Theoretical Upperbound of the Spurious-Free Dynamic Range in Direct Digital Frequency Synthesizers Realized by Polynomial Interpolation Methods

In this paper, a universal mathematical method is proposed to determine the upperbound of the spurious-free dynamic range (SFDR) in direct digital frequency synthesizers (DDFSs) realized by piecewise polynomial interpolation methods. The Fourier series is used to establish a linear matrix relationship between the frequency spectrum of the interpolated sinusoidal signal and the coefficients of the interpolating polynomials. This matrix relationship can be considered as a linear overdetermined system of equations, which can be solved for the ideal spectrum where the fundamental harmonic has an amplitude of one and the other harmonics are zero. It is shown that the Moore-Penrose pseudoinverse and Chebyshev minimax methods find the coefficients corresponding to the largest signal-to-noise ratio and maximum SFDR designs, respectively. The proposed method is used to show that the maximum SFDR of a DDFS based on the even fourth-order polynomial interpolation is 74.35 dBc. A DDFS based on the aforementioned method is designed and its architecture is optimized to obtain an SFDR of 72.2 dBc. A VLSI implementation of the proposed DDFS is also reported.     

一种基于最佳平方逼近算法的数字频率综合器

提出一种基于最佳平方逼近算法的数字频率综合器的设计方法,同时采用非均匀分段纠正误差方式对输出正余弦波形进行优化。通过MATLAB系统仿真分析结果表明,采用这种新方法设计的数字频率综合器性能具有精度高、误差小和结构简单的优点,最差情况下的无杂散动态范围(SFDR)小于-80dBc。     

A 12-Bit Nonlinear DAC for Direct Digital Frequency Synthesis

A 12-bit nonlinear digital-to-analog converter (DAC) was fabricated in a 0.35-$mu$m SOI CMOS process. The nonlinear DAC can implement a piecewise-linear approximation to a sine function and results in significant reduction of complexity and power dissipation when used in direct digital frequency synthesizers (DDFSs). The DDFS look-up table only needs to store offset and gain values for each segment. The look-up table size can be reduced from 11K bits to 544 bits for a 12-bit DDFS with 72 dB spurious-free dynamic range (SFDR). The nonlinear DAC consists of a 12-bit binary-weighted offset DAC and a multiplying DAC. The DACs use a current steering architecture for high-speed operation and the 5 most significant bits of the offset DAC are unary encoded to reduce glitches. The multiplying DAC consists of binary-weighted current sources switched by the partial products of the inputs. Test results show that the DAC has 12-bit accuracy after digital trimming, operates up to 600 MS/s and provides differential outputs of 0.5 V into 50 $Omega$ loads. The SFDR is over 60 dBc below 20 MHz with a maximum of 72 dBc. Radiation tests show the nonlinear DAC can tolerate a total ionizing dose of 200 Krad Si.      

一种新的正交直接数字频率合成器设计方案

为了提高正交直接频率合成器输出频谱纯度和降低逻辑单元占用率,提出了一种新的分解二阶多项式近似算法。这种算法是将正(余)弦函数分解为几个相关函数,进行二阶多项式近似。与传统二阶多项式近似算法相比,该算法输出频谱纯度较高,无杂散动态范围(SFDR)可达到99.3dBc;该算法所占用的逻辑单元比二阶多项式近似算法减少20%。实验表明,在设计高频谱性能的正交直接数字频率合成器(Quadrature-DDFS)方面,该算法具有明显优势。     

Design of low-power ROM-less direct digital frequency synthesizerusing nonlinear digital-to-analog converter

A design technique that uses nonlinear digital-to-analog converter (DAC) for implementing low-power direct digital frequency synthesizer (DDFS) is proposed. The nonlinear DAC is used in place of the ROM look up table for phase-to-sine amplitude conversion and the linear DAC in a conventional DDFS. Since the proposed design technique for DDFS does not require a ROM, significant saving in power dissipation results. The design procedure for implementing the nonlinear DAC is presented. To demonstrate the proposed technique, two quadrature DDFSs, one using nonlinear resistor string DACs and the other using nonlinear current-mode DACs, were implemented. For a 3.3-V supply, the resulting power dissipation for both DDFSs are 4 and 92 mW at a clock rate of 25 MHz and 230 MHz, respectively. For both DDFSs, the spurious free dynamic ranges are over 55 dB for low synthesized frequencies     

Direct digital frequency synthesizers with polynomial hyperfolding technique

A new approach to design the phase to sine mapper of a direct digital frequency synthesizer (DDFS) is presented. The proposed technique uses an optimized polynomial expansion of sine and cosine functions to achieve either a 60-dBc spurious free dynamic range (SFDR), with a second-order polynomial, or a 80-dBc SFDR, with third-order polynomials. Polynomial computation is done by using new canonical-signed-digit (CSD) hyperfolding technique. This approach exploits all the symmetries of polynomials parallel computation and uses CSD encoding to minimize hardware complexity. CSD hyperfolding technique is also presented in the paper. The performances of new DDFS compares favorably with circuits designed using state-of-the-art Cordic algorithm technique.     

An 800-MHz low-power direct digital frequency synthesizer with an on-chip D/a converter

An 800-MHz low-power direct digital frequency synthesizer (DDFS) with an on-chip digital-to-analog (D/A) converter is presented. The DDFS consists of a phase accumulator, two phase-to-sine converters, and a D/A converter. The high-speed operation of the DDFS is enabled by applying parallelism to the phase-to-sine converter and by including a D/A converter in a single chip. The on-chip D/A converter saves delay and power consumption due to interchip interconnections. The DDFS considerably reduces power consumption by using several low-power techniques. The pipelined parallel accumulator consumes only 22% power of a conventional pipelined accumulator with the same throughput. The quad line approximation (QLA) and the quantization and error ROM (QE-ROM) minimize the ROM to generate a sine wave. The QLA saves 4 bits of the sine amplitude by approximating the sine function with four lines. The QE-ROM quantizes the ROM data by magnitude and address and then it stores the quantized values and the quantization errors separately. The ROM size for a 9-bit sine output is only 368 bits. A DDFS chip is fabricated in a 0.35-/spl mu/m CMOS process. It consumes only 174 mW at 800 MHz with 3.3 V. The chip core area is 1.47 mm/sup 2/. The spurious-free dynamic range (SFDR) is 55 dBc.     

A 100-MHz 8-mW ROM-less quadrature direct digital frequency synthesizer

A low-power quadrature direct digital frequency synthesizer (DDFS) is presented. Piecewise linear approximation is used to avoid using a ROM look-up table to store the sine values as in a conventional DDFS. Significant saving in power consumption, due to the elimination of the ROM, renders the design more suitable for portable wireless communication applications. To demonstrate the proposed technique, a quadrature DDFS has been implemented using 0.5-/spl mu/m CMOS process and occupies an active area of 1.4 mm/sup 2/. It consumes 8 mW at 100 MHz and operates from a single 2.7-V supply. The spurious-free dynamic range is better than 59 dBc at low synthesized frequencies and the frequency resolution is 1.5 kHz.     

Circuit modelling of 2-AG indirect pathway via astrocyte as a catalyst for synaptic self repair

A 32-bit read-only memory (ROM)-based direct digital frequency synthesizer with a maximum operating frequency of 2 GHz is presented. The proposed ROM-based design is capable of increasing the operation speed of traditional ROM-based DDFS by eliminating the complex control circuits and adopting a novel pseudo differential ROM. With a 14-bit partially segmented DAC based on Q² Random Walk switching scheme, the prototype DDFS produces a minimum spurious-free dynamic range of 46.38 dBc up to Nyquist frequency at the clock frequency of 2 GHz. This 0.13 μm CMOS chip occupies an active area of 0.55 mm² and dissipates 450 mW with a 1.2-V digital supply and 3.3-V analog supply.     

Efficient, ROM-less DDFS using non-linear interpolation and non-linear DAC

A non-linear interpolation based ROM-less Direct Digital Frequency Synthesisiser (DDFS) is more efficient than previous systems as each current cell in a non-linear DAC is used more effectively. This was achieved by forming an analogue voltage from a small linear DAC addressed by phase bits that are usually discarded. The analogue voltage was connected to a selected current source in a thermometer decoded non-linear DAC to allow non-linear interpolation between the conventional, phase limited output levels. By increasing the number of phase bits the spurious free dynamic range (SFDR) was improved without increasing the size of the non-linear DAC. Modelling and simulation of the non-linear response of the differential switch based current cell revealed suitable parameters. The architecture of 64 current cells used a modified thermometer decoder and three-state switch in each current cell. Simulation and testing of 10 sample circuits demonstrated a robust DDFS with SFDR better than −60 dBc and suitable for use in a wide range of instrumentation systems.     

一种高性能低功耗直接数字频率合成器的设计

文章基于分段线性近似算法提出分段泰勒二阶近似算法，从频谱纯度分析了该算法的优越性，讨论了系数位数和分段数的选取，最后结合硬件优化的系统结构，设计实现了SFDR达102．3dB的数字频率合成器。综合结果表明，该算法实现的系统面积上要比分段线性近似算法的系统小20％，功耗上也小39．5％。与现有的其他数字频率合成器比较表明，在设计高频谱性能DDFS方面，其在功耗和面积上都具有较大优势。     

A direct digital frequency synthesizer with fourth-order phase domain /spl Delta//spl Sigma/ noise shaper and 12-bit current-steering DAC

This paper presents a direct digital frequency synthesizer (DDFS) with a 16-bit accumulator, a fourth-order phase domain single-stage /spl Delta//spl Sigma/ interpolator, and a 300-MS/s 12-bit current-steering DAC based on the Q/sup 2/ Random Walk switching scheme. The /spl Delta//spl Sigma/ interpolator is used to reduce the phase truncation error and the ROM size. The implemented fourth-order single-stage /spl Delta//spl Sigma/ noise shaper reduces the effective phase bits by four and reduces the ROM size by 16 times. The DDFS prototype is fabricated in a 0.35-/spl mu/m CMOS technology with active area of 1.11mm/sup 2/ including a 12-bit DAC. The measured DDFS spurious-free dynamic range (SFDR) is greater than 78 dB using a reduced ROM with 8-bit phase, 12-bit amplitude resolution and a size of 0.09 mm/sup 2/. The total power consumption of the DDFS is 200mW with a 3.3-V power supply.     

基于线性插值的DDFS中的相位-幅度映射研究

提出了采用线性插值的方法来实现直接数字频率合成器（DDFS）结构中相位到正弦曲线幅度之间的映射（简称“相幅映射”）。该方法使用具有分段连续性质的线性分段来近似正弦函数曲线的第一象限部分；然后根据正弦曲线的象限对称性，重构完整的正弦曲线。文中分析了基于线性插值技术的DDS的频谱特性；然后对基于该方法的DDS的“无杂散动态范围”进行了研究。最后，提出了线性插值系数选择的详细、系统的步骤，从而取得期望的SFDR。     

Exact analysis of spurious signals in Direct Digital Frequency Synthesizers due to amplitude quantization

Amplitude quantization is one of the main sources of spurious noise frequencies in Direct Digital Frequency Synthesizers (DDFSs), which affect their application to many wireless telecommu- nication systems. In this paper, two different kinds of spurious signals due to amplitude quantization in DDFSs are exactly formulated in the time domain and detailedly compared in the frequency do- main, and the effects of the DDFS parameter variations on the spurious performance are thoroughly studied. Then the spectral...     

Novel FPGA implementations of Walsh-Hadamard transforms for signalprocessing

The paper describes two approaches suitable for a field-programmable gate-array (FPGA) implementation of fast Walsh-Hadamard transforms. These transforms are important in many signal-processing applications including speech compression, filtering and coding. Two novel architectures for the fast Hadamard transforms using both a systolic architecture and distributed arithmetic techniques are presented. The first approach uses the Baugh-Wooley multiplication algorithm for a systolic architecture implementation. The second approach is based on both a distributed arithmetic ROM and accumulator structure, and a sparse matrix-factorisation technique. Implementations of the algorithms on a Xilinx FPGA board are described. The distributed arithmetic approach exhibits better performances when compared with the systolic architecture approach     

基于六线逼近法的DDFS算法的实现

为了提高直接数字频率合成技术的资源利用率,结合三角函数的对称性和线性幅值逼近算法对正弦信号分段算法进行研究,提出基于六线线性逼近优化算法,使用6段不大于正弦值的均与分段的线段逼近之后,使用QE-ROM (量化-误差存储)存储线段与正弦值差值的办法,在不影响频率特征和最大误差特性基础上,实现了算法的简化,并压缩了误差补偿存储器所需存储空间。实验结果表明对于9 bit正弦输出只需使用336 bit存储器和4个加法器3个选择器一个比较器即可实现整个系统,并且最大的工作频率达到了210 MHz,共消耗110个LE,49个存储器。压缩比远远高于传统的压缩算法。     

Direct Digital Synthesizer With Sine-Weighted DAC at 32-GHz Clock Frequency in InP DHBT Technology

A direct digital synthesizer (DDS) implemented in InP double heterojunction bipolar transistor (DHBT) technology is reported. This DDS uses a sine-weighted digital to analog converter (DAC) architecture that eliminates the need for a ROM. This enables operation at high frequencies with lower power consumption compared to traditional approaches. The phase accumulator is 8-bits wide and the sine-weighted DAC uses the five most significant bits (MSBs) for phase to amplitude conversion. The DDS operates up to a 32-GHz clock frequency for all frequency control words (FCWs) and can synthesize sine-wave outputs from 125 MHz to 16GHz in 125-MHz steps. The spurious free dynamic range (SFDR) is measured over the Nyquist bandwidth to be 31.00 dBc for the fundamental output frequency of 125 MHz. Over the full range of FCWs, the worst case SFDR is 21.56 dBc at an FCW of 95, and the average SFDR is 26.95 dBc. The circuit is implemented with 1891 transistors and consumes 9.45 W of power.