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Published byGarret Larman Modified over 2 years ago

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Filter Design (2) Jack Ou ES590

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

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

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

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Use a Low Pass Prototype Value for RSRL

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Comparison: RS=RL

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Frequency and Impedance Scaling

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Matlab Calculation

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Low Frequency Response

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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.

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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

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

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

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Low Pass Filter Design Requirement f c =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

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0.1 dB Attenuation Chart

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0.1 dB, n=2, Chebyshev

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Matlab Calculation

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Chbysehv, 0.1 dB Ripple, LPF ripple

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

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Butterworth Vs. Chebyshev Butterworth: n=4, 40 dBChebyshev: n=4, 48 dB, but R S R L We have to settle for n=5, 62 dB.

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Chebyshev, 5 th Order, 0.1 dB Ripple

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

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Minimum Required Q

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

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

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

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Attenuation Possible to achieve 9dB

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Bessel LPF Prototype Elementary Value

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Matlab Calculation

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

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Phase of Bessel LPF (n=2)

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Genesys BPF Design Example

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

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Butterworth Vs. Chebyshev Butterworth: n=4, 40 dBChebyshev: n=4, 48 dB, but R S R L We have to settle for n=5, 62 dB.

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Start Geneysis Start Genesys Select Passive Filter

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Filter Properties

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Comparison Synthesized Via Genesis Synthesized using Charts

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Change Settings

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Q L =50, Q C =100

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Q L =10, Q C =100

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Export Schematic to ADS (Not sure. ADS project is open)

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Tune You can also fine-tune the value of a component and see how it changes the filter response

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