### Introduction

Many system designers use Σ-Δ ADCs together with RTDs (resistance temperature detectors) for temperature measurements, but have difficulties achieving the high performance as specified by the data sheet of the ADC they are using. For example, some designers may only be able to get 12 to 13 noise-free bits from a 16-bit to 18-bit ADC. The front-end techniques introduced in this article will enable designers to achieve 16+ noise-free bits in their system designs.

Using RTDs in a ratiometric measurement has the advantage in that it eliminates sources of error such as the accuracy and drift of the excitation current source. Below is a typical circuit for a 4-wire RTD ratiometric measurement circuit. The 4-wire configuration has the advantage that the error due to lead resistance can be cancelled.

From the circuit above, we can derive the following two equations:

The general expression used to calculate the RTD resistance (RRTD) when the ADC is operating in bipolar differential mode is given by:

where:

*Code*_{RTD }is the ADC code.

Code_{ADC_Fullscale} is the ADC full-scale code.

The measured resistance value of the RTD is theoretically only related to the precision and drift of the reference resistor. Normally R_{REF} is an accurate and low drift resistor with 0.1% precision.

When engineers design their products using this type of circuit, they will add some resistors and capacitors before the analog input, external reference pins for low-pass filtering, and overvoltage protection as shown in Figure 2. In this article, we will show what should be considered in choosing suitable resistors and capacitors for better noise performance.

From Figure 2 we can see that R_{1}, R_{2}, C_{1}, C_{2}, and C_{3} are used as a first-order, low-pass RC filter that provides attenuation for both differential and common-mode voltage signals. The values of R_{1 }and R_{2} should be the same and similarly for the values of C_{1} and C_{2}. Similarly, R_{3}, R_{4}, C_{4}, C_{5}, and C_{6} are used as a low-pass filter for the reference path.

### Common-Mode Low-Pass RC Filter

Figure 3 shows the common-mode, low-pass filter equivalent circuit.

Because the common-mode voltage at Point a is equal to the voltage at Point b, there is no current flowing through C_{3}. Therefore, the common-mode cutoff frequency can be expressed as

### Differential Mode Low-Pass RC Filter

To better understand the low-pass RC filter cutoff frequency for differential signals, the C_{3} capacitor in Figure 4 can be thought of as two separate capacitors C_{a} and C_{b} in Figure 5.

From Figure 5, the differential mode cutoff frequency is:

Normally the value of C_{3} is 10× larger than the value of C_{cm}. The purpose of this is to decrease the effects that are introduced by the mismatch of C_{1} and C_{2}. For example, with an analog front-end design used in the Analog Devices circuit note CN-0381 as seen in Figure 6, the cutoff frequency for differential signals is around 800 Hz and the cutoff frequency for common-mode signals is 16 kHz.

### Resistor and Capacitor Considerations

Other than being part of the low-pass filter, R_{1 }and R_{2} can also provide overvoltage protection. If 3 kΩ resistors are used before the AD7124-4 A_{IN} pins in Figure 6, these can protect against up to 30 V miswiring. It's not recommended to use larger resistors before the A_{IN} pins for the following two reasons. First of all, they will generate more thermal noise. Secondly, the A_{IN} pins will have input currents that will flow across these resistors and introduce errors. These input currents do not have a constant value and when combined with a mismatch between them they will generate noise that will increase with the size of the resistors.

The resistor and capacitor values play a vital role in determining the performance of the final circuit. Designers need to understand their field requirements and calculate the resistor and capacitor values according to the equations above. For ADI Σ-Δ ADC parts and precision analog microcontrollers with an integrated excitation current source, it is recommended to use the same resistor and capacitor values before the A_{IN} and reference pins. This design ensures that the analog input voltage remains ratiometric to the reference voltage and any errors in the analog input voltage due to the temperature drift and noise of the excitation current are compensated by the variation of the reference voltage.

### Measured Noise Performance on ADuCM360 with Ratiometric Measurement

The ADuCM360 is a fully integrated, 3.9 kSPS, 24-bit data acquisition system that incorporates dual high performance, multichannel Σ-Δ ADCs, a 32-bit ARM^{®} Cortex^{®}-M3 processor, and Flash/EE memory on a single chip. It also integrates programmable gain instrumentation amplifiers, a precision band gap reference, programmable excitation current sources, a flexible multiplexer, and many other features. It allows a direct interface to resistive temperature sensors.

When using the ADuCM360 for RTD measurements, the REF– pin is normally connected to ground so R_{4} and C_{5} from Figure 2 can be removed as there is no current flowing across them. C_{4} and C_{6} are in parallel so these two can be added together. However, because C_{4} is much smaller than C_{6}, it can be ignored. This results in the simplified analog front-end circuit as shown in Figure 7.

Table 1 shows the noise level with matched and unmatched filters in front of the analog and reference input paths. A 100 Ω precision resistor is used instead of R_{RTD} to measure the noise voltage on the ADC input pins. The value of R_{Ref} is 5.62 kΩ.

Table 1. Noise Test Results

ADC Gain | I_{SOURCE} (µA) |
Noise Voltage on 100 Ω Resistor (µV) | |

R_{1} = R_{2} = R_{3} = 1k |
R_{1} = R_{2} = 10k R _{3 }= 1k |
||

16 | 100 | 1.6084 | 1.8395 |

16 |
200 | 1.6311 | 1.7594 |

16 | 300 | 1.6117 | 1.9181 |

16 |
400 | 1.6279 | 1.9292 |

From Table 1 we can see that using a matched analog front-end circuit where the values of R_{1 }and R_{2} are the same as R_{3}, the noise decreases by around 0.1 µV to 0.3 µV as compared to the unmatched circuit, which means that the number of ADC noise-free bits increases by about 0.25 bit to 16.2 bits with an ADC PGA gain of 16.

### Conclusion

Using matched RC filter circuits and choosing the right resistor and capacitor values based on field requirements according to the considerations introduced in this article, the RTDs in ratiometric measurement applications can achieve optimum results.

### References

CN-0381 Circuit Note. "Completely Integrated 4-Wire RTD Measurement System Using a Low Power, Precision, 24-Bit, Sigma-Delta ADC." Analog Devices, Inc.

CN-0267 Circuit Note. "Complete 4 mA to 20 mA Loop-Powered Field Instrument with HART Interface." Analog Devices, Inc.