a switched capacitor based realization of.pptx
TRANSCRIPT
A Switched Capacitor based Realization of
Fractional Order Low-pass Filters
A Presentation by Ranjan Das (PhD Scholar, IIT Bombay)
Background
• Conventional Digital Signal Processing (DSP) deals with rational pole-zero models of FIR/IIR structures and looks at stability, causality, and other properties of these models.
• Many physical signals and other phenomena have been shown to possess inherently fractional order dynamics and hence fractional calculus is naturally able to model these processes with greater accuracy.
• Hence, fractional order signal and system theory will play a pivotal role in the coming eras of scientific development.
Current Work: An Overview
• Realisations of a particular family of fractional order low-pass filters, all having a cut-off frequency 1 rad/s. We varied the order of the filter from 0.2 to 0.9 in steps of 0.1 .
• We rationalized those fractional order systems using Charef’s approximation technique [1].
• The approximated transfer functions are realized using operational amplifiers and passive components.
Overview …contd
• The designed circuits were tested in OrCAD pSpice platform.
• The resistances were replaced by switch capacitor approximations, and then these modified circuits were simulated in the same platform.
• To verify correctness, the result were compared with ideal responses.
Charef’s Approximation Technique
The transfer function we started with was,
(m= fractional order < 1)
By Charef’s method, this
function will be approximated as-
Following formulae were used to get the values of zi and pi
The Poles and Zeros as Computed From the Charef’s Method :
Ideal Simulation for the Generated Transfer Functions in MATLAB:
Final Circuit with Stray-Insensitive Configuration:
Final Simulation Results
Comparison with Ideal Responses
Order Ideal Drop-rate Observed drop-rate at Corner Frequencies
0.3 6 dB/decade 6.93 dB/decade
0.4 8 dB/decade 9.54 dB/decade
0.5 10 dB/decade 11.4 dB/decade
0.6 12 dB/decade 12.04 dB/decade
0.7 14 dB/decade 14.52 dB/decade
0.8 16 dB/decade 16.12 dB/decade
0.9 18 dB/decade 18.58 dB/decade
Conclusion
References: