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Modeling techniques currently utilized in design of Σ∆- Modulator are based on MATLAB Yi-Lung Shih1, Jia-Yarn Wong2 Abstract Sigma-Delta (Σ∆) Analogue-to-Digital Converters (ADC) have been hugely successful in realizing high-resolution consumer audio products, such as MP3 players and cellular mobile phones, for some time now. Matlab7 offers a technical computing environment for high-performance numeric computation. It integrates numerical analysis, matrix computation and graphics in an easy-to-use environment without the u s e of tedious language syntax. The M a l t a environment is ideal for the behavioral simulation of Σ∆ converters because signals can be treated as vectors (matrices with only one row or column) and the modulator operation itself can be described simply as a set of difference equations. The output bit stream(s) from the modulators can be easily transformed into the frequency domain by making use of M a t lab’s excellent signal processing functions, such as the various windowing functions and the Fast Fourier Transform (FFT). Furthermore the results can be displayed graphically and the noise and signal components can be quickly summed up separately to compute the SQNR. An example of the difference equation modeling of a 3rd order feed- forward modulator (using a 4-level quintile and over sampling rate of 76.8) is shown in Figure2 along with the output spectrum and the computed SQNR. 1. INTRODUCTION There is a great deal of interest in extending the bandwidth of sigma -delta-modulators for wideband applications. There are many ways to increase the bandwidth of a sigma-delta converter. Each method involves an alteration of one or more of the parameters available to the designer, that is the sampling frequency, the number of bits in the quantizer, the oversampling ratio and the modulator loop order. An alternative to increase the effective sampling frequency is to lower the OSR. There are several ways to do so. One solution is to improve the noise -shaping characteristic by employing higher-order modulators, [1]. Another alternative and perhaps the most practical approach, is to replace the single-bit quantizer by a multi-bit quantizer, [2]. This allows the OSR to be reduced without trading resolution to

maintain stability. One approach to escape the DAC nonlinearity effects is to cascade a single-bit and a multi-bit modulator [1]. 2. SYSTEM-LEVEL SIMULATION BY SIMULINK Fig. 1 shows the block diagram of a traditional third order 5-bit- modulator. Fig. 2 shows the block diagram of the third order 5-bit-modulator that is proposed in this work .The noise-shaping filter is a third-order topology with a cascade of integrators in a single loop and a feedforward signal path. This topology differs from the previous third-order-modulators. The feedforward signal path concept [3] has been extended to third-order noise shaping to realize a reduced sensitivity to opamps nonlinearities and to relax the stability requirements. In the traditional third-order- modulators the output is given by: Figure 1. Block diagram of the traditional 3rd order 5-bit- modulator Figure 2. Block diagram of the 3rd order 5-bit - modulator with feedforward path

The signal transfer function is STF(z) = z-3 and the noise transfer function is NTF(z)=(1-z-1)3. In this case the harmonics of the input signal created due to the nonlinear opamps will appear at the modulator output shaped by third-order high-pass transfer function. In wideband applications, the attenuation provided by a order high-pass transfer function at a low oversampling ratio is not enough. One 3 solution is to design low distortion opamps. rd In the-modulator with feedforward path the nonlinearity problem is achieved by making the signal transfer function, STF(z) exactly equal to 1. The proposed topology combines the advantage of sigma-delta modulator with feedforward path and the multibit quantizer to achieve high dynamic range and wideband A/D conversion.This topology uses only one DAC in the feedback path. This advantage is very important for multibit quantizer because of this reduces the complexity of circuit and the chip area. Another advantage of this topology is that the integrators process quantization noise only and than their performance requirements are relaxed. By applying linear analysis, the output of the third orde-modulator with feedforward path is given by where the signal transfer function must be STF(z)=1, without changing the third-order noise transfer function, NTF(z). The noise transfer function for the topology presented in Fig. 1 is: where for b1=1, D(z) is The design of 3rd order multibit-modulator with feedforward path was done using the CLANS methodology[1], and several MATLAB simulations [4]. The coefficients were chosen for generating the peak SNDR of the modulator and to guarantee that the baseband quantization noise is independent of the input signal. By using the Sigma-Delta ADC Toolbox of MATLAB in Figure 3 ,the final values for th e coefficients are a1 =1, a2=0.7499, a3=1, a4=1, b2=1.6374, b3=2.6062.

NTF STF

Coefficients Figure 3. Sigma-Delta ADC Toolbox of MATLAB 3. Simulation and Measure Result: To further aid the designer, an empirical study of high order Σ∆-modulators has been conducted and has resulted in a CAD toolbox (based in Matlab and freely available) that allows Σ∆-modulator design and performance simulations to be carried out with ease. In particular, the toolbox is comprised of various functions (written in Matlab) that allow the user to synthesize different discrete noise transfer functions and map these NTF onto different topologies so that the modulator coefficients can be determined. A further function is also available to optimize the NTF for a low-pass multi- bit Σ ∆ -modulator based on the “Closed-loop An al ys is of Noise-Shaper” toolbox from (CLANS) method from. This function uses Matlab.Figure3 show the toolbox of ADC.Figure4 show the Third order Σ∆-modulator CIFB Structure, and Figure5 and Figure6 show the results of waveform of simulation and measure . Figure7 and Figure8 show the results of Frequency response of simulation and measure. the optimization Figure 4. Third order Σ∆-modulator CIFB Structure

Figure 5. MATLAB simulation waveform Figure 6. measure waveform Figure 7. Frequency response by using Matlab Figure 8. Frequency response of Implement by circuits

REFERENCES [1]S.R.Norsworthy, R.Schreier and G.C. Temes, Delta-Sigma Converters-Theory, Design and Simulation, New York: IEEE Press, 1997, pp. 244-278. [2] M. R. Miller and C. S. Perie, “A Multi-Bit Sigma-Delta ADC for Multi-Mode Receivers”, in Proc. IEEE Custom Integrated Circuits Conference, 2002, pp. 191-194. [3] J. Silva, U. J. Moon and G. C. Temes, “Wideband low-distortion delta-sigma ADC topology” , IEE Electronics Letters, no. 12, pp. 737-738, Jun. 2001. [4] P.G.A. Jespers, “Integrated converters: D to A and A to D Architecture, Analysis and

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