### Filter Design (2)

```Filter Design (2)
Jack Ou
ES590
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
(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
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 Genesys
Select Passive Filter
Filter Properties
Comparison
Synthesized Via Genesis
Synthesized using Charts
Change Settings
QL=50, QC=100
QL=10, QC=100