The "Resonance" Phenomenon of Switched Capacitor Filter and Its Countermeasures

The anti-aliasing filter is an important component in the hardware system of the signal processing instrument. According to the requirements of signal division, the cut-off frequency range of the anti-aliasing filter is controlled within 10Hz～20kHz. In order to improve the frequency resolution of the signal, the bandwidth of the anti-aliasing filter is required to be variable. For example, to analyze signal characteristics within 100 Hz, the bandwidth of the low-pass filter is best selected as 100 Hz. When designing, according to the principle of 1, 2, 4, and 5 times multiplication, the 20kHz frequency range is divided into 14 different bandwidths for processing. If a general analog low-pass filter is used, the circuit must be complicated, inconvenient to shift gears, too large, and not very practical. The use of integrated switched capacitor filters has developed rapidly, and there are many production companies, and the devices are now serialized. It is very convenient to change the cutoff frequency, as long as it is close to different sampling frequencies. Therefore, the 8-order switched capacitor elliptical low-pass filter MAX293 is selected as an anti-aliasing filter. In theory, the 8-order low-pass filter is suitable for making anti-aliasing filters. The attenuation after the cut-off frequency is 160dB/10 times the frequency. According to literature (1), if the cut-off frequency is 1kHz, the signal will attenuate at 1.5kHz. 80dB, close to the ideal low-pass filter, which is determined by the characteristics of the elliptical filter. The measured filter map (amplitude-frequency characteristic) also has similar results. However, during the trial production process, it was found that the filter had a "resonance" phenomenon. The following is a trial analysis of this phenomenon.

 

1 The "resonance" phenomenon of switched capacitor filters

 

When testing the amplitude-frequency characteristics of the M AX293 with the NW1232 low-frequency frequency characteristics, it is found that in addition to the expected amplitude-frequency characteristics on the screen, there is a narrow band-pass shape peak at the sampling frequency and its integer multiples, and its height reaches or exceeds The maximum value of the flat part of the previous amplitude-frequency characteristic. In other words, this phenomenon occurs when the input signal frequency is equal to the sampling frequency or an integer multiple of the sampling frequency. This phenomenon has never been reported in the literature. It is temporarily called a "resonance" phenomenon. If it is not processed during use, it will seriously interfere with useful signals. In order to find out the reason, the experiment was repeated. Using methods such as automatic scanning, manual scanning, and scanning after changing the sampling frequency, this phenomenon has always occurred as expected. In order to filter out the "high-frequency interference", after the MAX293 circuit, an analog low-pass filter is connected. However, regardless of whether the two-by-two low-pass or fourth-order low-pass analog filter is connected, the "interference" still exists in its output, and there is no reduction in amplitude.

 

2 Explanation of "resonance" phenomenon

 

Experiments with analog low-pass filters, of course, this phenomenon does not exist. Therefore, the reason must lie in the switched capacitor with the sampling link. In a switched capacitor filter, when the switching frequency (ie sampling frequency, clock frequency) is greater than the signal frequency (reference (2) points out, it is generally greater than 20 times), the switched capacitor is equivalent to the resistance in the analog RC filter , It can be deduced that its equivalent resistance R=1/(C·fc), where C is the capacitance and fc is the switching filter. Through analysis, when the signal frequency and the sampling frequency are the same frequency, the phenomenon shown in Figure 1 will appear.

 

In the figure, the input signal vi is a sine wave (the same is true for a square wave), and 1, 2... are samples of the same frequency. When the phase is appropriate (as shown in Figure 1), the peak of the input signal will appear on the capacitor of the switched capacitor filter. The phase is different, the sampled value is also different, but the value sampled at each sampling point is the same. Therefore, a DC signal is generated on the sampling capacitor to make the wave device output a DC level. When observing the amplitude-frequency characteristics, the above-mentioned so-called "resonance" phenomenon occurs when the input signal and the sampling signal are at the same frequency and have the right phase. And the subsequent low-pass analog filter can't do anything about it. Similarly, when the signal frequency is an integer multiple of the sampling frequency, the same phenomenon will obviously occur.

 

3 Test results

 

In order to confirm the above analysis, the first-order low-pass filter as shown in Figure 2 (a) was used for the test. In the figure, vi is a sine wave input, φ1, φ2 are two-phase pulses as sampling switch signals, and vo is an output signal.

 

Tested on a low-frequency characteristic tester, the frequency fφ of φ1 and φ2 is 10kHz. In addition to the low-pass amplitude-frequency characteristics that turn at nearly 100Hz, peaks appear at 10kHz and 20kHz. Here fφ is the above-mentioned switching frequency fc, and its relationship with the corner frequency of the low-pass filter depends on the ratio of C1 and C2 in Figure 2(a). At this time, the voltmeter is used to measure vo as a DC voltage of 4V, and the input signal value measured by a transistor millivoltmeter is 2.8V. Thus confirming the above analysis.

 

In order to remove the "resonance" phenomenon, the range of the input signal should be limited to be less than the sampling frequency. Therefore, when using an integrated switched capacitor low-pass filter (such as MAX293), an analog low-pass filter must be added in front of it to effectively exclude high-frequency signals at the sampling frequency and above.

4 Practical anti-aliasing filter based on MAX293

 

The integrated switched capacitor filter is small in size, high in order, steep attenuation edge, and very convenient to change the passband width. Therefore, it has a wide range of applications, especially where different bandwidths are required. Its disadvantage is its own switching noise, especially the above-mentioned "resonance" phenomenon. Therefore, when using it, necessary measures must be taken according to different requirements. Now take the use of MAX293 to make an anti-aliasing filter as an example to illustrate.

Among them, the MAX293 and the analog low-pass filters before and after it together form a passband programmable anti-aliasing filter.

 

According to the size of the signal measured and displayed on the interface, use the keyboard on the PC to select the magnification of the range programmable amplifier to obtain a signal with a suitable amplitude. Before and after the AMX293 filter, there are two programmable analog low-pass filters. They have three synchronized programmable corner frequencies. The address is given by the PC and the filter capacitors of different values ​​are switched to achieve. The double second-order programmable analog low-pass filter before the MAX293 filter is used to eliminate the "resonance" phenomenon, and the second-order low-pass filter at the back is used to eliminate the noise caused by the sampling frequency signal fc. Since the MAX293 is divided into 14 gears from 10z to 20kHz, the ratio of its cut-off frequency to the sampling frequency fc is 1:100, so the corner frequency of the analog filter is 100Hz, 1kHz, and 10kHz. They can target fc and above. Harmonic filtering of the signal is excluded. The different cut-off frequencies of MAX293 are obtained by changing fc by the PC. All analog filters are designed as Butterworth filters. Several sets of this hardware system and corresponding software systems have been sold, and passed the appraisal organized by the Machinery Industry Technology Development Foundation in November 2001.