As we depart from this “figure of merit” (as we must do to produce the 40kHz notch in our example), performance will gradually deteriorate. Those conditions which produce the best results for a particular parameter are called its “figure of merit.” For example, in the case of the LTC1064, the best specs for clock to center frequency ratio (f CLK/f 0) accuracy are published for a clock frequency of 1MHz and a Q of 10. Switched-capacitor filter devices give the best performance when certain operating parameters are kept within particular ranges. A working filter with an attenuation of 60dB can be achieved, but only be deviating significantly from the advice provided by FilterCAD. This 8th order filter claims an actual stopband attenuation of greater than 80dB, a level of performance that would be exceedingly difficult to achieve in the real world. Given these parameters, FilterCAD synthesizes the response shown in Table 23.12.
We’ll specify a maximum passband ripple of 0.1dB, an attenuation of 60dB, a center frequency of 40kHz, a stop bandwidth of 2kHz, and a pass bandwidth of 12kHz. We will start by using FilterCAD to enter the parameters for an elliptic notch response. Some of these techniques will be examined here. Notches of up to 60dB can be obtained, but to do so requires techniques not covered by this version of FilterCAD. This is primarily due to the sampled data nature of the universal filter blocks signals of equal amplitude and opposite phase do not ideally cancel when summed together as they would do in a purely analog system. You may design a notch filter with FilterCAD, with specifications that purport to yield a stopband attenuation of greater than 60dB, and find that in practice an attenuation of 40dB or less is the result. Notch filters, especially those with high Qs and/or high attenuations, are the most difficult to implement with universal switched-capacitor filter devices. Worse yet, time and temperature variation may force adjustment of the filter frequency after the controller is placed in operation. Because the values of analog passive components vary from one unit to another and, to a lesser extent, over time and temperature, analog notch filters often must be “tweaked in” on every application. In the case of analog systems, notch filters become more complicated to configure.
In such a case, the notch filter may have to be manually tuned for every control system.
For example, resonant frequencies often vary slightly from one system to another. However, there are many cases where the noise or resonant frequency will vary. If the offending frequency is known, digital notch filters can be set to filter it with great accuracy. To be useful, the notch filter must be tuned to the frequency of resonance or of noise generation. Notch filters work on only a narrow band of frequencies. Bode plot for a notch filter.Īlthough notch filters improve the primary shortcoming of low-pass filters (the reduction of phase margin), they are still used less regularly. The design of the acoustic filter presented in this study and the corresponding analysis should motivate further development of thin acoustic filters.Figure 9.3. We confirmed that the experimental transmittance spectra of fabricated notch filters, which consisted of between one and six HRs, agreed with the simulated transmittance spectra. Simulated transmittance spectra showed that the depth of the dip in the transmittance increased with the number of uniformly arranged HRs. Therefore, the arrangement of HRs is essential for realizing a planar notch filter. The total pressure emitted from the HRs is equal regardless of the number of HRs connected to the hole. A simulated pressure distribution revealed that this uniform arrangement of HRs improves the silencing effect because the uniform applied waves emitted from the HRs act as canceling waves to the cross-section of the short hole (in this case, the length of the hole is sub-wavelength). The HRs were placed at the in-plane vertices of a regular polygon. The developed notch filter consists of a number of spherical Helmholtz resonators (HRs) connected to a hole created in a plate. This paper reports on an acoustic planar notch filter with a sub-wavelength thickness at the notch frequency.