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Filter Design (1)
Jack OuES590
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
• 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
9 dB of attenuation at fc/f of 2.
(fc/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)
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 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
Transformation
Component Calculation
Schematic
Av on Log(f)
Av on Linear f
Band Rejection Filter
LPF to BRF Conversion
Substitute BWC/BW for fc/fon the normalized frequency axis.
Design Example
f1=2472.5 MHzf2=2472.72f3=2494.28f4=2494.5 MHz (22)/(21.56)=1.0204
Center Freq: 2483.5 MHz
Determine # of Stages
Hmm…. not enough suppression.
Design Example
f1=27 MHzf2=45 MHzf3=75 MHzf4=125 MHz
(98)/(45)=2.1778Thus 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 MHzf2=45 MHzf3=75 MHzf4=125 MHz