8.1.1 Filter Usage

The modulator generates only a bitstream, which does not output a digital word like an A/D converter. In order to output a digital word equivalent to the analog input voltage, the bitstream must be processed by a digital filter.

A very simple filter, built with minimal effort and hardware, is the sinc³ filter shown in Equation 2:

Equation 2.

This filter provides the best output performance at the lowest hardware size (for example, a count of digital gates). For oversampling ratios in the range of 16 to 256, this is a good choice. All the characterizations in the data sheet are also done using a sinc³ filter with an oversampling ratio of OSR = 256 and an output word width of 16 bits.

In a sinc³ filter response (see Figure 32 and Figure 33), the location of the first notch occurs at the frequency of output data rate f_DATA = f_CLK / OSR. The –3-dB point is located at half the Nyquist frequency or f_DATA / 4. For some applications, it may be necessary to use another filter type for better frequency response.

Figure 32. Frequency Response of Sinc³ Filter

Figure 33. Pulse Response of Sinc³ Filter
(f_MOD = 10 MHz)

This performance can be improved, for example, by a cascaded filter structure. The first decimation stage can be a sinc³ filter with a low OSR and the second stage a high-order filter.

For more information, see the Combining the ADS1202 with an FPGA Digital Filter for Current Measurement in Motor Control Applications application note, available for download at www.ti.com.

The effective number of bits (ENOB) can be used to compare the performance of A/D converters and ΔΣ modulators. Figure 34 shows the ENOB of the ADS1204 with different filter types. In this data sheet, the ENOB is calculated from the SNR as shown in Equation 3:

Equation 3.

Figure 34. Measured ENOB vs OSR

In motor control applications, a very fast response time for overcurrent detection is required. There is a constraint between 1 µs and 5 µs with 3 bits to 7 bits resolution. The time for full settling is dependent on the filter order. Therefore, the full settling of the sinc³ filter needs three data clocks and the sinc² filter needs two data clocks. The data clock is equal to the modulator clock divided by the OSR. For overcurrent protection, filter types other than sinc³ might be a better choice. A simple example is a sinc² filter. Figure 35 compares the settling time of different filter types. The Sincfast is a modified sinc² filter as Equation 4 shows:

Equation 4.

Figure 35. Measured ENOB versus Settling Time

For more information, see the Combining the ADS1202 with an FPGA Digital Filter for Current Measurement in Motor Control Applications application note, available for download at www.ti.com.