A new architecture for a multistage bandpass sigma-delta modulator which tolerates imperfections in the resonator function is proposed. The architecaue involves using a FIR filter to reduce the non-cancellation of the quantization noise of the fist stage resulting from circuit non-idealities. Computer simulations of two difFerents structures illustrate the superiority of the new architecture and confirm its ability to withstand resonable circuit non-idealities.conversion because of the high sensitivity, as will be shown in section 3.In Qder to estimate the feasability of cascaded bandpass sigma delta modulators, we have studied the influence of the sensitivity to circuit non-idealities of an example of this kind of modulator by means of extensive simulations. The modulator is presented in section 2 and the result ae mumed in section 3. Section 4 introduces the new modulator whose robustness is examined in section 5. Thereafter, conclusions on the capacity of this new struchm are established. 1. INTRODUCTION 2. SIXTH ORDER NOISE SHAPER Bandpass delta-sigma converters in superheterodyne receivers allows digital filtering and demodulation of the intermediate-frequency (I@ signal and implementation of a digital ampljfii-gain control (AGC). For the latter, the resolution of the conversion is generally about 14/15 bits.In the following of the paper, this is the range of performances whose are expected.Such performances can be achieved in two ways using one-bit modulators, which am inherently linear. The first is to increase the oversampling ratio (OSR) and the second is to increase the order of the noise-shaping filter.The inmasing of the oversampling ratio is rather difficult because of the wide bandwith of the signal.Consequently, the second solution is of great interest as it allows the designer to reduce the sampling frequency, which is often high in such applications. However, deltasigma modulators are subject to instability problems with orders higher than four. Nonetheless, the design of highorder modulators based on the cascade of fourth or &-order modulators eliminates any stability problems at the expense of an increase in sensitivity of the modulator to analog circuit imperfections. In lowpass conversion, this structure has shown itself to be very interesting in many applications and generally allows a higher dynamic range than a one loop structure to be obtained. However, up to now, this architectm has seldom been used in bandpas Figure 1 shows the structure used performances of multi-stage modulators.to evaluate the -pgJ Fig. 1 : 4* O r d e~2~d Order Cascade Modulator This structure consists of the cascade of a fourth-order and second order modulator. It has been obtained from the lowpass modulator by performing a lowpass to bandpass transformation by replacing z-l with -r2. Consequently, Ri(z) are resonators whose ideal transfer function is : Ri(z) = 1/( 1+2-2) 0-7803-3073-0/96/$5 .OO O1996 IEEE 13
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