Analog 2D fan filters from discrete domain transfer functions

A continuous-time discrete-space 2D IIR fan filter is proposed for ultra-wideband beamforming for uniform linear arrays of antennas. The proposed signal-flow-graph replaces sampled unit-delays in a 2D FIR digital prototype fan filter using time-delays of the same duration using an ideal delay line. Thereafter, ideal delays are approximated using an RC-active VLSI circuit consisting of high-order all-pass filters aimed at the 90 nm CMOS technology. The paper covers transfer function design, 2D input spectra in continuous-time, delay approximation, CMOS all-pass circuits and simulation. Finally, a prototype with fan axis directed along θ = 30° (from temporal frequency axis) and half fan angle ε = 6° is simulated and the frequency response from DC to 3.6 GHz is obtained using data from a BSIM4 model of a 10^th- order all-pass filter. The proposed novel analog 2D fan filters are free of aliasing, quantization noise, switching power consumption, and do not require an array of high-speed analog-to-digital converters.