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, including the selection of R, L, and C components, with specific calculations for component values. The design uses a resistor, inductor, and capacitor. The project includes the circuit diagram and explains how the filter works, emphasizing the role of the capacitor in blocking DC signals and the frequency response characteristics. The document also includes a bode plot. The document concludes with a bibliography of relevant sources. The assignment aims to provide a practical understanding of filter design and its applications within electrical engineering.

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.