Matching the amp to the ADC

Engineers frequently use operational amplifiers to drive ADCs because of their low output impedance. In this role, an amplifier isolates impedances in the signal chain. You can add other features, such as gain and filtering, around the amplifier to give it a multitasking flavor. At a high level, these features are easy to understand, but it's important to remember the basics. Regardless of the features you put around your amplifier, how do you know that the device you choose will preserve the integrity of the signal as it travels through the amplifier/ADC combination?

One critical performance issue in this type of signal chain is noise. If the amplifier is too noisy, the ADC will reliably convert the noise from the amplifier circuit to the digital output. On the other hand, an ADC can be noisier than the amplifier circuit. Choosing an extremely low-noise amplifier without evaluating the system is like spending too much money for an SUV when you should have chosen a simple sedan. By using a few tricks in your calculations, such as taking advantage of your frequency range and the square root of the sum-of-the-squares formula, you can quickly determine the compatibility of your amplifier/ADC combination.

Because noise is a statistical phenomenon, you can get only an estimate as to whether it will be a problem. The example in Figure 1 uses a 12-bit ADC with an SNR typical specification of 73.2 dB and an amplifier with a typical voltage-noise specification of e_n=30 nV/ at 10 kHz. The amplifier circuit is part of a 100-kHz, second-order lowpass filter with a gain of 50V/V. These factors are all you need to reach a productive conclusion.

Note that the amplifier circuit has only an RTI (referred-to-input) specification for noise. You can calculate the output noise of the amplifier from dc to 100 kHz through rigorous methods, but in this circuit, the higher frequency noise dominates the output noise. With that scenario in mind, the following simple calculation generates an estimate of the op-amp RTO (referred-to-output) noise:

Amp noise (RTO)=G·e_n·, where G is 50V/V, e_n is 30 nV/, and BW (bandwidth) is 100 kHz. From this formula, amp noise (RTO) is 474 µV rms.

Further, using that formula, you can now calculate the SNR at the output of the amplifier:

SNR=20 log₁₀ ((signal rms)/(noise rms)); thus, SNR (op amp)=20 log₁₀ ((FSR/2)/(amp noise (RTO)); thus, when FSR (full-scale range) is 5V, SNR (op amp) is 71.4 dB.

Now you can determine the total noise of the system by using the op-amp SNR and the ADC SNR and applying the theorem of taking the square root of the sum of the squares in the following formula:

SNR (total)=–20 log₁₀·, or SNR (total) is 69.21 dB.

You have lost nearly 1 bit in this system because of the noise in the amplifier. Taking the circuit to the bench proves this situation.

With the devices in the circuit, the SNR performance is always equal to or less than the lowest value. Given this interaction between the amplifier and the ADC, picking a lower noise amplifier gives the best results. For instance, if you use an amplifier with a typical voltage-noise specification of e_n=15 nV/ at 10 kHz, the total SNR is 71.8 dB. In contrast, if you use a 13-bit ADC instead of a 12-bit ADC with an SNR of 78.5 dB, the total SNR is 70.6 dB.

To be sure, other factors have an effect on your amplifier selection, but amplifier noise could have a significant effect on your digital-code outcome. Determining the potential noise in a circuit is always a daunting challenge, but you can apply some general rules of thumb to overcome these problems. Use the circuit's frequency range to your advantage in the calculations, and, when you combine noise sources, use square root of the sum-of-the-squares equations.