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