Welcome back to the ADAQ798x ADC driver configuration blog series! Today, we’ll conclude this series with an overview of the Sallen-Key active low-pass filter topology for the ADAQ798x. This configuration is one of the simpler active filtering implementations, and allows the ADAQ798x to maximize performance even when interfacing with noisy input sources and sensors.

**Sallen-Key Low-Pass Filter**

The Sallen-Key topology can be used to configure the ADAQ798x’s ADC driver as an active, two-pole, low-pass filter. This configuration is relatively simple, since the ADC driver is set in a simple non-inverting configuration, so the filter doesn’t directly impact its performance and bandwidth (see ADI’s Linear Circuit Design Handbook). The implementation of the low-pass filter requires two resistors (R_{1} and R_{2}) and two capacitors (C_{1} and C_{2}) to set the filter cut-off, and an optional two resistors (R_{f} and R_{g}) to add signal gain:

The configuration can be thought of as cascading a -40 dB/decade filter followed by a gain stage:

The values of R_{1}, R_{2}, C_{1} and C_{2} determine the filter’s shape and response. For this blog post we’ll focus on a configuration where R_{1} = R_{2} and C_{1} = C_{2}. This combination results in a filter with a Q factor of 0.5, and behaves similarly to two equivalent RC low-pass filters in series. The frequency response for this case is:

Assuming R_{1} = R_{2} = R and C_{1} = C_{2} = C, the filter corner frequency is given by:

At the corner frequency f_{c}, the response of the filter is roughly -6 dB from its dc gain. The dc gain of the filter is given by the non-inverting gain relationship we saw in previous posts:

This configuration can reduce out-of-band noise from the signal source, sensor, or other analog front-end circuitry. If these pieces of the signal chain feature significantly more noise than the components included in the ADAQ798x, and the signal bandwidth is small compared to the Nyquist rate of the ADC, then using this configuration can help improve the system noise performance. The rms voltage noise from a source connected to the filter input (v_{n rms}) is:

where e_{in} is the noise spectral density from the input source, A_{V} is the gain of the ADC driver (shown above), and f_{ENBW} is the effective noise bandwidth of the filter. This assumes that the active filter cutoff frequency is significantly lower than that of the ADAQ798x’s integrated RC filter (which will virtually always be the case). f_{ENBW} for the filter described above is simply:

The filter cutoff frequency can be selected near the maximum input frequency required for the application to maximize noise reduction. Let’s look at an example to see how this configuration can improve system noise performance.

For a system with an input noise spectral density of 500 nV/√Hz, and a signal gain of 1, what would the cutoff frequency (f_{c}) need to be to make sure the input source contributes no more than 100 μV rms noise to the system? Solving for f_{c} in the equation used above gives:

Using R_{1} = R_{2} = 1.2 kΩ and C_{1} = C_{2} = 2.7 nF can be used to achieve a filter cutoff close to this (~49 kHz).

**Closing Thoughts**

Today, we looked at a simple implementation of an active, 2-pole low-pass filter using the ADAQ798x’s integrated ADC driver. This is one of many potential configurations that can be used for achieving active filtering with the ADAQ798x.

System noise performance can be further improved by combining active filtering with oversampling and decimation. Oversampling and decimation is a form of digital filtering, where a certain number of consecutive samples are averaged together to reduce out-of-band noise at the expense of signal bandwidth (see this article for more information).

One thing to keep in mind when designing an active filter is the flatness of the filter’s pass band. Many filters exhibit some deviation in the pass band, especially if they result in resonance or peaking at a certain frequency. When deciding on and designing an active filter topology, be aware of the application’s required gain flatness across the bandwidth of interest.

Thanks again for joining me for this last entry in our blog series about alternate configurations for the ADAQ798x’s integrated ADC driver! Hopefully you’re now equipped to begin taking advantage of the device’s flexible analog front-end for your application!

Have any questions? As always, feel free to ask in the comments section below!