Presentation on theme: "Filter Design (1) Jack Ou ES590. Outline Butterworth LPF Design Example LPF to HPF Conversion LPF to BPF Conversion LPF to BRF Conversion."— Presentation transcript:
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 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)
Low Pass Filter Design Requirement f c =1 MHz Attenuation of 9 dB at 2 MHz.
Determine the number of elements in the filter 9 dB of attenuation at f/f c of 2.
Low Pass Filter
Frequency and Impedance Scaling
Design Requirement for a Butterworth Low Pass Filter The cut-off frequency is not known in this design specification.
Design Process Since f 2 =2f 1, then n=3. (fo=1.45 MHz)
Elementary Prototype Value
Calculation of Component Values
LPF to HPF Conversion
High Pass Filter Design Requirement f c =1 MHz Attenuation of 9 dB at 0.5 MHz.
Determine the number of elements in the filter 9 dB of attenuation at f c /f of 2. (f c /f)
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)
LPF to BPF Conversion
LPF TO BPF Conversion
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/f c
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.
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
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 f c /f=2 Center Freq: 58.1 MHz
Determine # of Stages f c /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.