Oversampled SAR ADC with PGA Achieving Greater Than 125 dB Dynamic Range
Figure 1. Wide Dynamic Range Signal Conditioning Circuit with Autoranging PGA and Oversampling SAR ADC (Note: All Connections and Decoupling Not Shown)
Figure 2. Increasing Oversampling Ratio (OSR) Reduces Noise
Oversampling is the process of sampling the input signal at a much higher rate than the Nyquist frequency. As a general rule, every doubling of the sampling frequency yields approximately a 3 dB improvement in noise performance within the original signal bandwidth. The oversampling ADC is followed by digital post-processing to remove the noise outside the signal bandwidth, as shown in Figure 2.
To achieve maximum dynamic range, a front-end PGA stage can be added to increase the effective signal-to-noise ratio (SNR) for very small signal inputs. Consider a system dynamic range requirement of >126 dB. First, calculate the minimum rms noise required to achieve this dynamic range. For example, a 3 V input range (6 V p-p) has a 2.12 V full-scale rms value (6/2√2). The maximum allowable system noise is calculated as
126 dB = 20 log (2.12 V/rms noise)
Thus, the rms noise ≈ 1 µV rms.
Now, consider the system update rate, which will determine the oversampling ratio and the maximum amount of noise, referred to the input (RTI), that can be tolerated in the system. For example, with the AD7985 16-bit, 2.5 MSPS PulSAR ADC running at 600 kSPS (11 mW dissipation) and an oversampling ratio of 72, the effective throughput rate of the system after averaging and decimation is 600 kSPS ÷ 72 = 8.33 kSPS. The input signal is therefore limited to a bandwidth of approximately 4 kHz.
The total rms noise is simply the noise density (ND) times √f, so the maximum allowable input spectral noise density (ND) can be calculated as
1 µV rms = ND × √4 kHz
Or, ND = 15.8 nV/√Hz.
From this figure of merit for RTI system input noise, a suitable instrumentation amplifier can be chosen that will provide sufficient analog front-end gain (when summed with the SNR of the ADC, with associated oversampling) to achieve the required 126 dB. For the AD7985, the typical SNR figure is 89 dB, and oversampling by 72 yields another ~18 dB improvement (72 is approximately 26, and each doubling adds 3 dB). Achieving 126 dB DR still requires more than 20 dB improvement, which can come from the gain provided by the analog PGA stage. The instrumentation amplifier must provide a gain of ≥20 (or whatever will not exceed a noise density specification of 15.8 nV/√Hz).
A system-level solution to implement front-end PGA gain and ADC oversampling as discussed above is shown in Figure 1. The input stage uses the AD8253 very low noise 10 nV/√Hz digitally controlled instrumentation amplifier. Gain options are the following: G = 1, 10, 100, 1000.
The AD8021 is a 2.1 nV/√Hz low noise, high speed amplifier capable of driving the AD7985. It also level shifts and attenuates the AD8253 output. Both the AD8253 and AD8021 are operated with an external common-mode bias voltage of 2.25 V, which combine to maintain the same common-mode voltage on the input to the ADC. With a 4.5 V reference, the input range of the ADC is 0 V to 4.5 V.
Figure 3. Test Setup Used to Measure Performance of System
The output of the AD8021 is measured using a high speed ADC. The PGA gain can be dynamically set based on the amplitude of the input signal. For small signal inputs, a gain of 100 is programmed. For larger inputs, the gain is reduced to 1.
Digital post-processing is implemented using the AD7985 16-bit, 2.5 MSPS PulSAR ADC (11 mW dissipation) in a QFN package, which, by virtue of its fast sampling rates, can also be used to implement high orders of oversampling for low input bandwidth applications. Since the complete system noise budget is 15.8 nV/√Hz maximum, referred to the input (RTI), it is useful to calculate the dominant noise sources of each block to ensure that the 15.8 nV/√Hz hard limit is not exceeded. The AD8021 has an input-referred noise specification of <3 nV/√Hz, which is negligible when referred back to the input of the gain-of-100 AD8253 stage. The AD7985 has a specified SNR of 89 dB, using an external 4.5 V reference, for a noise resolution of <45 µV rms.
Considering the Nyquist bandwidth of 300 kHz for the ADC, it will contribute ~83 nV/µHz across this bandwidth. When referred back to the input of the AD7985, its <1 nV/√Hz noisewill be negligible in the system, where the RTI noise sources are summed using a root-sum-of-squares calculation.
A further benefit of using the AD8253 is that it has digital gain control, which allows the system gain to be dynamically changed in response to changes in the input. This is achieved by intelligently using the system’s digital signal processing capability. The main function of digital processing in this application is to produce a higher resolution output, using the AD7985 16-bit conversion results. This is achieved by averaging and decimating the data and switching the analog input gain automatically, depending on the input amplitude. The oversampling process results in a lower output data rate than ADC sample rate, but with a greatly increased dynamic range.
To prototype the digital side of this application, a field-programmable gate array (FPGA) was used as the digital core. To rapidly debug the system, the analog circuitry and the FPGA were consolidated onto a single board using the system demonstration platform (SDP) connector standard to allow easy USB connectivity to the PC, as shown in Figure 3. The SDP is a combination of reusable hardware and software that allows easy control of and data capture from hardware over the most commonly used component interfaces.
This module outputs a new gain setting based on the current gain setting, two raw ADC samples, and some hard-coded threshold figures. Four thresholds are used in the system. The selection of these thresholds is critical to maximizing the analog input range of the system, ensuring the G = 100 mode is used for as much of the signal range as possible, while also preventing the ADC input from being overdriven. Note that this gain block operates on every raw ADC result, not on data that has been normalized. Bearing this in mind, an illustrative example of some thresholds that could be used in a system such as this (assuming a bipolar system with a mid-scale of zero):
When in the G = 1 mode, the inner limits, T1 and T2, are used. When an actual ADC result is between T1 and T2, gain is switched to the G = 100 mode. This ensures that the analog input voltage that the ADC sees is maximized as quickly as possible. Then in the G = 100 mode, the outer limits, T3 and T4, are used. If an ADC result is predicted to be above T3 or below T4, the gain is switched to the G = 1 mode to prevent the input of the ADC from being overranged, as shown in Figure 4.
Figure 4. The Gain from the Amplifier Input to the Converter Input Is Reduced by 100 When the Analog-to-Digital Converter Input Is Predicted to Be Outside the Threshold Limits (Blue Line: Amplifier Input; Red Line: Converter Input.)
When in the G = 100 mode, if the algorithm predicts that the next ADC sample would be just outside the outer threshold (using a very rudimentary linear prediction), giving an ADC result of +32510, the gain is switched to G = 1, so that, instead of +32510, the next ADC result is +325.
Performance of the Full System
With fully optimized gain and decimation algorithms, the full system is ready to be tested. Figure 5 shows the system response to a large signal 1 kHz input tone of –0.5 dBFS. When the PGA gain of 100 is factored in, the dynamic range achieved is 127 dB. Similarly, when tested for small signal inputs in Figure 6, with an input tone of 70 Hz @ –46.5 dBFS, up to 129 dB of dynamic range is achieved. The improvement in performance at the smaller input tone is expected, as no active switching of gain ranges occurs during this measurement.
Figure 5. Response to Large-Scale 1 kHz Signal Showing 127 dB Dynamic Range
Figure 6. Response to 70 Hz Small-Scale Input Signal
The system’s performance relies on the ability to switch the gain dynamically to handle both small- and large-signal inputs. While sigma-delta technology provides excellent dynamic range, the SAR-based solution offers a way to dynamically change the front-end gain based on the input signal, without compromising system performance. This allows both small-signal and large-signal ac and dc inputs to be measured in real time without waiting for system settling time or incurring large glitches due to delayed gain changing.
It is important to use a low noise, low distortion signal source for the input, such as an Agilent 33120A, Audio Precision System Two 2322, or equivalent.
|ADR439||Ultralow Noise XFET® 4.5V Voltage Reference w/Current Sink and Source Capability|
|AD8021||Low Noise, High Speed Amplifier for 16-Bit Systems||
|AD8253||10 MHz, G = 1, 10, 100, 1000 iCMOS® Programmable Gain Instrumentation Amplifier||
|AD7985||16-Bit, 2.5 MSPS PulSAR 11 mW ADC in QFN||
|ADA4004-2||1.8nV/√Hz, 36 V Precision Dual Amplifier||