Mixed-Signal VLSI Design Course Code: EE719/EE410 Department: - PowerPoint PPT Presentation

Mixed-Signal VLSI Design Course Code: EE719/EE410 Department: Electrical Engineering Semester: Spring 2011 Instructor Name: M. Shojaei Baghini E-Mail ID: mshojaei@ee.iitb.ac.in 1

2 2 Date: Jan. 14, 2011 Date: Jan. 14, 2011 Analog Filter Approximation Analog Filter Approximation (continuation from Lecture 02) (continuation from Lecture 02) Contents Contents  Function Approximations  Frequency Transformations  Passive Filter to Active Filter Conversion IIT-Bombay Lecture 3 M. Shojaei Baghini

3 3 Brief Review of Analog Brief Review of Analog Filter Approximation Filter Approximation  Butterworth Approximation (lecture 02)  Chebyshev Approximation  Elliptic Approximation  Bessel Approximation IIT-Bombay Lecture 3 M. Shojaei Baghini

4 4 Reference Tables Reference Tables Element Values - Example Element Values - Example Normalized Butterworth LP Filter with Rs=RL=1 Butterworth LP Filter with Rs=RL=1   Normalized -3dB cutoff frequency of normalized normalized LP Butterworth filter = LP Butterworth filter = -3dB cutoff frequency of 1rad/s. 1rad/s. 5 4 IIT-Bombay Lecture 3 M. Shojaei Baghini

5 5 Chebyshev Approximation All-pole transfer function based on  Chebyshev polynomials where poles lie on Chebyshev polynomials where poles lie on an ellipse. an ellipse. Chebyshev polynomials have local Chebyshev polynomials have local  maximum and minimum values at finite maximum and minimum values at finite frequencies. frequencies. For normalized Chebyshev polynomials all For normalized Chebyshev polynomials all  maximum and minimum values occur at maximum and minimum values occur at ⇒ r frequencies between -1 and 1 ⇒ ripple in ipple in frequencies between -1 and 1 passband. passband. IIT-Bombay Lecture 3 M. Shojaei Baghini

6 6 Chebyshev Approximation Source: Harry Y-F. Lam, 1979 IIT-Bombay Lecture 2 M. Shojaei Baghini IIT-Bombay Lecture 3 M. Shojaei Baghini

7 7 Elliptic Approximation Elliptic Approximation Finite Transmission Zeros   Transmission Zeroes are poles of the elliptic rational functions (more details in filter design text books, e.g. Harry Y-F. Lam, 1979, ...) .  Ripple in both pass band and stop band  Steeper roll-off in transition band compared to BW and Chebyshev filter. IIT-Bombay Lecture 2 M. Shojaei Baghini IIT-Bombay Lecture 3 M. Shojaei Baghini

8 8 Comparison of Magnitude of Comparison of Magnitude of Normalized TF Normalized TF Butterworth Chebyshev type I Chebyshev type II Elliptic Source: Wikipedia IIT-Bombay Lecture 2 M. Shojaei Baghini IIT-Bombay Lecture 3 M. Shojaei Baghini

9 9 BW Filter Characteristics BW Filter Characteristics • Maximally flat in passband • No zero • No ripple in passband and stopband IIT-Bombay Lecture 2 M. Shojaei Baghini IIT-Bombay Lecture 3 M. Shojaei Baghini

10 10 Chebyshev Filter Characteristics Chebyshev Filter Characteristics  Ripple in the passband  No zero  Narrower transition band compared to Butterworth  Poorer group delay compared to Butterworth IIT-Bombay Lecture 2 M. Shojaei Baghini IIT-Bombay Lecture 3 M. Shojaei Baghini

11 11 Chebyshev Type II Filter Chebyshev Type II Filter Characteristics Characteristics  No ripple in the passband  Zeros in stopband  Narrower transition band compared to Butterworth  Improved group delay compared to Chebyshev IIT-Bombay Lecture 2 M. Shojaei Baghini IIT-Bombay Lecture 3 M. Shojaei Baghini

12 12 Elliptic Filter Characteristics Elliptic Filter Characteristics  Ripple in the passband  Zeros in stopband  Narrower transition band and poorest group delay compared to Butterworth and two forms of Chebyshev filters IIT-Bombay Lecture 2 M. Shojaei Baghini IIT-Bombay Lecture 3 M. Shojaei Baghini

13 13 Bessel Approximation Bessel Approximation  Phase Approximation  Linear Phase (or Constant Group Delay) Approximation, having maximally flat delay response.  The Bessel approximation has a smooth pass band and stop band response, like Butterworth but with less attenuation in stop band.  All transmission zeros occur at s=infinite. IIT-Bombay Lecture 2 M. Shojaei Baghini IIT-Bombay Lecture 3 M. Shojaei Baghini

14 14 Magnitude Characteristics of Bessel Filters |H(j  ) 2 | 1.0 0.8 0.6 0.4 0.2 0.0 Source: Harry Y-F. Lam, 1979 IIT-Bombay Lecture 2 M. Shojaei Baghini IIT-Bombay Lecture 3 M. Shojaei Baghini

15 15 Phase Characteristics of Bessel Filters Source: Harry Y-F. Lam, 1979 IIT-Bombay Lecture 2 M. Shojaei Baghini IIT-Bombay Lecture 3 M. Shojaei Baghini

16 16 Group Delay Characteristics of Bessel Filters 1.0 0.8 0.6 0.4 0.2 Source: Harry Y-F. Lam, 1979 IIT-Bombay Lecture 2 M. Shojaei Baghini IIT-Bombay Lecture 3 M. Shojaei Baghini

17 17 Properties – Bessel Filter Properties – Bessel Filter  Similar to Butterworth but with wider transition band  No zeros  Low Q poles, outside unit circle makes group delay of Bessel filter the best compared to Butterworth, Chebyshev I & II and Elliptic filters. IIT-Bombay Lecture 2 M. Shojaei Baghini IIT-Bombay Lecture 3 M. Shojaei Baghini

18 18 Element Values - Example Element Values - Example Normalized Bessel LP Filter Bessel LP Filter Normalized with Rs=RL=1   with Rs=RL=1 Source: Harry Y-F. Lam, 1979 IIT-Bombay Lecture 2 M. Shojaei Baghini IIT-Bombay Lecture 3 M. Shojaei Baghini

19 19 Frequency Scaling Frequency Scaling IIT-Bombay Lecture 2 M. Shojaei Baghini IIT-Bombay Lecture 3 M. Shojaei Baghini

20 20 Frequency Scaling - Example Frequency Scaling - Example Scaling 1rad/s to 10 5 rad/s results in the following new values of components. 0.51H → 5.1  H 0.11H → 1.1  H 1.06F → 10.6  F 0.32F → 3.2  F IIT-Bombay Lecture 2 M. Shojaei Baghini IIT-Bombay Lecture 3 M. Shojaei Baghini

21 21 Frequency Transformation - Frequency Transformation - Example Example 1 -3dB BW=1 ω (rad/s) 0 1 ω (rad/s) -100k 0 100k -3dB BW=40Krad/s IIT-Bombay Lecture 3 M. Shojaei Baghini IIT-Bombay Lecture 2 M. Shojaei Baghini