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

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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

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IIT-Bombay Lecture 3 M. Shojaei Baghini

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

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IIT-Bombay Lecture 3 M. Shojaei Baghini

 Butterworth Approximation

(lecture 02)

 Chebyshev Approximation  Elliptic Approximation  Bessel Approximation

Brief Review of Analog Brief Review of Analog Filter Approximation Filter Approximation

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Reference Tables Reference Tables Element Values - Example Element Values - Example

Normalized Normalized Butterworth LP Filter with Rs=RL=1 Butterworth LP Filter with Rs=RL=1 

3dB cutoff frequency of
3dB cutoff frequency of normalized

normalized LP Butterworth filter = LP Butterworth filter = 1rad/s. 1rad/s.

IIT-Bombay Lecture 3 M. Shojaei Baghini

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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 frequencies between -1 and 1 frequencies between -1 and 1 ⇒ ⇒ r ripple in ipple in passband. passband.

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Chebyshev Approximation

Source: Harry Y-F. Lam, 1979

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

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.

Elliptic Approximation Elliptic Approximation

IIT-Bombay Lecture 3 M. Shojaei Baghini

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Comparison of Magnitude of Comparison of Magnitude of Normalized TF Normalized TF

Butterworth Chebyshev type I Chebyshev type II Elliptic Source: Wikipedia

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BW Filter Characteristics BW Filter Characteristics

Maximally flat in passband
No zero
No ripple in passband and stopband

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Chebyshev Filter Characteristics Chebyshev Filter Characteristics

 Ripple in the passband  No zero  Narrower transition band compared to

Butterworth

 Poorer group delay compared to

Butterworth

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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

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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

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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.

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Magnitude Characteristics

f Bessel Filters

Source: Harry Y-F. Lam, 1979

1.0 0.8 0.6 0.4 0.2 0.0

|H(j)2|

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Phase Characteristics of Bessel Filters

Source: Harry Y-F. Lam, 1979

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Group Delay Characteristics

f Bessel Filters

Source: Harry Y-F. Lam, 1979

1.0 0.8 0.6 0.4 0.2

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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.

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Element Values - Example Element Values - Example

Normalized Normalized Bessel LP Filter Bessel LP Filter with Rs=RL=1 with Rs=RL=1 

Source: Harry Y-F. Lam, 1979

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Frequency Scaling Frequency Scaling

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Frequency Scaling - Example Frequency Scaling - Example

Scaling 1rad/s to 105rad/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

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Frequency Transformation - Frequency Transformation - Example Example

IIT-Bombay Lecture 3 M. Shojaei Baghini

ω (rad/s) ω (rad/s) 100k

100k

1

3dB BW=1
3dB BW=40Krad/s

1

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Frequency Transformation Frequency Transformation

LP to HP LP to BP ω0: Center of pass band

(geometrical symmetry not arithmetic symmetry)

B: BW

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Frequency Transformation Frequency Transformation (cont'd)

(cont'd)

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Frequency Transformation Frequency Transformation (cont'd)

(cont'd)

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IIT-Bombay Lecture 3 M. Shojaei Baghini

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

Date: Jan. 14, 2011 Date: Jan. 14, 2011

Analog Filter Approximation Analog Filter Approximation

(continuation from Lecture 02) (continuation from Lecture 02)

Contents Contents

Conversion

(lecture 02)

Brief Review of Analog Brief Review of Analog Filter Approximation Filter Approximation

Reference Tables Reference Tables Element Values - Example Element Values - Example

Normalized Normalized Butterworth LP Filter with Rs=RL=1 Butterworth LP Filter with Rs=RL=1 

normalized LP Butterworth filter = LP Butterworth filter = 1rad/s. 1rad/s.

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 frequencies between -1 and 1 frequencies between -1 and 1 ⇒ ⇒ r ripple in ipple in passband. passband.

Chebyshev Approximation

Finite Transmission Zeros

elliptic rational functions (more details in filter

design text books, e.g. Harry Y-F. Lam, 1979, ...).

compared to BW and Chebyshev filter.

Elliptic Approximation Elliptic Approximation

Comparison of Magnitude of Comparison of Magnitude of Normalized TF Normalized TF

BW Filter Characteristics BW Filter Characteristics

Chebyshev Filter Characteristics Chebyshev Filter Characteristics

Butterworth

Butterworth

Chebyshev Type II Filter Chebyshev Type II Filter Characteristics Characteristics

Butterworth

Chebyshev

Elliptic Filter Characteristics Elliptic Filter Characteristics

group delay compared to Butterworth and two forms of Chebyshev filters

Bessel Approximation Bessel Approximation

Approximation, having maximally flat delay response.

band and stop band response, like Butterworth but with less attenuation in stop band.

Magnitude Characteristics

Phase Characteristics of Bessel Filters

Group Delay Characteristics

Properties – Bessel Filter Properties – Bessel Filter

transition band

group delay of Bessel filter the best compared to Butterworth, Chebyshev I & II and Elliptic filters.

Element Values - Example Element Values - Example

Normalized Normalized Bessel LP Filter Bessel LP Filter with Rs=RL=1 with Rs=RL=1 

Frequency Scaling Frequency Scaling

Frequency Scaling - Example Frequency Scaling - Example

Scaling 1rad/s to 105rad/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

Frequency Transformation - Frequency Transformation - Example Example

Frequency Transformation Frequency Transformation

LP to HP LP to BP ω0: Center of pass band

(geometrical symmetry not arithmetic symmetry)

B: BW

Frequency Transformation Frequency Transformation (cont'd)

(cont'd)

Frequency Transformation Frequency Transformation (cont'd)

(cont'd)

End of Lecture 3