RTD Signal Conditioning—4Wire Configuration, Ratiometric Measurement, & Filtering
Learn about RTD (resistance temperature detector) signal conditioning through a fourwire configuration, ratiometric measurement, and input RC filters.
Previously, we explored twowire and threewire configurations for both voltage and currentexcited RTD measurements. This article extends the discussion to the fourwire configuration and delves into ratiometric measurement, which is widely used in RTD applications. In addition to that, we’ll go over how RC input filters can be used in ratiometric configurations and learn how matched input and reference path filters can improve the noise performance of a ratiometric configuration.
RTD 4Wire Configuration—Voltage Drop and Kelvin Sensing
Figure 1 below shows a fourwire wiring technique for a currentexcited RTD.
Figure 1. Block diagram of a fourwire technique in a currentexcited RTD.
The analogtodigital converter (ADC) inputs are high impedance, which causes the excitation current flows through R_{wire1}, R_{rtd}, and R_{wire4}. Since no current flows through R_{wire2} and R_{wire3}, no voltage drops across these two resistors, and the ADC can accurately measure the RTD voltage V_{rtd}.
While a threewire configuration requires two matched current sources to eliminate the wire resistance error, the fourwire configuration can achieve this with a single current source. Note that the above method, also called Kelvin sensing, is a general resistance measurement technique that finds use in many other areas, such as resistive current sensing applications.
The fourwire measurement concept can also be applied to a voltageexcited RTD, as illustrated in Figure 2.
Figure 2. A block diagram showing the fourwire measurement concept in a voltageexcited RTD.
Again, no voltage drops across R_{wire2} and R_{wire3}, and the ADC accurately measures the voltage across the RTD V_{rtd}. In a voltageexcited system, the excitation voltage V_{exc} is known. However, it is impossible to determine the RTD resistance by knowing V_{rtd} and V_{exc} because some unknown voltages also drop across R_{wire1} and R_{wire4}. To combat this problem, we can make an extra measurement at a node, such as node B in the above diagram, to figure out the current flowing through the sensor. This is similar to the method we used when discussing the voltageexcited threewire configuration in the previous article.
Note that with the current excitation, a second measurement is not required because the current flowing through the sensor, I_{exc}, is already known. The current excitation method is a more straightforward implementation, especially when the wire resistance error is an issue.
Basics of Ratiometric Measurement
All RTD measurement circuits require an accurate and stable excitation source, as the RTD voltage is a function of the excitation source. For example, consider the circuit diagram in Figure 1. The voltage measured by the ADC relates to the RTD resistance by the following equation:
\[V_{ADC}=R_{rtd}\times I_{exc}\]
If the excitation current is noisy or drifts with temperature or time, the voltage across the RTD changes even when the temperature is fixed. To maintain high accuracy, the designer needs to use precision components to minimize variations in I_{exc}.
Alternatively, you could use ratiometric measurement. Rather than minimizing the excitation source variations, ratiometric measurement changes the circuit so that the output becomes proportional to the ratio of I_{exc} to another current (or voltage) in the system.
Let's assume that the circuit is modified in a way that the output equation is changed to:
\[V_{ADC}=R_{rtd}\times\frac{I_{exc}}{I_{x}}\]
Where I_{x} is a current in the circuit. Also, if we derive I_{x} from I_{exc} in a way that they both experience the same variation, the ratio \(\frac{I_{exc}}{I_{x}}\) can be kept constant. This makes the measurement system insensitive to the excitation source variations.
In the next section, we’ll see that ratiometric measurements can usually be implemented inexpensively. This inexpensive implementation allows us to use ratiometric configurations to improve accuracy and relax the requirements of certain components, such as the excitation voltage or current source.
Ratiometric RTD Measurement
Figure 3 shows how the fourwire currentexcited measurement can be modified to have a ratiometric configuration.
Figure 3. Block diagram showing the fourwire currentexcited measurement can be modified to have a ratiometric configuration.
In this case, the excitation current is passed through a precision reference resistor R_{ref} to create the ADC reference voltage. A buffer is used to sense the voltage across R_{ref} without causing any loading effect on this resistor. Although the buffer is shown as an external component, it is normally integrated into the ADC chip, and an external buffer is not required.
From here, let’s see how the above circuit can produce a ratiometric measurement. The ADC input voltage and reference voltage are given by the following equations:
\[V_{ADC}=R_{rtd}\times I_{exc}\]
Equation 1.
\[V_{ref}=R_{ref}\times I_{exc}\]
Equation 2.
The digital output produced by an nbit ADC can be typically described by the following equation:
\[Digital\,Value=\frac{Analog\,Input\,Voltage}{ADC\,Reference\,Voltage}\times{\Big(}2^{n}1{\Big)}\]
The ADC output is proportional to the ratio of the input voltage to its reference voltage. Substituting Equations 1 and 2 into the above equation, we obtain:
\[Digital\,Value=\frac{R_{rtd}\times I_{exc}}{R_{ref}\times I_{exc}}\times{\Big(}2^{n}1{\Big)}\]
This simplifies to:
\[Digital\,Value=\frac{R_{rtd}}{R_{ref}}\times{\Big(}2^{n}1{\Big)}\]
The ADC output is no longer a function of the excitation current. However, R_{ref} should be a low tolerance and low drift resistor since any unwanted variation in R_{ref} directly translates into an error in the measurement result. Figure 4 shows the ratiometric configuration for a threewire RTD application.
Figure 4. Example ratiometric configuration of a threewire RTD application. Image used courtesy of TI
The ratiometric measurement concept can also be applied to a voltageexcited RTD. An example is shown in Figure 5.
Figure 5. An example ratiometric measurement block diagram of a voltageexcited RTD. Image used courtesy of Microchip
The above diagram uses the same voltage as the ADC reference voltage and the RTD excitation signal.
Using an RC Low Pass Filter in Ratiometric Configurations
To attenuate the noise from the excitation current and the environment, RC lowpass filters are placed at the ADC input and reference paths of a ratiometric system. This is illustrated in Figure 6.
Figure 6. Using an RC lowpass filter at the ADC input and reference paths of a ratiometric system.
The ratiometric circuit can work without the use of external RC filters; however, the addition of lowpass RC filters can improve the circuit's immunity to radio frequency interference (RFI) and electromagnetic interference (EMI). The filter response for a commonmode noise can be understood by examining the following circuit diagrams in Figures 7a and 7b.
Figure 7. Example diagrams showing the filter response for commonmode noise.
As shown in Figure 7(a), with a commonmode input, the nodes C and D have the same potential. Thus, no current flows through C_{2,} and this capacitor can be removed from the circuit model. This means that the C_{1} capacitors determine the commonmode cutoff frequency, which leads to Equation 3:
\[f=\frac{1}{2 \pi R_1 C_1}\]
Equation 3.
On the other hand, for a differential input, C_{2} can be replaced by a series connection of two 2C_{2} capacitors, as shown in Figure 8(b).
Figure 8. Example series connection diagrams.
Therefore, the differential cutoff frequency can be expressed as:
\[f=\frac{1}{2 \pi R_1 \big ( C_1 + 2C_2 \big)}\]
Equation 4.
Alternatively, Figure 7(b) shows that the commonmode cutoff frequency for nodes C and D are determined by the upper and lower C_{1} capacitors, respectively. A mismatch between these two capacitors can lead to a mismatch between the cutoff frequencies of the two paths. Through unequal attenuation of these two filters, the commonmode noise can produce a differential noise at the filter output, which is not at all desired.
To suppress the differential noise produced by mismatched commonmode capacitors, it is recommended that the differential capacitor C_{2} be at least 10x greater than the commonmode capacitor C_{1}. In other words, the differential capacitor reduces both commonmode and differential noise components.
Several tradeoffs should be considered when designing these simple RC filters. A thorough discussion on selecting the filter components to balance these tradeoffs is not the goal of this article. However, an important point regarding ratiometric measurements needs to be highlighted: the effect of filter matching on the noise performance of a ratiometric system.
Matched Filtering to Improve Noise Performance
In the previous section, we discussed that the mismatch of the C_{1} capacitors within each filter can cause problems (and hence, we added a differential capacitor to each filter). What about the mismatch between the input and reference path filters? To answer this question, note that the ratiometric system tries to make the measurement insensitive to the excitation source variations. This is achieved only if the excitation source variations have the same effect at the ADC analog inputs (IN+ and IN) and reference inputs (REF+ and REF). A mismatch between the cutoff frequency of the input and reference paths can lead to unequal attenuation of the excitation noise and reduce the effectiveness of the ratiometric configuration.
The remaining question is: what component values assure that the filters have the same cutoff frequency? Based on Equations 3 and 4, another application note from Analog Devices recommends using the same filters for the input and reference paths. The application note also provides some test results for the circuit diagram shown in Figure 9.
Figure 9. Example app note diagram. Image used courtesy of Analog Devices
Note that, compared to the general circuit in Figure 6, one resistor and two capacitors are eliminated in the reference path of the above circuit. This is because the REF pin is connected to the ground in this design. The test results of this circuit are shown in Table 1.
Table 1. Data used courtesy of Analog Devices
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 
This test uses a 100 Ω precision resistor instead of the RTD, and the noise voltage at the ADC input pins is measured. The value of R_{Ref} is 5.62 kΩ. When the two filters are identical (R_{1 }= R_{2 }= R_{3 }= 1 kΩ), the noise voltage is reduced by about 0.1 µV to 0.3 µV compared to the unmatched case where R_{1 }= R_{2 }= 10 kΩ and R_{3 }= 1 kΩ. In the above example, identical RC filters improve noise performance, but this is not necessarily the maximum achievable noise performance. This will be discussed in the following section.
Improving Current Source Noise Cancellation
For example, an application note from Texas Instruments discusses that identical filters at the input and reference paths don't produce the maximum cancellation of the current source noise. When deriving Equations 3 and 4, we assumed that a common mode or differential noise appears at the filter inputs (nodes A and B).
This type of analysis is conceptually similar to applying a voltage source to nodes A and B to model the input noise. With this analysis, the effect of the R_{rtd} and R_{ref} resistors, which is in parallel with the filters, is not considered. These two resistors actually modify the time constant of the RC networks. Since R_{rtd} and R_{ref} are unequal, identical filters cannot have identical cutoff frequencies. The TI document I mentioned above suggests using the zerovalue time constant technique to derive cutoff frequency equations of the two filters.
The zerovalue time constant is a method of estimating the bandwidth of a system. For zerovalue time constant analysis, the resistance “seen” by each capacitor is determined while the signal source is set to zero (the excitation current is replaced with an open circuit), and the rest of the capacitors are replaced with open circuits. The reason this method is called the zerovalue time constant is that all capacitors except the capacitor of interest are set equal to zero to perform the calculation. If the circuit has m capacitors and the resistance seen by a given capacitor C_{j} is $$R^0_j$$ then the 3 dB bandwidth of the system can be estimated as:
\[\omega_{3dB} =\frac{1}{\sum_{j=1}^{m}R_j^0 C_j}\]
Equation 5.
For example, to determine the resistance across the C_{2} and C_{4} capacitors in Figure 6, we obtain the circuit diagrams in Figure 10(a) and (b), respectively.
Figure 10. Diagrams showing the resistance across C_{2} (a) and C_{4} (b) capacitors
Equations 6 and 7 show the zerovalue time constant (ZVT) associated with C_{2} and C_{4}, respectively:
\[{ZVT}_{2}=C_2 \big (2R_1 + R_{rtd} \big)\]
Equation 6.
\[{ZVT}_{4}=C_4 \big (2R_2 + R_{ref} \big)\]
Equation 7.
Originally, the zerovalue time constant method was developed to estimate the 3 dB bandwidth of the circuit. To do this, we calculate the time constant of all capacitors in the circuit and then plug them into Equation 5. However, the equation for each individual time constant shows how that particular capacitor interacts with its surrounding resistors to contribute to the circuit bandwidth.
Returning to our RTD measurement system, the input and reference paths will have identical bandwidths if the zerovalue time constant of the three capacitors is the same. Therefore, ZVT_{2 }= ZVT_{4}, which leads to the following equation:
\[C_2 \big (2R_1 + R_{rtd} \big)=C_4 \big (2R_2 + R_{ref} \big)\]
Equation 8.
If C_{2 }= C_{4}, then the R_{1} and R_{2} resistors should be chosen appropriately to yield the same time constant. Based on the above discussion, the TI application note suggests the following example diagram in Figure 11.
Figure 11. Example block diagram of ADS1248. Image used courtesy of TI
The sensor resistance is assumed to change from 0 to 250 Ω. Since the variation in the sensor resistance changes the circuit time constant (Equation 6), relatively large resistors are used for the input filter (R_{1 }= R_{2 }= 6.04 kΩ). This makes the effect of the RTD variation on the frequency response of the input filter insignificant.
According to Analog Devices’ article, the resistors used in the reference path should be 6.04 kΩ. However, the TI design suggests using 5 kΩ resistors to match the bandwidth of the two filters. Figure 12 shows how the inputreferred noise of the system changes with the input voltage level (i.e. the voltage across the RTD).
Figure 12. Graph showing the inputreferred noise vs input voltage. Image used courtesy of TI
As you can see, the inputreferred noise of the system is about 0.35 µVrms. The inputreferred noise of the employed ADC (ADS1248) is typically 0.34 µVrms when the device is configured with a PGA gain of 8 V/V with a data rate of 20 SPS. Additionally, the system noise is close to the reported noise performance of the ADC. Note that when the input and reference path filters are not matched, the inputreferred noise of the system can increase with the input signal level to values much higher than that of the ADC. Please refer to the above TI document for more information.
As a final note, it’s worthwhile to mention that the design in Figure 11 only matches the zerovalue time constant of the differential capacitors (C_{IN_DIFF} and C_{REF_DIFF}). The time constant of the commonmode capacitors is not exactly the same. However, since the differentialmode capacitors are 10x larger than the commonmode capacitors, it seems that matching the time constant of the differentialmode capacitors has a greater impact on the frequency response of the filters.
Featured image used courtesy of Adobe Stock
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