Date post: | 31-Dec-2015 |
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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)
Design Requirement for a Butterworth Low Pass Filter
The cut-off frequency is not known in this design specification.
Typical Bandpass Specifications
When a low-pass design is transformed into a bandpass design, the attenuation bandwidth ratios remain the same.
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.
Design Example
f1=2472.5 MHzf2=2472.72f3=2494.28f4=2494.5 MHz (22)/(21.56)=1.0204
Center Freq: 2483.5 MHz
Design Example
f1=27 MHzf2=45 MHzf3=75 MHzf4=125 MHz
(98)/(45)=2.1778Thus fc/f=2
Center Freq: 58.1 MHz
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.