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Lecture 4 Filter design
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Filter Design (2)
Jack OuES590
Last Time Outline
• Butterworth LPF Design – 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– Bandpass Design Example
• 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
9 dB of attenuation at f/fc of 2.(Same as before)
Use a Low Pass Prototype Value for RS≠RL
Comparison: RS=RL
Frequency and Impedance Scaling
Matlab Calculation
Low Frequency Response
Comments about Butterworth Filter
• 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
Start GenesysSelect Passive Filter
Filter Properties
Comparison
Synthesized Via Genesis
Synthesized using Charts
Change Settings
QL=50, QC=100
QL=10, QC=100
Export Schematic to ADS
(Not sure. ADS project is open)
Tune
• You can also fine-tune the value of a component and see how it changes the filter response