Modelling the Output Spectrum of a Direct Digital Synthesizer exploiting a Digital to Time Converter

Ekelmans, P.D.A. (2016) Modelling the Output Spectrum of a Direct Digital Synthesizer exploiting a Digital to Time Converter.

Abstract:A DDS (Direct Digital Synthesizer) is a highly configurable system that is capable of outputting square waves with a large range of different frequencies. The system described in this paper uses the MSB of the output of an accumulator as a square wave signal. This edges in this signal suffer from large delays, which are corrected by using logic and a DTC (Digital to Time Converter). The delay of the edges are increased in such a way that a clean signal is created with equal periods and the desired frequency. Unfortunately, this signal is a victim of quantization caused by the digital nature of the input of the DTC and the output of the accumulator. This causes quantization spurs in the frequency spectrum, which is undesirable. By modelling these quantization spurs, the system can be analyzed and optimized. Due to the dependence of the output on a total of four parameters (the resolution, tuning number and clock frequency of the accumulator and the resolution of the DTC) an extensive model is needed to predict the energy of these spurs. This model is created by considering the difference between the delayed edge and the desired edge as error pulses subtracted or added from the ideal output signal. These error pulse can be modelled as square waves with a certain duty cycle and time-shift, which are also based on the four parameters defined previously. The duty cycle is determined by the duration of the pulse, while the time-shift is caused by the location of the pulse in the output signal. By defining all these components separately and using the law of superposition, a complete equation has been created. This equation is capable of predicting the exact energy for the carrier signal and every existing quantisation spur in the frequency spectrum of the output signal. A simulation shows how the equation matches the output of a simulated DTC-based DDS created in Matlab. Slight inaccuracies have been observed based on the sample size of the simulated output signal. The equation will be able to help in determining the quality of an existing DTC-based DDS and could provide information about ways to improve the system.
Item Type:Essay (Bachelor)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:53 electrotechnology
Programme:Electrical Engineering BSc (56953)
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