Introduce High-pass filter and functions
A high-pass filter also referred to as a low-cut filter or low-stop filter, is an essential component that allows frequencies higher than a specific cutoff frequency to pass through while significantly attenuating lower frequencies. It is primarily used to eliminate unnecessary low-frequency components or low-frequency interference from a signal.
High-pass filters consist of capacitors, inductors, resistors, and other devices that effectively permit signal components above a designated frequency to pass, while effectively suppressing signal components below that frequency. These filters exhibit characteristics that can be described in both the time domain and frequency domain, using impulse response and frequency response, respectively.
The frequency response of a high-pass filter is typically represented as a function of frequency, denoted as H(jω), where H(ω) represents the magnitude frequency response, and φ(ω) represents the phase frequency response. These characteristics describe the amplitude and phase changes experienced by different frequency signal components as they pass through the system from the excitation source.
The frequency response of a system is the Fourier transform of its impulse response. For linear passive systems represented by Nth-order linear differential equations, the frequency response H(jω) is a rational function, with the numerator and denominator corresponding to the right and left sides of the differential equation, respectively.
To classify high-pass filters, two common methods are used:
Based on the devices used:
a. Passive high-pass filter: Composed solely of passive components (such as resistors, inductors, and capacitors), this type of filter takes advantage of the variation in reactance of capacitive and inductive elements with frequency. Passive high-pass filters offer advantages such as simple circuitry, no need for a DC power supply, and high reliability. However, they have disadvantages such as energy loss for signals in the passband, noticeable load effects, susceptibility to electromagnetic induction when using inductive elements, and limitations in low-frequency applications due to the size and weight of the filter, especially with large inductance values.
b. Active high-pass filter: Comprising both passive components (usually resistors and capacitors) and active devices (such as operational amplifiers), active high-pass filters offer several advantages. They entail no energy loss for signals in the passband, allow signal amplification, have minimal load effects, exhibit minimal mutual interference when cascaded in multiple stages, enable easy construction of high-order filters using simple cascading methods, and provide compact size and light weight without the need for magnetic shielding. However, active high-pass filters have limitations such as a passband range restricted by the bandwidth of active devices (e.g., operational amplifiers), the requirement of a DC power supply, lower reliability compared to passive filters, and unsuitability for high-voltage, high-frequency, and high-power applications.
Based on mathematical characteristics:
High-pass filters can also be classified as first-order, second-order, and so on, based on their mathematical characteristics. This classification method is independent of the devices used. Active high-pass filters, such as first-order and second-order active high-pass filters, are more commonly encountered.
In conclusion, high-pass filters are crucial components in signal processing that allow higher frequencies to pass through while attenuating lower frequencies. They can be categorized based on the devices used (passive or active) and their mathematical characteristics (order). Active high-pass filters, in particular, are widely used due to their advantages in terms of signal amplification, minimal load effects, and easy construction of high-order filters.