Analog Active Filters: Approaches Cascade of Biquadratic (Biquad) and Bilinear cells State Variable Filters Simulation of LC filters with active RC networks Paolo Bruschi Progettazione Mixed Signal

Common Filter Responses fc synonyms: Corner frequency Cut-off frequency fCL Corner Freq – Low fCH Corner Freq – High Paolo Bruschi Progettazione Mixed Signal

Parameters of a real frequency response The Low Pass filter is the reference for other types Frequency are general given as angular frequencies (w) A Transition Band (TB) is introduced Note: wp is generally different from wc (-3 dB frequency) Paolo Bruschi Progettazione Mixed Signal

Analog Filters: State Variable Filter It is an Integrator-based Architecture Paolo Bruschi Progettazione Mixed Signal

Biquad with State Variable Archirecture Function b0 b1 b2 Low Pass 1 High Pass Band Pass Notch Paolo Bruschi Progettazione Mixed Signal

OTA: definitions and basic circuits OTA-C (Gm-C) Integrator OTA (Transconductor) Ideal operation Typical non-idealities: Finite Rout Input Capacitance Frequency dependence of Gm Input/Output ranges Paolo Bruschi Progettazione Mixed Signal

Ota-Based summing circuits Summing Integrator (inverting / non-inverting) Summing amplifier (inverting / non-inverting) Paolo Bruschi Progettazione Mixed Signal

Gm-C integrator with feed-forward input Paolo Bruschi Progettazione Mixed Signal

Gm-C Universal Biquad Paolo Bruschi Progettazione Mixed Signal

Self-Tuning of OTA Filters Master Phase detector Characteristic Slaves Tuning law of transconductors Paolo Bruschi Progettazione Mixed Signal

Switched Capacitors Integrator Parasitic Insensitive SC resistors Negative SC resistor Positive SC resistor SC Integrator Phase 1: Hold Phase 2: Virtual ground Paolo Bruschi Progettazione Mixed Signal

SC resistors: charge transfer Negative Resistor Positive Resistor Phase 1 DQ<0 DQ>0 Phase 2 Paolo Bruschi Progettazione Mixed Signal

SC Summing Integrator We assume that ck inputs vin-p and vin-n are sampled at the end of phase 2 ck ck Paolo Bruschi Progettazione Mixed Signal

Discrete time integral Forward Euler Integration Exact response Approximation for f<<fck Paolo Bruschi Progettazione Mixed Signal

Integrator comparison Euler Continuous Time bilinear 0.5 Paolo Bruschi Progettazione Mixed Signal

SC-integrator equivalent block diagram Paolo Bruschi Progettazione Mixed Signal