Welcome back to the ADAQ798x ADC driver configuration blog series! In our last post, we looked at a modification to the non-inverting configuration for bipolar inputs within the range of ±V_{REF}, but wasn’t compatible with signals larger than that. Today, we’ll look at a configuration that introduces another slight modification that enables the ADAQ798x to convert larger bipolar signals (±10 V, for example). We’ll first see how to select the relevant resistances to achieve a desired input range, and then look at how these values affect the system’s input impedance and noise floor.

**The Non-inverting Summing Configuration for Attenuation**

The following configuration can be used to perform bipolar-to-unipolar conversion with attenuation for signals larger than ±V_{REF}.

This configuration is similar to the one we discussed last time, except R_{f} and R_{g} are no longer required and R_{3} is added to provide extra signal attenuation. The transfer function for this configuration is:

The math required to derive the ratios of R_{1} to R_{2} to R_{3} is a bit more complicated this time, but we can use a similar method as we did in the previous configuration. After finding the ratios of the resistors, one can select specific values depending on the needs of the application. In the interest of brevity, we won’t go through every step of the derivation, but we’ll see how transfer function simplifies to give us the resistor ratios when looking at the minimum and maximum values of v_{IN}.

The ratio of R_{1} to R_{2} is found using the configuration’s transfer function by plugging in the minimum value of v_{IN}, which results in v_{AMP_OUT} equal to 0 V:

R_{3} drops out of the equation, and solving for R_{1} and R_{2} gives:

The ratio of R_{1} to R_{3} is found by plugging in the maximum value of v_{IN}, which results in v_{AMP_OUT} equal to V_{REF}:

This time, R_{2} drops out and solving for R_{1} and R_{3} gives:

At this point, we can pick a value for any three of these resistors (given V_{REF} and the range of v_{IN}) and then calculate the value of the other two. As before, the major trade-offs are input impedance vs. system noise and offset error. The input impedance (Z_{IN}) of this circuit is:

Let’s revisit the example we mentioned last time, where v_{IN} = ±10 V and V_{REF} = 5 V, and design the configuration with an input impedance of 1 MΩ. For this combination of v_{IN} and V_{REF}, R_{1} must be twice R_{2} and equal to R_{3}. Using the ratios of R_{2} and R_{3} to R_{1} in the input impedance equation, we get R_{1} = 750 kΩ. R_{2} and R_{3} are therefore 375 kΩ and 750 kΩ, respectively.

As we mentioned in "Adding Gain for Bipolar Inputs", there is a trade-off between input impedance and system noise performance. Achieving a high input impedance requires large resistors, which produce more thermal noise and interact with the input current noise of the ADC driver to create more input voltage noise. Both of these increase the effective rms voltage noise at the input of the ADC, which can dramatically degrade performance. In the above example, the total system noise is roughly 334 μV rms (with a 5 V reference, dynamic range drops a whole 15.5 dB, from 92 dB to 74.5 dB)!

But there’s hope! This configuration can actually achieve near optimal performance if we limit its input bandwidth. For instance, if we limit the input bandwidth in the above example to 20 kHz, the full system noise drops by almost a factor of ten to 48 μV rms (a dynamic range of 91.4 dB for V_{REF} = 5 V)! We can limit the input bandwidth (BW_{in}) by adding a shunt capacitor C_{S}, as shown below. Note that for these noise calculations, we can treat R_{1}, R_{2}, and R_{3} as a single resistor, R_{S}, where R_{S} is the parallel combination of R_{1}, R_{2}, and R_{3}.

MT-049 shows how to calculate the noise created by R_{S} (including thermal noise and its interaction with the ADC driver’s input current). The main difference for the ADAQ798x is that the noise bandwidth is set by the integrated RC filter (rather than the amplifier bandwidth, as it is in the tutorial). The rms noise that R_{S} adds at the input to the ADC is:

(e_{n }is the Johnson noise of R_{S }and G is the ADC driver gain.)

C_{S} reduces the noise that reaches the ADC by reducing the bandwidth at the ADC driver’s input. If the cutoff frequency of R_{S} and C_{S} is much smaller than that of the integrated RC filter’s (4.42 MHz), then the noise contributions from R_{S} can be calculated using R_{S} and C_{S} in place of R and C in the above equation.

The total system noise is the root-sum-square of the individual noise sources in the ADAQ798x, including those from R_{S}, the ADC driver’s input voltage noise, and the ADC’s RMS noise. The following plot shows the system noise vs. the input bandwidth for several values of R_{S}.

Note that as input bandwidth decreases, the full system noise tends towards the ADAQ798x’s total rms noise (44.4 μV rms). This means that noise benefits of reducing the bandwidth give diminishing returns at a certain frequency, which depends on the effective value of R_{S}.

**Closing Thoughts:**

In today’s post, we looked at an ADC driver configuration that allows the ADAQ798x to accept bipolar inputs that are larger than ±V_{REF}, and how to calculate the input impedance and system noise based on the resistor values (and with an optional shunt capacitor C_{S}).

Although adding C_{S} proved to reduce noise, it also limits the usable input bandwidth. For this reason, it’s often impractical to achieve a high input impedance when using this configuration for wide bandwidth applications. This configuration is typically only recommended for low bandwidth applications that require high input impedance. (If your application requires wide bandwidth, be sure to tune in to our next post!)

Thanks again for joining me in this blog series! In our next entry, we will be stepping away from the non-inverting configurations we’ve discussed to this point to look at a difference amplifier configuration for bipolar inputs. Follow the EngineerZone Spotlight to be notified when the next addition to this series is available!

Have any questions? Feel free to ask in the comments section below!