Using Finite Impulse Response Feedback DACs to design Σ∆ modulators based on LC filters.

This paper proposes a general method to design the noise-transfer-function of a continuous-time Σ∆ modulator having high-order passive LC loop filters. The feedback signals can have arbitrary shapes and can be applied either at internal nodes or only at the input node. As a design example, this technique is used to design a 4 th order Σ∆ modulator where the internal nodes of the loop filter are removed for a more efficient circuit implementation. I. INTRODUCTION Nowadays, in Software Defined Radio (SDR) receivers, we try to displace the analog-to-digital conversion closer the antenna. The use of LC filters in a continuous-time (CT) bandpass (BP) Σ∆ modulator allows to consider the digitization of the signal directly at RF frequencies (1). One problem, induced by using LC filters, is the loss of the parity between the order of the loop filter and the number of internal nodes (Fig.1). This implies limited degrees of freedom to design the noise-transfer-function (NTF) of the modulator. The different solutions proposed to solve this problem imply to add one additional feedback at each node of the loop filter of the modulator to compensate the lack in degrees of freedom (2)(3). These papers treated only LC-resonators based Sigma- Delta with rectangular pulse shape feedback digital-to-analog converters (DAC) applied to each node of the modulators. In this paper we present a solution based on finite-impulse response feedback DAC (FIRDAC) to design CT modulators with n th order LC filters (Fig.2). The FIRDACs have already been used to improve the stability of the high order Σ∆ modulators (4) or to decrease the effects of non-idealities like clock-jitter (5)(6). Here we use FIRDACs to provide the sufficient degrees of freedom for designing the NTF of the modulator.