Sigma-Delta ADC Application Brief

This application note is intended to help designers optimize the connection circuits between industrial sensors and high-performance ADCs in high-performance, multichannel data acquisition systems (DAS). Taking a power grid monitoring system as an example, this article explains the advantages of using the MAX11040 Σ-Δ ADC and how to select the appropriate architecture and peripheral components to optimize system performance.

introduction

In many high-end industrial applications, a high-performance data acquisition system (DAS) needs to provide appropriate interface circuits with various sensors. If the signal interface requires multi-channel, high-precision amplitude and phase information, these industrial applications can take advantage of the high dynamic range, simultaneous sampling, and multi-channel advantages of ADCs such as the MAX11040. This article introduces the MAX11040's Σ-Δ architecture and how to properly select the design architecture and external components to achieve the best system performance.

Advantages of High-Speed, Sigma-Delta Architecture

Figure 1 shows a high-end three-phase power line monitoring/measurement system. This type of industrial application requires accurate multi-channel simultaneous data acquisition with a dynamic range of up to 117dB and a sampling rate of 64ksps. In order to obtain the highest system accuracy, the signals from the sensors (for example, the CT and PT transformers in Figure 1) must be properly processed to meet the requirements of the ADC input range, thereby ensuring that the performance indicators of the DAS meet the requirements of relevant standards in different countries.

Figure 1. MAX11040-based DAS in power grid monitoring applications.

As can be seen from Figure 1, two MAX11040 ADCs can simultaneously measure the voltage and current of the three phases and the zero phase of the AC power. The ADC is based on the Σ-Δ architecture and uses oversampling/averaging processing to obtain higher resolution. Each ADC channel uses its proprietary capacitive switch Σ-Δ modulator for analog/digital conversion. The modulator converts the input signal into a low-resolution digital signal, and its average value represents the quantized information of the input signal. The corresponding sampling rate is 3.072Msps when the clock frequency is 24.576MHz. The data stream is sent to the internal digital filter for processing to eliminate high-frequency noise. After processing, a resolution of up to 24 bits can be obtained.

The MAX11040 is a 4-channel simultaneous sampling ADC. Its output data is a processed average value. These values ​​cannot be regarded as the values ​​of the sampling "instant" like the output of a successive approximation register (SAR) ADC¹,².

The MAX11040 can provide designers with many functions and features that the SAR architecture does not have, including: a dynamic range of up to 117dB at a sampling rate of 1ksps; integral nonlinearity and differential nonlinearity (INL, DNL) are also far superior to SAR ADCs; the unique sampling phase (sampling point) adjustment can internally compensate for the phase offset introduced by external circuits (drivers, transformers, input filters, etc.).

In addition, the MAX11040 integrates a digital lowpass filter to process the data stream generated by each modulator to obtain noise-free, high-resolution data output. This lowpass filter has a complex frequency response function, which depends on the programmable output data rate. The resistor/capacitor (RC) filter at the input end combined with the MAX11040's digital lowpass filter greatly simplifies the design of the MAX11040 input signal path antialiasing filter, and can even completely eliminate the antialiasing filter. Table 1 lists some of the features of the MAX11040. For detailed information about the MAX11040 digital lowpass filter or the characteristics listed in the table, please refer to the device data sheet.

Table 1. Key specifications for the MAX11040 ADC Part Channels Input range (VP-P) Resolution (Bits) Speed ​​(ksps, max) SINAD (1ksps) (dB) Input impedance

MAX110404±2.22464117High, (130kΩ, approx)

ADC performance requirements for power line applications

In power-line monitoring applications, the output range of CT (current) transformers and PT (voltage) transformers is typically ±10V or ±5V peak-to-peak (VP-P). The input range of the MAX11040 is ±2.2VP-P, which is lower than the typical output of CT and PT transformers. However, a simple, low-cost solution can be used to adjust the ±5V or ±10V transformer output to the lower input range of the MAX11040, as shown in Figure 2.

The circuit connected to Channel 1 represents a single-ended design. In this configuration, one end of the transformer is grounded and signal conditioning is accomplished using a simple resistor divider and capacitors.

For applications where common-mode noise (noise with the same amplitude at both ADC inputs) is a serious problem, a differential connection circuit as shown in channel 4 is recommended. The true differential input of the MAX11040 greatly reduces the impact of common-mode noise.

Figure 2. The block diagram of the MAX11040 in a typical power-line monitoring application shows a transformer interface with ±10V or ±5V outputs. The interface circuit for channel 4 is a differential design, while the interface circuit for channel 1 is a single-ended design.

The PT and CT measurement transformer is equivalent to a low-resistance mutual inductor (the equivalent impedance RTR is usually in the order of 10Ω to 100Ω). For the convenience of calculation, it is assumed in the following examples that the transformer is equivalent to a voltage source with an effective output resistance RTR = 50Ω; for the sake of demonstration, the transformer can be replaced by a low-distortion function generator with a 50Ω output impedance, as shown in Figure 3. The input impedance of the MAX11040 is related to the clock rate and the ADC input capacitance. Connecting an appropriate bypass capacitor C3 and setting the XIN clock frequency = 24.576MHz, the input impedance RIN is equal to 130kΩ ±15%, and the error depends on the fluctuation of the internal input capacitance.

The resistor divider network composed of R1 and R2 converts the ±10V or ±5V input signal to the ±2.2V full-scale range (FSR) required by the ADC. To ensure that the circuit works properly, the resistor values ​​of R1 and R2, as well as the selection of capacitors C1, C2, and C3, need to be optimized to meet the ±10V or ±5V input requirements. Resistors R1 and R2 must have high enough impedance to avoid overloading the CT and PT transformer outputs. At the same time, the resistance of R2 must be small enough to avoid affecting the input impedance of the ADC (R2 << RIN).

For a single-ended design, the input voltage VIN(f) of Channel 1 of the MAX11040 in Figure 2 can be calculated using Equation 1:

(Formula 1)

Where:

VTR is the output voltage of the CT and PT transformers.

RTR is the equivalent impedance of the transformer.

R1 and R2 form a resistor voltage divider network.

RIN is the input impedance of the MAX11040.

R2llRIN is the parallel impedance of R2 and RIN.

C3 is the input bypass capacitor.

f is the input signal frequency.

VIN(f) is the input voltage of the MAX11040.

A similar approach can be used for differential input design.

To maintain a high-precision resistor divider ratio and correct bypass characteristics, metal film resistors with low temperature coefficients and 1% or better accuracy should be selected. Capacitors should be high-precision ceramic capacitors or film capacitors. It is best to purchase these components from reputable suppliers such as Panasonic®, Rohm®, Vishay®, Kemet®, and AVX®.

The MAX11040EVKIT provides a fully functional, 8-channel DAS system. The evaluation board can help designers accelerate product development, for example, verifying the recommended schematic solution in Figure 2.

Figure 3. Block diagram of a development system based on the MAX11040EVKIT. Two precision instruments are required to properly calibrate the measurement channels. The measurement results can be sent to a PC via USB and converted into an Excel® file for further processing.

The ±5V signal from the function generator is connected to the MAX11040's Channel 2, while the ±10V signal from the other function generator is connected to the MAX11040's input Channel 1. The resistor divider networks R1/R2 and R3/R4 scale the ±5V or ±10V inputs accordingly to the ADC's full-scale range (FSR = ±2.2VP-P).

The values ​​of the resistor divider network R1 and R2 and the bypass capacitors C1 and C2 are shown in Table 2, all calculated by Equation 1, and are close to the optimal input dynamic range (approximately ±2.10VP-P). This dynamic range is limited to a fairly high accuracy range of 0.05%, which is very suitable for the MAX11040. For more information on accuracy specifications, refer to the MAX11040 data sheet.

Table 2. Calculation of VTR for resistors and bypass capacitors in Figure 3

±VP-PRTR

(Ω)R1

(Ω)R2

(Ω)RIN

(Ω)C3

(µF)f

(Hz)VIN

±VP-PVADC

(VRMS)Calibration

factor-KCALCalibration

factor error (%)

Calculations for nominal VTR and standard components (nominal) values

105033209091300000.1502.112681.49394.733010.70

550249018201300000.1502.070261.463952.415160.99

Measured values ​​for VTR, VIN, VINRMS with real components values ​​and tolerances used in the experiment

9.86350 ± 10%3320 ± 1%909 ± 1%130000 ± 15%0.1 ± 10%502.098721.4838994.6999120

4.93250 ± 10%2490 ± 1%1820 ± 1%130000 ± 15%0.1 ± 10%502.061511.458332.39140

050 ± 10%2490 ± 1%1820 ± 1%130000 ± 15%0.1 ± 10%5000.00048NANA

The calculated values ​​listed in Table 2 are derived from the results of Equation 1 and the precise measurements defined in Figure 3. The top of the table shows the theoretical calculation results of Equation 1 at the nominal input voltage, selecting standard discrete components. The bottom of Table 2 shows the actual measured component values ​​and test errors in the demonstration system, as well as the KCAL coefficient used for FSR calibration and calculation, calculated as follows:

The calibration coefficient KCAL is calculated according to formula 2:

KCAL = VTRMAX/(VADCMAX - VADC0) (Equation 2)

Where:

VTRMAX is the input maximum value, representing ±5V or ±10V input signal respectively.

VADCMAX is the measured, processed ADC value. The MAX11040 EV kit is set up the same as in Figure 3, with the input signal set to VTRMAX.

VADC0 is the measured, processed ADC value with the same MAX11040 EV kit setup as in Figure 3, with the input signal set to VIN = 0 (system zero-offset measurement).

KCAL (in this experiment) is the calibration coefficient for a particular channel, which is calculated based on the input signal VTR from VADC.

KCAL error calculations show that a "theoretical" KCAL based only on nominal values ​​may have an error of about 1% from the KCAL calculated based on actual measured values.

Therefore, relying solely on theoretical calculations is not enough to support actual requirements; if the design needs to achieve the 0.2% accuracy required by the EU IEC 62053 standard, full-scale (FSR) calibration must be performed on each measurement channel.

The results shown in Table 3 verify the measurement of the ½ FSR input signal. The data was measured using a high-precision HP3458A multimeter, and the calibration factor KCAL in Equation 2 was used to obtain the ADC measured and calculated values.

Table 3. Measurement results for verifying a ½ FSR input signalGeneratorMAX11040CalculationVerrRequirements

Nominal signal (½ FSR)VTR_m - signal measured by HP3458AVIN measured by ADCVTR_C = VIN × KCAL(VTR_M - VTR_C) × (100/VTR_C)IEC 62053

(VP-P)(VRMS)(VRMS)(VRMS)(%)(%)

Channel 1: ±5.0003.48920.742593.490126-0.0265440.2

Channel 2: ±2.5001.74710.73071.747384-0.0162650.2

In Table 3, VTR_M represents the measured value when the input signal is ½ FSR, while VTR_C represents the calculated value based on the MAX11040 measured value and KCAL processing.

The results show that the measurement error VERR of the conditioned circuit is less than 0.03%, which can easily meet the 0.2% accuracy indicator required by the EU IEC 62053 specification.

Figure 4. The MAX11040EVKIT GUI allows the user to easily set various measurement conditions: 12.8ksps, 256 samples/cycle, and 1024 conversions. In addition, the calculation section of the GUI provides a convenient tool for performing quick engineering calculations.

The measurement results can also be transferred to a PC via the USB port for detailed data analysis using the powerful (and free) Excel.

in conclusion

High-performance, multichannel, simultaneous-sampling, Σ-Δ ADCs such as the MAX11040 are ideal for data-acquisition systems in industrial applications. These new ADC designs offer up to 117dB of dynamic range, improved integral and differential nonlinearity, and sampling rates up to 64ksps. With the proper choice of signal conditioning, the MAX11040 can meet or exceed the specifications of advanced "smart" grid monitoring systems¹.