Three guiding principles for designing anti-aliasing Filters (reproduced)

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Anti-aliasing filters are designed with an oversampling architecture and a complementary digital decimation filter. The oversampling architecture places the quest frequency away from the signal bandwidth, while the digital decimation filter attenuates most harmful out-of-band signals. When combined, they enable more free antialiasing filter responses, which can be achieved with just a few discrete components.

Figure 1: Use an appropriate antialiasing filter to block these aliasing

We know that it is useful to use antialiasing filters in high-precision ADC applications, but it is equally important to design an appropriate antialiasing filter-if you are not careful, it is easy to introduce harmful errors into your system as if you were to eliminate the harmful errors from the system. When designing antialiasing filters for your application, consider the following 3 general guidelines:

1. Select your filter cutoff frequency

The simplest antialiasing filter is a unipolar, low-pass filter, shown in 2, which uses a series resistor (R) and a common mode capacitor (CCM). The first step in designing this filter is to select the desired cutoff frequency, FC. On the FC, the response of the filter is rolled down to -3db, and the frequency range continues to be reduced by the speed of the -20db/10 times octave.

Select a cutoff frequency that is at least 10 times times lower than the ADC modulator sampling frequency, which is designed to suppress out-of-band noise at 10 times or more fMOD at these frequencies. For increased attenuation, the cutoff frequency is further reduced by increasing the values of R and CCM. As I mentioned in my previous article, the purpose of your digital decimation filter is to provide help, so it is not necessary to set your antialiasing filter cutoff frequency immediately after the desired signal bandwidth.

Equation 1 calculates the cutoff frequency for a unipolar, low-pass filter of -3db:

Figure 2. Single-pole, low-pass filter on ADC inputs

Sometimes a single-pole, low-pass filter may not be enough. Applications such as vibration sensing may be using less oversampling to analyze signals on wider bandwidths. This makes the bandpass of the digital decimation filter closer to the Fmod, and makes the anti-aliasing filter's roll-down space smaller. In these cases, you can add a second or third pole with additional RC pairs to achieve a more sensitive filter response.

The response of the unipolar and bipolar filters designed for the ADC is shown in Figure 3, and the ADC samples the input on fmod = 1MHz. The Bipolar filter Flat pass band extends outward to approximately 20kHz, and still achieves -60db attenuation on 1MHz.

Figure 3: Frequency response of a unipolar and bipolar low-pass filter

2. Consider the relationship between differential and co-mode filters

Many ADCs convert voltages between two independent inputs, such as INP and inn, so designers often put a common-mode filter on each input to maintain system common-mode rejection (CMR). However, the component tolerance will cause any two filters to be mismatched and will degrade the CMR performance over the frequency range because of the different filtering operations for the common signal. This creates a differential signal error through a common-mode-to-differential conversion known to the people.

Equation 2 uses resistor tolerances, rtol, and capacitor tolerances, CTOL, to calculate the CMR of a common-mode antialiasing filter at a specified frequency:

For applications requiring high CMR, as shown in 4, consider adding a differential filter to complement the 2 common-mode filters. By increasing the differential capacitor cdiff to 10 times times larger than the CCM, the differential cutoff frequency is set to 10 times times lower than the common-mode cutoff frequency. This reduces the errors introduced by the mismatch of the common modules and generates a more sensitive overall filter response. Equation 3 calculates the cutoff frequency of the differential low-pass filter. It is important to note that there is an additional factor of 2 in the denominator.

Figure 4: A common-mode filter with a differential filter added

3. Select the appropriate component value

Adding resistors to the signal path will introduce harmful noise and errors into the measurement, so it is necessary to control them to a reasonable extent whenever they are needed.

Resistor noise-Also known as Johnson or thermal noise-can be modeled as a voltage source in tandem with your ideal "noise-free" resistor. In general, you do not want the thermal noise of the resistor to occupy the entire signal chain, so it is important to keep it below the noise floor of the ADC. Equation 4 Calculates the noise density of the resistor's thermal noise, VN:

Here, K = Boltzmann constant (1.38E-23 j/k), and T is the temperature value, in Kelvin.

The series resistor also introduces a small offset voltage when the input bias current occurs. Although you may be able to calibrate this value later, it is important to limit the size of the resistor as much as possible, especially if the bias current is likely to become large.

Unlike filter resistors, the higher the value of the capacitor you can use, the better the effect. To understand why, it is important to know how the ADC samples the input.

Incremental-Additive ADC inputs that do not include an integrated buffer are directly connected to the switching capacitor sampling structure of the ADC modulator. This sampling structure includes a switching network and a sampling capacitor with a capacitance value of approximately 10pF or 20pF. Figure 5 shows a simplified example.

Figure 5. Simplified switching capacitor sampling structure in one ADC

During sampling, the switching capacitor circuit places a transient load on the external circuit. This filter capacitor helps reduce sample charge injection from the modulator and provides some instantaneous current required for the sampling capacitor, csample, charging. The larger the filter capacitor, the more charge is available. Due to its high Q factor, low temperature coefficient, and stable electrical characteristics, use a ceramic capacitor of the np0/c0g type. Larger capacitor values also improve AC specifications such as total harmonic distortion (THD), but keep in mind that this increases the RC time constants of the filter and requires a longer settling time.

I hope these 3 guiding principles have made you ready for the next antialiasing filter design.

Three guiding principles for designing anti-aliasing Filters (reproduced)