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Filter Design (1) Jack Ou ES590 Outline • • • • Butterworth LPF Design Example LPF to HPF Conversion LPF to BPF Conversion LPF to BRF Conversion Butterworth Filter (Attenuation of the Butterworth filter) Avoid ripples in the passband. As n increases, the responses assumes a sharper transition. The 3dB bandwidth remains independent of n. Low Pass Filter Design Requirement • fc=1 MHz • Attenuation of 9 dB at 2 MHz. Determine the number of elements in the filter 9 dB of attenuation at f/fc of 2. Low Pass Filter Frequency and Impedance Scaling Impedance Scaling Simulation Results Design Requirement for a Butterworth Low Pass Filter The cut-off frequency is not known in this design specification. Design Process Since f2=2f1, then n=3. (fo=1.45 MHz) Elementary Prototype Value Calculation of Component Values Simulation Results LPF to HPF Conversion High Pass Filter Design Requirement • fc=1 MHz • Attenuation of 9 dB at 0.5 MHz. Determine the number of elements in the filter (fc/f) 9 dB of attenuation at fc/f of 2. Low Pass Filter LPF to HPF Transformation 1. Swap L with C, and C with L. 2. Use the reciprocal value. Frequency and Impedance Scaling (same as before) Impedance Scaling HPF LPF to BPF Conversion LPF TO BPF Conversion Determine f3 Typical Bandpass Specifications When a low-pass design is transformed into a bandpass design, the attenuation bandwidth ratios remain the same. Determine n using f/fc 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 seriesresonant circuits. Transformation Example Resonate each low-pass element with an element of the opposite type and of the same value. Calculate Component Values Fourth Order Butterworth Filter Transformation Component Calculation Schematic Av on Log(f) Av on Linear f Band Rejection Filter LPF to BRF Conversion Substitute BWC/BW for fc/f on the normalized frequency axis. 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 Determine # of Stages Hmm…. not enough suppression. Design Example f1=27 MHz f2=45 MHz f3=75 MHz f4=125 MHz (98)/(45)=2.1778 Thus fc/f=2 Center Freq: 58.1 MHz Determine # of Stages fc/f 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. Component Calculations Band Rejection Filter LPF Elementary Prototype BRF Transformation Band Rejection Filter f1=27 MHz f2=45 MHz f3=75 MHz f4=125 MHz