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Filter Design (1) Jack Ou ES590

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Outline Butterworth LPF Design Example LPF to HPF Conversion LPF to BPF Conversion LPF to BRF Conversion

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Butterworth Filter Avoid ripples in the passband. As n increases, the responses assumes a sharper transition. The 3dB bandwidth remains independent of n. (Attenuation of the Butterworth filter)

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Low Pass Filter Design Requirement f c =1 MHz Attenuation of 9 dB at 2 MHz.

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Determine the number of elements in the filter 9 dB of attenuation at f/f c of 2.

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Low Pass Filter

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Frequency and Impedance Scaling

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Impedance Scaling

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Simulation Results

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Design Requirement for a Butterworth Low Pass Filter The cut-off frequency is not known in this design specification.

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Design Process Since f 2 =2f 1, then n=3. (fo=1.45 MHz)

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Elementary Prototype Value

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Calculation of Component Values

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Simulation Results

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LPF to HPF Conversion

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High Pass Filter Design Requirement f c =1 MHz Attenuation of 9 dB at 0.5 MHz.

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

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Low Pass Filter

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LPF to HPF Transformation 1.Swap L with C, and C with L. 2. Use the reciprocal value.

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Frequency and Impedance Scaling (same as before)

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Impedance Scaling

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HPF

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LPF to BPF Conversion

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LPF TO BPF Conversion

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Determine f3

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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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Determine n using f/f c

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Transformation from LPF to BPF The Actual Transformation from LPF to BPF is accomplished by resonating each low-pass element with an element of the opposite type and of the same value. All shunt elements of the low-pass prototype circuit becomes parallel resonant circuits, and all series elements become series- resonant circuits.

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Transformation Example Resonate each low-pass element with an element of the opposite type and of the same value.

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Calculate Component Values

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Fourth Order Butterworth Filter

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Transformation

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Component Calculation

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Schematic

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Av on Log(f)

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Av on Linear f

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Band Rejection Filter

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LPF to BRF Conversion Substitute BWC/BW for fc/f on the normalized frequency axis.

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Design Example f1=2472.5 MHz f2=2472.72 f3=2494.28 f4=2494.5 MHz (22)/(21.56)=1.0204 Center Freq: 2483.5 MHz

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Determine # of Stages Hmm…. not enough suppression.

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Design Example f1=27 MHz f2=45 MHz f3=75 MHz f4=125 MHz (98)/(45)=2.1778 Thus f c /f=2 Center Freq: 58.1 MHz

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Determine # of Stages f c /f

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Transformation from LPF Replace each shunt element with a shunt series resonant circuit. Replace each series element with a series parallel resonant circuit. Both elements in each of the resonant circuits have the same normalized value.

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Component Calculations

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Band Rejection Filter

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LPF Elementary Prototype

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BRF Transformation

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Band Rejection Filter f1=27 MHz f2=45 MHz f3=75 MHz f4=125 MHz

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