DESIGN OF SECOND ORDER SIGMA-DELTA MODULATOR FOR AUDIO APPLICATIONS 1 DHANABAL R, 2 BHARATHI V, 3 NAAMATHEERTHAM R SAMHITHA, 4 G.SRI CHANDRAKIRAN, 5 SAI PRAMOD KOLLI 1 Aitant Profeor (Senior Grade), VLSI diviion, SENSE, VIT Univerity, 2 Aitant Profeor, GGR College of Engineering, Anna Univerity, Vellore, 3 MTECH Student, SENSE, ECE Department, VLSI Diviion, VIT Univerity, Vellore, 4 BTECH Student, SENSE, ECE Department, VIT Univerity, Vellore, 5 BTECH Student, SCSE, CSE Department, VIT Univerity, Vellore- 632014, TN, INDIA E-mail: 1 rdhanabal@vit.ac.in, 2 bharathiveerappan@yahoo.co.in, 3 amhitha.nr@gmail.com, 4 chandar_ck@yahoo.com, 5 kolliaipramod@gmail.com ABSTRACT The paper include the deign of econd order igma-delta modulator. A comparative tudy between a firt order and econd order igma-delta modulator i carried out. The econd order i preferred over the firt order igma-delta modulator due to it better ignal-to-noie ratio (SNR). The comparative tudy between the modulator i done in Matlab, the econd-order igma-delta modulator i deigned and modelled in Verilog-A and imulated in Cadence SpectreS. The econd order igma-delta modulator provide an enhancement of 27% in SNR a compared to the firt order igma-delta modulator. Keyword: Sigma Delta, SNR, Overampling, Noie Shaping 1. INTRODUCTION The preciion of ignal between the analog and digital interface limit the performance of communication ytem a well a Digital Signal Proceing. Digital modulation i ued to tranfer digital bit tream correponding to the analog ignal input. Sigma-delta Modulation (SDM) i a digital modulation technique which can be ued a an analog-to-digital converter. In other word, SDM can act a interface between analog and digital ignal. The analog-to-digital and digital-to-analog converter form the baic element of mixed ignal IC deign. Generally, the converter operate at Nyquit frequency. But operating in Nyquit frequency limit the peed a well a make the deign of anti aliaing filter complex and critical. On the other hand, SDM ue the technique of overampling, noie haping and filtering that reduce the noie and make the deign imple. SDM convert analog ignal into pule frequency where the number of pule in an interval can be counted [1] [2]. It i the one of the technique for converting analog ignal into digital. By thi, an accurate digital repreentation of the analog ignal can be obtained during that particular interval. Thi i one of the reaon why SDM i preferred. In igma delta modulator, a combination of overampling & noie haping (quantization error haping) are employed. Thee modulator are deigned by imple analog circuit uch a a comparator, one or more integrator, and umming circuit [1]. Thi paper include an analytical tudy between a firt order and econd order igma-delta modulator. The analyi how that the econd order igmadelta modulator provide a better SNR value. The econd order igma-delta modulator i then deigned for a given input modulating ignal, f m f at a ampling rate of. 702
Fig. 1. Noie Shaping ampling rate) [2]. If practically the noie i greater than the RMS quantization noie value then the reolution will be le than the required number of bit. In order to avoid thi ituation, a Kf higher ampling frequency i being choen. The RMS quantization noie of 12 will be preent but it i being ditributed over a wider Kf bandwidth, which i greater than the Nyquit band. A a conequence of thi, the reolution increae. In order to ditribute the noie occurred due to quantization over a wide band and to provide an increae in the reolution of bit, overampling i being employed with an overampling ratio (OSR), K i given by equation (1). The entire paper i divided into ix ection. In ection I introduction to SDM i given. In ection II propertie of SDM are dicued. Section III and IV provide the analyi and modelling of SDM. V and VI ection explain about reult and concluion that are obtained repectively. 2. SIGMA DELTA MODULATION Sigma-delta modulation (SDM) i a technique ued for encoding analog ignal into digital ignal or low-reolution digital ignal into high-reolution digital ignal. The SDM operation i baed on two main ignal proceing technique called overampling & noie haping [1] [2]. Overampling include the ampling of the input modulating ignal, f m at a rate greater than the Nyquit rate. Noie haping i imply quantization error filtering. When we ample and quantize an analog ignal, it give rie to ome quantization noie. Quantization noie i due to the rounding-off of the value during quantization. A. Overampling A perfect ampling (i.e. ampling at Nyquit rate) ha an RMS quantization noie of 12 which i uniformly ditributed within the Nyquit f band2 (where LSB i value and f i Fig. 2. Firt Order Sigma-Delta f OSR = K = 2 f m (1) Hence, it can be concluded that overampling provide an enhancement in the reolution and due to the reduction in the quantization noie, there i an improvement in SNR [2, 3]. The improvement in SNR can be calculated by uing equation (2). SNR = 6.02N + 10logOSR + 1.76 (2) B. Noie Shaping The SNR of the overampled ignal can be further increaed uing a noie haping circuit [2]. The noie haping circuit hift the noie power to the top band of the overampled ignal a hown in Fig. 1. The firt order noie haping circuit provide an additional enhancement in 703
SNR given by equation (3). Further, it can be een that the circuit alo provide an improvement in the reolution. SNR = 6.02N + 30logOSR 3.4 (3) II. Analyi Of Firt And Second Order Sigma- Delta A. Firt order igma-delta modulator The modulator in Fig. 2 illutrate a firt order igma-delta modulator. It comprie of an integrator, a 1-bit quantizer, and a 1-bit DAC. The integrator ramp the input ignal up and down. The integrator act a the noie haping circuit which hift the noie from pa band to top band. The output of the integrator i given to the comparator and then the comparator output i fed back through a 1-bit DAC to the umming circuit. B. Second order igma-delta modulator Second order igma-delta modulator a hown in Fig. 3 include the ame component a firt order but will include an additional ummer and an integrator. The uage of more than one ummer and integrator tage in the igma-delta modulator enable to achieve higher order of quantization noie haping. A order i increaed, the noie haping will be better which reult in high SNR, but due to the intability by increaing the order, high order of modulator i not preferred. While uing the econd order noie haping circuit we will achieve better reolution for a given over ampling ratio than the firt order igma delta modulator. The analytical tudy between the firt and econd order igma-delta modulator have been carried out. The igma-delta modulator are etup in Matlab igma-delta toolbox and then the power pectral denity (PSD) and the SNR are obtained for the modulator. 3. MODELLING OF SECOND ORDER SIGMA-DELTA MODULATOR The econd order igma-delta modulator i deigned in Verilog-A [6] and the output i being imulated in Spectre-S imulator. Uing Verilog-A, the compact model of econd order and firt order igma-delta model are created. The compact model are ued to decribe and analyze the performance of the device. Verilog-A i a high level language which i ued to decribe the analog behavior of electrical, mechanical ytem. The modulated output i then demodulated uing Low Pa Filter (LPF) a LPF i the only component ued for demodulating igma modulated output [5]. The output i analyzed and found that the original ignal can be recontructed from the modulated output. 4. RESULTS AND DISCUSSION The normal quantizer, delta modulator and firt order igma-delta modulator i analyzed in Matlab and Matlab Simulink [4] [7]. By analyzing the Power Spectral Denity (PSD), the noie harmonic of the igma-delta modulator i found to be very le compared to normal quantizer and delta modulator. Then uing the igma-delta toolbox in Matlab, the SNR and PSD of the firt order and econd order igma-delta modulator are analyzed. The Matlab imulation reult of SNR and PSD of firt and econd order igma-delta modulator are hown in Fig. 4 and Fig. 5, repectively. It i found that the SNR of firt order i 55.1dB and that of econd order i 75.7dB for an overampling ratio, OSR = 64. Hence, it provide an SNR improvement of 27% for econd order igma-delta modulator when compared to the firt order igma-delta modulator. Fig. 3. Second Order Sigma-Delta 704
and econd order igma delta modulator are hown repectively in Fig. 6 and Fig. 7. Fig. 4. PSD And SNR Of Firt Order Delta Sigma Fig. 6. Simulation Reult Of Firt Order Sigma Delta Fig. 5. PSD And SNR Of Second Order Delta Sigma Fig. 10 how the demodulated output with variou value of OSR. It mut be noted that the demodulation become effective a the OSR value i being increaed. The amount of noie power in the demodulated output i being reduced. The compact model of firt and econd order igma delta i imulated in Spectre-S imulator in Cadence. The imulation reult which include the input, clock, modulated output and demodulated output of the firt order Fig. 8. PSD Of The Firt Order Sigma Delta 705
REFRENCES: Fig. 9. PSD Of The Second Order Sigma Delta The PSD of both the modulator hown in Fig. 8 and Fig. 9 are analyzed and compared. It i been oberved that there are more harmonic in the firt order than econd order, i.e. when econd order i ued, the over-all noie reduction i better than firt order. [1] Joe M. de la Roa., Sigma-Delta : Tutorial Overview, Deign Guide, and State-of-the-Art Survey, IEEE Tranaction on circuit and ytem I: regular paper, vol. 58, No. 1, Jan. 2011. [2] Sangil Park., Principle of Sigma-Delta Modulation for Analog-to-Digital Converter, APR8/D Rev 1. Motorola. [3] Johua D. Rei., Undertanding Sigma Delta Modulation: The Solved and Unolved Iue. J. Audio Eng. Soc., Vol. 56, No. 1/2, January/February 2008. [4] Thuneibat, S. A., & Ababneh, M. S., Sigma- Delta Simulation and Analyi uing MatLab. Computer and Information Science, Vol. 5, No. 5. 2012. [5] Simon Haykin., Communication Sytem, Newyork: Jon Wiley & on,inc. [6] Verilog A reference Manual, Agilent Technologie, 2005. [7] Jaykar. S, Palodkar. P, Dakhole, P., "Modeling of Sigma-Delta Non-Idealitie in MATLAB/SIMULINK," International conference on Communication Sytem and Network Technologie (CSNT), pp.525-530, June 2011. Fig. 10. Demodulated Output For Different OSR Value 5. CONCLUSION A the order of the igma delta increae the SNR alo increae. But due to the limitation on tability higher order are not preferred. In thi paper the firt and econd order of igma delta modulator are deigned in Verilog-A and imulated in Cadence Spectre-S. While analyzing the PSD, the effect of noie i found to have le effect on econd order compared to firt order igma delta modulator. Thu econd order igma delta modulator i efficient. 706