Passive Second Order High-Pass Filter Design and Analysis

This project details the design of a passive second-order high-pass filter, focusing on a cutoff frequency of 400Hz. The assignment begins with an introduction to high-pass filters, explaining their function and the distinction between them and low-pass filters. It details the design process, incl...Read More

Design of a Passive Second Order High-Pass Filter with cut-off Frequency of 400Hz
By (name)
Institutional Affiliation

Introduction
Whereas low pass filter allows only signals whose frequency is less than the cut-off point fc to
pass through, a high pass filter only allow signals whose frequencies are higher than the cut-off
to pass through1. It therefore eliminate all the frequencies of the waveforms that are lower than
fc. This paper involves a design of a passive high pass filter. The designed filter is made up of
purely passive elements (R, L and C). After the design, its functionality is evaluated by
simulating frequency analysis and response.
The design
Generally, an RLC high-pass filter (second order) takes a circuit is shown below
The design process involves carefully choosing the values of R, L and C.
The cutoff frequency =400Hz
Cuff-off frequency
Fc= 1
2 π √LC
Therefore
400= 1
2 π √ LC
Using a capacitor value
C=100 μ
Therefore
400= 1
2 π √L ×100 ×10−6
From which the value of L is computed as
L=1.5 mH
1 Remus Narcis Beres et al., “A Review of Passive Power Filters for Three-Phase Grid-Connected Voltage-Source
Converters,” IEEE Journal of Emerging and Selected Topics in Power Electronics 4, no. 1 (March 1, 2016): 54–69,
https://doi.org/10.1109/JESTPE.2015.2507203.
Nien-Che Yang and Minh-Duy Le, “Optimal Design of Passive Power Filters Based on Multi-Objective Bat Algorithm
and Pareto Front,” Applied Soft Computing 35 (October 1, 2015): 257–266,
https://doi.org/10.1016/j.asoc.2015.05.042.

The designed filter is as shown below;
With
R = 7.5Ω
C = 100uF
L = 0.0015H
Because for a second order high pass filter designed, the cut-off frequency does not depend on
the resistor value. A resistor value of 7.5Ω is used.
How the filter works
The capacitor that is in series with the resistor blocks all the signals from dc to the cut-off
frequency. This is evident in the attached Bode Plot. The magnitude plot shows that the signal is
damped or attenuated from DC (0Hz) with the output increasing at +20dB/decade until the cut-
off frequency. The frequency response reveals that the designed filter can pass all the signals
greater than fC=400Hz to infinity.

Bibliography
Beres, Remus Narcis, Xiongfei Wang, Marco Liserre, Frede Blaabjerg, and Claus Leth Bak. “A
Review of Passive Power Filters for Three-Phase Grid-Connected Voltage-Source
Converters.” IEEE Journal of Emerging and Selected Topics in Power Electronics 4, no.
1 (March 1, 2016): 54–69. https://doi.org/10.1109/JESTPE.2015.2507203.
Yang, Nien-Che, and Minh-Duy Le. “Optimal Design of Passive Power Filters Based on Multi-
Objective Bat Algorithm and Pareto Front.” Applied Soft Computing 35 (October 1,
2015): 257–266. https://doi.org/10.1016/j.asoc.2015.05.042.