Ten-Stage Pipelining

10. Simulation results

11. Spurious Performance of the proposed DDFS

12. Comparison

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