learnbin.net nav logo

A high-pass filter is a filter that significantly attenuates or rejects all frequencies below fc (critical frequency) and passes all frequencies above fc. The pass band of a high-pass filter is all frequencies above the critical frequency.

Actual response and the ideal response of a high pass filter
Figure 01: Actual response and the ideal response of a high pass filter

Active high pass filters

Circuit diagram of an active high pass filter
Figure 02: Circuit diagram of an active high-pass filter

Calculation of transfer function of an active high-pass filter

High pass filters eq 01

Let’s take,

High pass filters eq 02

To remove complex numbers in the equation, the 4th power of the complex part is taken and takes the 4th root. This mathematical operation can be done separately for two complex parts.

High pass filters eq 03

To remove the other complex part in the equation, the same operation can be done.

High pass filters eq 04

Therefore, the voltage gain of an active high pass filter can be written in,

High pass filters eq 05

The above equation gives the transfer function of an active high-pass filter. The voltage gain at each ω (Angular frequency of the signal) value can be calculated using the above equation.

Calculation of voltage gain at different ω (frequency) values using the transfer function of an active high-pass filter

  • When ω <<< ωc
High pass filters eq 06

  • When ω = ωc
High pass filters eq 07

  • When ω >>> ωc
High pass filters eq 08

Voltage gain at different ω values (Active high pass filter)
Table 01: Voltage gain at different ω values (Active high-pass filter)

Voltage Gain (dB) vs frequency response Graph (Active high pass filter)
Figure 03: Voltage gain (dB) vs frequency response graph (Active high-pass filter)

Passive high pass filters

Circuit diagram of a passive high pass filter
Figure 04: Circuit diagram of a passive high-pass filter

Calculation of transfer function of a passive high-pass filter

High pass filters eq 09

Take

High pass filters eq 10

To remove the complex part in the equation, the same operation that was done on the transfer function in the active filter can be used here.

High pass filters eq 11

The above equation gives the transfer function of a passive high-pass filter. The voltage gain at each ω (Angular frequency of the signal) value of a passive high-pass filter can be calculated using the above equation.

Calculation of voltage gain at different ω (frequency) values using the transfer function of a passive high-pass filter

  • When ω >>> ωc
High pass filters eq 12

  • When ω = ωc
High pass filters eq 13

  • When ω <<< ωc
High pass filters eq 14

Voltage gain at different ω values (Passive high pass filter)
Table 02: Voltage gain at different ω values (Passive high-pass filter)

Voltage Gain (dB) vs frequency response Graph (Passive high pass filter)
Figure 05: Voltage Gain (dB) vs frequency response Graph (Passive high-pass filter)

Buy me a coffee

References and Attributes

Figures:

The cover image was created using an image by Tide He from Pixabay


Express your thoughts below!
0 Comments
Inline Feedbacks
View all comments
© 2022 Learnbin.net. All rights reserved.
linkedin facebook pinterest youtube rss twitter instagram facebook-blank rss-blank linkedin-blank pinterest youtube twitter instagram