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The Bessel linear phase filter is used in audio equipment because it has the same delay to all frequencies below its cutoff frequency. In audio equipment, it must be in the band without damage. Eliminate out-of-band noise on the premise of the phase relationship of the signal. In addition, the Bessel filter has a fast step response and no overshoot or ringing, which makes it a smoothing filter at the output of the audio DAC or an anti-aliasing filter at the input of the audio ADC. Excellent choice. Bessel filters can also be used to analyze the output of Class D amplifiers and to eliminate switching noise in other applications to improve the accuracy of distortion measurements and oscilloscope waveform measurements.
Although the Bessel filter provides flat amplitude and linear phase (ie, uniform group delay) response in its passband, its selectivity is better than the same order (or number of poles) Butterworth filter. The Chebyshev filter is worse. Therefore, in order to achieve a specific level of stopband attenuation, a higher order Bessel filter needs to be designed, which in turn requires careful selection of amplifiers and components to achieve the lowest noise and distortion.
Figure 1 shows the schematic of a high performance 8th order 30 kHz low pass Bessel filter. This design uses standard values ​​for 1% tolerance resistors and 5% tolerance ceramic capacitors. Instead, a 10% tolerance capacitor can be used at the expense of increased group delay variation within the frequency band. For best results, use a temperature-stable capacitor.
In this application, the filter processes some of the up and down oscillating audio signals, and its amplifier draws power from a ±2.5V supply. The rail-to-rail output capability helps achieve maximum output voltage swing at these low supply voltages. In order to achieve a high signal to noise ratio in high quality audio services, the amplifier must exhibit unity gain stability and very low intrinsic noise. For example, Analog Devices' AD8656 low noise, high precision CMOS dual op amp meets all of these requirements.
By connecting these amplifiers as inverting gain stages, a constant input common-mode voltage is maintained and distortion is minimized. Using a resistor below 1 kΩ throughout the circuit reduces the thermal noise effects of the resistor. Each AD8656 amplifier delivers less than 3 nV/√Hz in a 30 kHz bandwidth and a total noise of less than 3.5 mV rms over a 30 kHz bandwidth. For a 1Vrms input signal, the circuit produces a signal-to-noise ratio better than 109 dB, and for a 1 kHz, 1Vrms input signal, the circuit produces a THD+N (total harmonic distortion plus noise) factor better than 0.0006%.
Figure 2 shows the amplitude response of the measured filter to the 1Vrms input signal. For frequencies up to 20 kHz, the filter's 0dB passband gain is flat over 1.2 dB. The 8th order Bessel filter is at -3 dB at 30 kHz, exhibiting a theoretical attenuation of -110 dB at 300 kHz and decreasing at -160 dB/decade at higher frequencies. This feature provides sufficient attenuation of repetitive noise caused by switching power supplies and other sources, typically occurring at 300 kHz and higher.
Figure 3 depicts the phase shift and group delay of the filter, which is relatively constant at approximately 17 ms, even for frequencies up to 40 kHz. Note the linear scale on the frequency axis of Figure 3, which clearly depicts the linear phase behavior of the filter in the passband. The following formula defines the negative partial derivative of the group delay phase shift for the frequency:
Group delay = -δφ/δf.
In the case of direct current, resistor R 1 sets the input resistance of the filter to 383 Ω. If the application requires a higher input impedance, a unity gain buffer can be inserted in front of the filter at the expense of increased distortion and noise. For devices that require a ±15V supply, a higher voltage amplifier can be used instead of the AD8656, such as Analog Devices' AD8672 low distortion, low noise (3.8nV/√Hz) dual op amp.
Dual-band Bandpass Filters (BPFs) provide the functionality of two separate filters, but in the size of a single filter. Dual band pass filter applications are at the leading edge of fiber optical modules and systems. Using DBPFs is a new concept in multiplex and de-multiplex module design used in optimizing wavelength ranges or channel management. The application of DBPFs makes it possible to reduce the component quantity in optical modules, enhances their performance, and enables faster data transfer in the optical backbone of major networks.
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