Design of the hottest active analog bandpass filte

Design of active analog bandpass filter

filter is a circuit with frequency selection function, which can make useful frequency signals pass through. At the same time, suppression (or attenuation) does not need to transmit signals within the frequency range. In practical engineering, it is often used for signal processing, data transmission and interference suppression. At present, it is widely used in communication, sonar, measurement and control, instrumentation and other fields

1 Structure and classification of filter

in the past, this kind of filter circuit was mainly composed of passive components R, l and C. Since the 1960s, integrated operational amplifier has developed rapidly. The active filter circuit composed of it, R and C has the advantages of no inductance, small size, light weight and so on. In addition, because the open-loop voltage gain and input impedance of the integrated operational amplifier are very high, and the output impedance is relatively low, the active filter circuit also has a certain role of voltage amplification and buffer

frequency response is usually used to describe the characteristics of filters. For the amplitude frequency response of the filter, the frequency range of the signal that can pass through is often defined as the passband, while the frequency range of the blocked or attenuated signal is called the stopband, and the limit frequency of the passband and stopband is called the cut-off frequency

the filter should have zero attenuation amplitude frequency response and linear phase response in the passband, and infinite amplitude attenuation in the stopband. According to the position distribution of pass band and stop band, filters are usually divided into low-pass filter, high pass filter, band-pass filter and band stop filter

combined with examples, this paper introduces some problems that should be paid attention to in designing a second-order active analog bandpass filter working in low frequency band

2 design of second-order active analog bandpass filter

2.1 setting of basic parameters

circuit of second-order active analog bandpass filter, as shown in Figure 1. In the figure, R1 and C2 form a low-pass circuit, R3 and C1 form a high-pass circuit, and a, RA and Rb form an in-phase proportional amplification circuit. Together, they form a second-order active analog bandpass filter with amplification effect, which is hereinafter referred to as a second-order bandpass filter

according to figure L, the transfer function of the band-pass filter can be derived as

equation (5) is a typical expression of the transfer function of the second-order band-pass filter, where 0 is called the center angular frequency

let s=j, substituting into equation (4), the frequency response characteristic of the band-pass filter can be obtained as

and its amplitude frequency response curve can be drawn, as shown in Figure 2. In the figure, when = 0, the voltage magnification is the largest. The passband width of the bandpass filter is bw0.7= 0/(2 q) =f0/Q. obviously, the higher the Q value, the narrower the passband

the narrower the passband, the better the frequency selectivity and the stronger the suppression ability. The ideal amplitude frequency characteristic should be a rectangular curve with a width of bw0.7, as shown in Figure 3 (a). A (f) is flat in the passband, while various interference signals outside the passband have infinite suppression ability. Various bandpass filters always strive to approach the ideal rectangular characteristics

however, the amplitude frequency characteristic curve of the actually designed bandpass filter is shown in Figure 3 (b)

in engineering, the difference between the upper and lower limit frequencies when the gain decreases by 3 dB (i.e. 0.707 times) from a (F0) is defined as the passband, represented by bw0.7. Its value is required to be greater than the spectrum width of the useful signal to ensure the undistorted transmission of the signal

to sum up, when the in-phase amplification factor of the active bandpass filter changes, it will affect both the passband gain A0 and the Q value (and then the passband bw0.7), while the center angular frequency 0 has nothing to do with the passband gain A0

2.2 actual circuit design effect electrohydraulic servo universal testing machine clamping drive fault analysis and Troubleshooting Analysis

in order to better understand the application effect of second-order bandpass filter in actual circuit, the circuit shown in Figure 4 is designed for experimental verification. In the figure, U1A part is an amplification circuit, and ULB part is a second-order bandpass filter circuit

according to equations (2) to (4) used in the wear-resistant parts of household appliances, a second-order band-pass filter with a central frequency around 30 kHz, a quality factor Q of 1.55 and a bandwidth of about 19.35 kHz is designed, and the voltage and frequency data produced by the first to fourth cascade are recorded respectively. The recorded results are drawn into a voltage/V ~ frequency/kHz diagram, as shown in Figure 5

as can be seen from Figure 5 (a), with the increase of the number of cascades, a (F0) is gradually increasing, and bw0.7 is also gradually narrowing, indicating that its frequency selectivity is getting better and better, and its ability to suppress interference signals is also getting stronger and stronger

in addition to the cascade can enhance the frequency selection ability of the band-pass filter, this effect can also be achieved by changing the Q value of the quality factor. As we all know, if the quality factor Q is less than 0, the circuit will self oscillate and cannot work normally. It can be seen from Figure 2 that the higher the Q value, the narrower the passband, that is, the better the frequency selectivity of the filter and the stronger the suppression ability of the interference signal, but it is not that the larger the Q value, the better and more stable the circuit. For this purpose, the following experiments were also carried out, that is, according to equations (2) to (4), second-order band-pass filters with the same center frequency (theoretical value) with quality factors Q of 1.55, 2.99 and 7.87 were designed, and their voltage/v ~ frequency/khz diagrams were drawn respectively, as shown in Figure 5 (b)

from Figure 5 (b), it can be found that the larger the Q value of the quality factor, the larger its a (F0) and the narrower bw0.7 are. However, with the increase of Q value, its central frequency is also inclined to the low-frequency end, and the rising slope of the low-frequency end is steep, and the decreasing amplitude of the high-frequency end is slower than that of the low-frequency end. According to the previous analysis, it is not difficult to see that if the Q value is infinite, it will cause the self-excited oscillation of the circuit and cannot work normally. In order to determine this point, the output of two band-pass filters with Q values of 2.99 and 7.87 were also tested without signal input, as shown in Fig. 6 (a) and Fig. 6 (b). It can be seen from the diagrams of the two oscilloscopes that the greater the Q value, the greater the degree of self excitation. When the Q value reaches a certain value, the degree of self excitation is equal to or stronger than the input signal, which will affect the normal operation of the whole circuit

2.3 selection of values

it is worth noting that when designing the circuit, the central frequency of the band-pass filter must be determined first according to equation (3), because there are many components in the second-order band-pass filter, and the interaction is also cumbersome. Determining the center frequency first will greatly simplify the later numerical calculation. For convenience, you can also take r1=r3=r, c1=c2=c, ra=rb=r. If you want to design a band-pass filter with amplification, you can appropriately change the values of RA and RB to the desired amplification factor according to equation (2) or the in-phase amplification factor of the active band-pass filter after determining other values. Here, it is recommended not to change the values of RA and Rb by a large margin at will, because it can be seen from equation (4) that changing RA and Rb after determining other values will affect the Q value, and the size of Q value will directly affect the stability of the working state of the circuit. In addition, the Q value is sensitive to the value of components, so try to select components with high accuracy when selecting components

3 conclusion

although the active filter circuit composed of integrated operational amplifier and R, C has no inductance, small size, light weight, the open-loop voltage gain and input impedance of integrated operational amplifier are very high, and the output impedance is low. After forming the active filter circuit, it also has certain advantages such as voltage amplification and buffering. However, because the Q value of its quality factor cannot be made very large, it leads to that its passband width cannot be made very wide to avoid rust and keep the brightness narrow, resulting in the poor frequency selectivity of the filter and the weak suppression ability of the interference signal. Therefore, when selecting the design filter scheme, we should pay attention to the combination of the actual situation and reasonably select the design scheme of the filter under the condition of meeting the actual requirements