A Performance Prediction Method with an Equation-Based Behavioral Model for a Single-Bit Single-Loop Sigma-Delta Modulator

A Performance Prediction Method with an Equation-Based Behavioral Model for a Single-Bit Single-Loop Sigma-Delta Modulator

Shuenn-Yuh Lee (National Chung Cheng University, Chia-Yi, Taiwan) and Jia-Hua Hong (National Chung Cheng University, Chia-Yi, Taiwan)
DOI: 10.4018/jssci.2012100104
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Abstract

An equation-based behavioral model has been developed to predict the real performance of a single–loop single-bit Sigma Delta Modulator (SDM). By using this prediction flow, not only can the circuit specifications be acquired, including the gain, bandwidth, slew rate of the OPAMPs, and the capacitor value in the switched-capacitor circuits, but the real performance of the SDM can also be predicted. The switched-capacitor circuits according to the required circuit specifications are employed to design a fourth-order feed-forward (FF) SDM with an over-sampling ratio (OSR) of 64 and a bandwidth of 10kHz using a TSMC 0.35µm CMOS process. The measurement results reveal that the SDM with an input frequency of 2.5kHz and a supply voltage of 3.3V can achieve a dynamic range of 90dB and a spurious-free dynamic range (SFDR) of 85dB under the signal bandwidth of 10kHz and a sampling frequency of 1.28MHz, respectively. The precision of the equation-based behavioral model has been validated by experimental measurements, and its inaccuracy is less than 4%.
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2. Performance Prediction Issues

Figure 1 shows the proposed prediction flow of SDM performance. According to this flow, the real performance can easily be predicted, and the required specification of the building blocks in SDM can be obtained. First the specifications of SDM, including bandwidth, peak signal-to-noise ratio (PSNR), and maximum input range, should be defined, and then the designer can alter the oversampling ratio (OSR) and fit the required coefficients of the selected architecture according to the stability requirement. To tolerate the performance degradation of SDM as considering all the non-ideal circuit effects (Malcovati et al., 2003), the next step is to create the circuit behavioural model with SIMULINK and individually apply it to the SDM architecture in order to obtain the required circuit specifications. When acquiring the detailed specifications, the non-ideal effects can be integrated into the SDM with consideration of all the non-ideal effects at the same time. Therefore, the real SNR and dynamic range (DR) can be predicted by the proposed integrated behavioral model. According to this procedure, the designers can rapidly predict the real performance before the circuit implementation. If the final simulation results do not match the required system specification, the designers can try to revise the specification in order to tolerate the performance degradation caused by the circuit implementation.

Figure 1.

Prediction flow of SDM performance in circuit implementation

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