# Filter Design (2) Jack Ou ES590.

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Filter Design (2) Jack Ou ES590

Last Time Outline Butterworth LPF Design General Cases Other Filters
LPF to HPF Conversion LPF to BPF Conversion LPF to BRF Conversion General Cases Dual Networks RL≠RS Other Filters Chebyshev filter Bandpass Design Example Bessel filter Filter Synthesis via Genesis

Low Pass Filter Design Requirement
fc=1 MHz Attenuation of 9 dB at 2 MHz. RS=50 Ohms RL=25 Ohms

Determine the number of elements in the filter
(Same as before) 9 dB of attenuation at f/fc of 2.

Use a Low Pass Prototype Value for RS≠RL

Comparison: RS=RL

Frequency and Impedance Scaling

Matlab Calculation

Low Frequency Response

A medium –Q filter that is used in designs that require the amplitude response of the filter to be as flat as possible. The Butterworth response is the flattest passband response available and contains no ripples.

Chebyshev Response Chebyshev filter is a high-Q filter that is used when : (1) a steeper initial descent into the passband is required (2) the passband response is no longer required to be flat

Comparison of a third order Passband Filter
3 dB of passband ripples and 10 dB improvement in attenuation

Design Methodology Even though attenuation can be calculated analytically, we will use the graphical method. Even order Chebyshev filters can not have equal termination (RS≠RL)

Low Pass Filter Design Requirement
fc=1 MHz Attenuation of 9 dB at 2 MHz. RS=50 Ohms RL=25 Ohms Less than 0.1 dB of Ripple Design it with a Chebychev Filter

0.1 dB Attenuation Chart

0.1 dB, n=2, Chebyshev

Matlab Calculation

Chbysehv, 0.1 dB Ripple, LPF ripple

Typical Bandpass Specifications
When a low-pass design is transformed into a bandpass design, the attenuation bandwidth ratios remain the same.

Butterworth Vs. Chebyshev
Butterworth: n=4, 40 dB Chebyshev: n=4, 48 dB, but RS≠RL We have to settle for n=5, 62 dB.

Chebyshev, 5th Order, 0.1 dB Ripple

Effect of Limited Inductor Quality Factor
Assume each inductor has a quality factor of 10.

Minimum Required Q

Phase of Chebyshev Bandpass Filter
Phase is not very linear during the passband! You can get a lot of distortion!

Bessel Filter Bessel Filter is designed to achieve linear phase at the expense of limited selectivity!

Low Pass Filter Design Requirement
fc=1 MHz Attenuation of 9 dB at 2 MHz. RS=50 Ohms RL=25 Ohms

Attenuation Possible to achieve 9dB

Bessel LPF Prototype Elementary Value

Matlab Calculation

Bessel LPF 6.8 dB of attenuation at f/fc=2

Phase of Bessel LPF (n=2)

Genesys BPF Design Example

Typical Bandpass Specifications
When a low-pass design is transformed into a bandpass design, the attenuation bandwidth ratios remain the same.

Butterworth Vs. Chebyshev
Butterworth: n=4, 40 dB Chebyshev: n=4, 48 dB, but RS≠RL We have to settle for n=5, 62 dB.

Start Geneysis Select Passive Filter Start Genesys

Filter Properties

Comparison Synthesized Via Genesis Synthesized using Charts

Change Settings

QL=50, QC=100

QL=10, QC=100