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A filter can be defined as: it is a circuit used to reshape, modify, and block all unwanted frequencies. Typically, in low-frequency (<100 kHz) applications, passive filters are composed of resistors and capacitors. Therefore, it is called a passive RC filter. Similarly, for high-frequency signals (>100 kHz), passive filters can be designed as combinations of resistors, inductors, and capacitors. Therefore, these circuits are called passive RLC circuits. Three types of filter designs are commonly used: low-pass filters, high-pass filters, and band-pass filters. This article discusses the application of low-pass filters (http://yunrun.com.cn/tech/2613.html) in digital display instruments. What is a low-pass filter? A low-pass filter (LPF) is defined as a filter that is used to pass low-frequency signals while attenuating high-frequency signals. The frequency response of a low-pass filter depends primarily on its design. Below is an introduction to various types of LPFs. First-order low-pass filter: A first-order LPF is shown in the figure; note that the integrator is the basic building block of an LPF. http://yunrun.com.cn/upload/201907/12/201907121954131982.png First-order low-pass filter. The transfer function of a low-pass filter is such that the output decreases (attenuates) in proportion to the frequency. If the frequency is doubled, the output is halved (a decrease of -6dB for each doubling of frequency). Second-order low-pass filter: The figure below shows a second-order low-pass filter. http://yunrun.com.cn/upload/201907/12/201907121956225058.png The output of a second-order low-pass filter decreases (attenuates) in inverse proportion to the square of the frequency; if the frequency doubles, the output also doubles. (-An increase of one octave corresponds to 12 dB). Low-pass filter using an operational amplifier: The feedback loop of an operational amplifier can be used in combination with the basic components of a filter; thus, a high-performance LPF can be easily created by using the necessary components other than inductors. A first-order active LPF circuit using an operational amplifier, namely a single-pole active low-pass filter, is shown below. A low-pass filter circuit using an operational amplifier employs capacitors across the feedback resistors. The circuit performs better when the frequency is increased to boost the feedback level, as the reactive impedance of the capacitor decreases. http://yunrun.com.cn/upload/201907/12/201907122016216679.png http://yunrun.com.cn/upload/201907/12/201907122016312507.png A first-order low-pass filter using an operational amplifier can have its parameters calculated by considering the frequency at which the reactance of the capacitor is equal to that of the resistor. This can be obtained using the following formula: Xc=1/πfC, where Xc is the capacitive reactance in ohms ； π is a standard letter, and its value is 3.412 ； f is the frequency (unit: Hz) ； C is capacitance (Unit: Farads). By eliminating the effect of capacitors, the in-band gain of these circuits can be calculated in a simple manner. Since these types of circuits help to reduce high-frequency gain and provide a -6dB attenuation for each octave, such filters are referred to as first-order or single-pole low-pass filters. A second-order active LPT circuit using an operational amplifier allows for the design of a wide range of filters as well as attenuation models with different gain levels, by utilizing the operational amplifier. http://yunrun.com.cn/upload/201907/12/201907122033465114.png A second-order active LPF circuit using an operational amplifier, where R1=R2, C1=C2, and f=1-√4πRC2. When selecting a value, please ensure that the resistance value is within the range of 10 kiloohms to 100 kiloohms. Low-pass filter calculator: For an RC low-pass filter circuit, by calculating the crossover frequency and plotting the corresponding graph, it is known as a Bode plot. For example: if we know the values of the resistors and capacitors in a circuit, we can use the following formula to calculate the transfer function of a low-pass filter: Vout(s)/Vin(s) + 1/(CR·s) + 1/(CR). To determine the frequency at which a given resistor and capacitor work together, we use the formula fc = 1/(2πRC). http://yunrun.com.cn/upload/201907/12/201907122056483037.png Low-pass filter waveforms. Applications of low-pass filters include: ◆ Low-pass filters are used in telephone systems to convert audio frequencies from speakers into signals within a limited frequency range. ◆An LPF is used to filter out high-frequency signals from a circuit, known as “noise”; when a signal passes through this filter, most of the high-frequency components are removed. ◆Low-pass filters in image processing are used to enhance images. ◆Sometimes these filters are used for audio applications. ◆A low-pass filter is used in RC circuits, and such RC circuits are known as RC low-pass filters. ◆The LPF is used as an integrator in an RC circuit. ◆In multi-rate DSPs, an LPF is used as an anti-imaging filter when an interpolator is implemented. Similarly, when the extractor is executed, this filter is used as an anti-aliasing filter. ◆Low-pass filters are used for signals from medical devices attached to the human body, while tests using electrodes have lower frequencies. Therefore, these signals can pass through the LPF to eliminate some unwanted ambient sounds. ◆These filters are used to convert the duty cycle amplitude and for phase detection in phase-locked loops. ◆LPF is used in AM radios with diode detectors to convert the AM-modulated intermediate frequency signal into an audio signal. Source: Digital display instruments http://yunrun.com.cn/product/