Quadrature Control-Bounded ADCs

TL;DR

The paper tackles RF-band A/D digitization with tunable center frequency using a quadrature control-bounded ADC (QCBADC) framework. It extends two low-pass CBADCs into a band-pass, quadrature structure that oscillates at a tunable notch frequency $f_n$ via a local quadrature DC, while preserving stability, bandwidth, and $SNR$ by leveraging the LP building blocks. It provides analytical design equations for matched-signal strength, self-stability, and worst-case superposition, and validates the approach through behavioral simulations across multiple filter orders, notch frequencies, and oversampling ratios, along with Monte Carlo simulations to assess robustness to component variations. The result is a modular, reconfigurable RF-A/D frontend with guaranteed stability and preserved performance, enabling flexible digital receivers and SDR implementations without excessive analog complexity.

Abstract

In this paper, the design flexibility of the control-bounded analog-to-digital converter principle is demonstrated by considering band-pass analog-to-digital conversion. We show how a low-pass control-bounded analog-to-digital converter can be translated into a band-pass version where the guaranteed stability, converter bandwidth, and signal-to-noise ratio are preserved while the center frequency for conversion can be positioned freely. The proposed converter is validated with behavioral simulations for a variety of filter orders, notch-filter frequencies, and oversampling ratios. Finally, robustness against component variations is demonstrated by Monte Carlo simulations.

Figures (3)

• Figure 1: The quadrature Leapfrog analog system which is is the combination of two Leapfrog structures, as in Section \ref{['sec:leapfrog']}, connected by the $\omega_n$ paths. The system is stabilized via the control signals $s_1(t),\dots,s_N(t),\bar{s}_1(t),\dots,\bar{s}_N(t)$ resulting from $N$ quadrature local digital controls as shown in Fig. \ref{['fig:digital_control_zero_order_hold']}.
• Figure 2: The $\ell$th local quadrature DC, connecting $\bm{x}_\ell(t) = (x_\ell(t), (\bar{x}_\ell(t))$ with $\bm{s}_\ell = (s_\ell(.),\bar{s}_\ell(.))$ in Fig. \ref{['fig:leapfrog-structure']}. The output of the two comparators are considered continuous-time quantities $((\theta_\ell \ast s_\ell[.])(t), (\bar{\theta}_\ell \ast \bar{s}_\ell[.])(t))$, where $(\theta_\ell(.), \bar{\theta}_\ell(.))$ are the comparators' impulse responses and $(s[.], \bar{s}[.])$ are the discrete-time control decisions used in (\ref{['eq:estimate']}).
• Figure 3: The coefficients in (\ref{['eq:kappa_phi']})-(\ref{['eq:bar_tilde_kappa_phi']}) as a function of $\omega_n T$ where $2 \beta T = 1$, $\phi_\kappa = 0$, and $\tau_{DC} = 0$.