### Filter Design

```Filter Design (1)
Jack Ou
ES590
Outline
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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
```