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

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

3. 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)
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Progettazione Mixed Signal

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

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

6. 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
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Progettazione Mixed Signal

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

8. Gm-C integrator with feed-forward input
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Progettazione Mixed Signal

9. Gm-C Universal Biquad
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Progettazione Mixed Signal

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

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

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

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

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

15. Integrator comparison
Euler
Continuous Time
bilinear
0.5
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Progettazione Mixed Signal

16. SC-integrator equivalent block diagram
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Progettazione Mixed Signal