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Data acquisition


Noise analysis of precision data acquisition signal chain


I


n many applications, the analogue front end takes either a single-ended or differential signal and performs gain or attenuation, antialiasing filtering, and level shifting as required and then drives the inputs of the ADC at the full-scale level. This article from Analog Devices gives insight into noise analysis of the precision data acquisition signal chain and takes a deep dive to figure out the overall noise contribution from this signal chain. As shown in Figure 1, the low power, low


noise, fully differential amplifier, ADA4940-1, drives the differential inputs of the AD7982, 18- bit, 1 MSPS PulSAR ADC, while the ADR435, low noise, precision 5 V reference is used to supply the 5 V needed for the ADC. This signal chain eases analogue signal conditioning by eliminating the need for an extra driver stage and reference buffer, which results in board space and cost savings. A single-pole, 2.7 MHz, RC (22 Ω, 2.7 nF) low-pass filter is placed between the ADC driver output and the ADC inputs to help limit the noise at the ADC inputs and reduce the effect of kickbacks coming from the capacitive DAC input of a successive approximation register (SAR) ADC. When used as an ADC driver, the ADA4940-


1 allows the user to do the necessary signal conditioning, including level shifting and attenuating or amplifying the signal for more dynamic range using four resistors. This eliminates the need for an extra driver stage. The ratio of feedback resistors (R2 = R4) to gain resistors (R1 = R3) sets the gain, where R1 = R2 = R3 = R4 = 1 kΩ. For a balanced differential input signal, the


effective input impedance would be 2× the gain resistor (R1 or R3) = 2 kΩ, and for an unbalanced (single-ended) input signal, the effective impedance would be approximately 1.33 kΩ using the equation


A termination resistor in parallel with the input can be used if required. The ADA4940-1 internal common-mode


feedback loop forces common-mode output voltage to equal the voltage applied to the VOCM input and offers an excellent output balance. The differential output voltage depends on VOCM when two feedback factors β1 and β2 are not equal and any imbalance in output amplitude or phase produces an undesirable common-mode component in the output and causes a redundant noise and offset in the differential output. Therefore, it is imperative that the combination of input source impedance and


38


Figure 1. Low power, fully differential, 18-bit, 1 MSPS data acquisition signal chain (simplified schematic: all connections and decoupling not shown)


R1 (R3) should be 1 kΩ in this case (that is, β1 = β2) to avoid the mismatch in the common- mode voltage of each output signal and prevent the increase in common-mode noise coming from the ADA4940-1. As signals travel through the traces of a


printed-circuit board (PCB) and long cables, system noise accumulates in the signals and a differential input ADC rejects any signal noise that appears as a common-mode voltage. The expected signal-to-noise ratio (SNR) of this 18-bit, 1 MSPS data acquisition system can be calculated theoretically by taking the root sum square (RSS) of each noise source— ADA4940-1, ADR435, and AD7982. The ADA4940-1offers low noise performance of typically 3.9 nV/√Hz at 100 kHz as shown in Figure 2.


The noise gain of the differential amplifier is:


where and


are two feedback factors. The following differential amplifier noise sources should be taken into account: Since the ADA4940-1 input voltage noise is


3.9 nV/√Hz, its differential output noise would be 7.8 nV/√Hz. The ADA4940-1 common-mode input voltage noise (eOCM) is 83 nV/√Hz from the data sheet, so its output noise would be


Noise from the R1, R2, R3, and R4 resistors can be calculated based on the Johnson-Nyquist noise equation for a given bandwidth:


where kB is the Boltzmann constant (1.38065 × 10 – 23 J/K), T is the resistor’s absolute temperature in Kelvin, and R is the resistor value in ohms (Ω).


The noise from the feedback resistors would be


Figure 2. ADA4940 input voltage noise spectral density vs. frequency


It is important to calculate the noise gain of


the differential amplifier in order to find its equivalent output noise contribution.


November 2018 Instrumentation Monthly The noise from the R1 would be


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