Signal chains for measurement of analog quantities typically pose the toughest design challenges for engineers. Even a simple signal chain with a resistive sensor and an analog-to-digital data acquisition system involves multiple complex factors that have to be dealt with before a valid measurement can be made.

These factors are even more complex to manage when a system is working with different sensors. This article discusses different issues developers need to tackle for accurate measurement with illustrations of different type of resistive sensors.

On an abstract level, the analog signal chain in all the systems using resistive sensors will be more or less similar to as shown in **Figure 1** .

*Figure 1: Basic analog signal chain*

Though all signal chains look identical on a block level, the parameters for each block will differ based upon many factors. The most important of these factors to consider are change in resistance (and hence change in voltage) across the sensor for unit change in physical quantity, distance of sensor from the measurement system (i.e., the error in measurement due to wire resistance), required precision of the system, type of interference, and required accuracy.

These factors decide the type of excitation required, the way the sensor has to be connected to the measurement circuit, the gain required for the pre processing circuit and the ADC, the type of filter needed as well as its cut off frequency, and the resolution and input range of ADC.

Let’s look into different sensors and major constraints related to analog signal chains while using them, starting with a thermistor. Thermistors are extremely nonlinear over the temperature range. The variation of resistance over temperature is the complex nonlinear function is:

1/T = A + B ln(R) + C (ln(R))^{3}

where T is temperature and R is resistance. A, B and C are constants specific to the thermistor.

Due to the arithmetic complexity of the equation, it might not be advisable to implement it in a microcontroller. Hence, the general way of implementing this calculation is to use a look up table for the resistances and corresponding temperature values. The temperature is then calculated using piece-wise arithmetic.

While there may be errors in measurement due to gain variations and offsets, these errors are too small for the precision requirements of a thermistor-based temperature sensor.Gain variation and offsets will be discussed in the RTD section later in the article.

Considering the measurement of resistance, there can be multiple ways of direct measurement as shown in **Figure 2** .

*Figure 2(a), 2(b), 2(c): Resistance measurement topologies*

The topology shown in Figure 2(a) uses a voltage DAC to excite the resistor divider. One of the resistances in the circuit is the sensor itself and another resistance is the known value reference resistance. This topology will work; however, single-ended measurement has some drawbacks. One of them is the ground shift between the Vss near the sensor and actual internal Vss to ADC, which will result in an offset.

On the other hand, as shown in Figure 2(b), when the –ve input for the ADC is tapped near to the resistance, both analog ground and the ADC’s ground are same. Since the differential lines would be running close to each other until the sensor, any pick up on one will be replicated on the other. This signal, when measured using a differential measurement structure, gets cancelled since it is a common mode signal. Another point to be noted in this diagram is that while measuring the voltage across Rsensor, the +ve input is tapped near the sensor itself. This ensures there is no error in measurement due to wire resistance.

Figure 2(c ) shows the topology which uses a current DAC to excite the sensor. The voltage measured across the sensor will provide an accurate measure of its resistance. Current excitation is the best topology in terms of the number of external components needed. It does not need any reference resistance. However, to calibrate the system for gain errors, an external resistance is needed. Note that for those applications where very high accuracy is not needed, there is no need of gain error compensation and hence no external reference resistance is required.

**Resistance Temperature Detectors (RTD** )

RTDs (Resistance Temperature Detectors) have a resistance at 0^{o} C is of the order of 100 ohms with every degree change in temperature causing a change of close to 0.385 ohms.As RTDs have low resistance, the effect of wire resistance plays a major role in their accuracy.

RTDs are excited using a constant current source. The voltage across an RTD can be measured either using a 3-wire method or 4-wire method, based on the number of wires running parallel from the measurement system to the RTD.As RTDs are installed away from the measurement system, the 3-wire measurement method is typically preferred due to wire cost.**Figure 3** shows the diagram of an RTD interfaced for 3-wire measurement.

*Figure 3: 3-wire RTD measurement*

In Figure 3, when the voltage is measured on the first channel, it is not just the voltage across the RTD. In fact, it is the voltage drop measured across the RTD and the wire resistance between IDAC and RTD. The error due to wire resistance can be handled in multiple ways. One way is to measure the resistance of wire manually and then store it as a constant. Every time a measurement is made, this resistance can be subtracted.

Another way is to measure the voltage drop between the positive terminal of the RTD and the output pin of the DAC. If the wires are of same specifications, then they will have the same resistance and the voltage measured in the previous step can be subtracted from the voltage measured across the sensor. However, still there may be some error if the wires are not symmetrical. Also, this method will consume one additional pin to connect the DAC’s output pin to the ADC input.

*Figure 4: 4-wire RTD measurement*

For accurate measurements, the 4-wire configuration as shown in **Figure 4** is preferred.Both negative and positive inputs are tapped from close to the RTD, thereby eliminating error due to wire resistance. While designing the signal chain for the RTD, the input impedance of the chain needs to be very high to keep input current negligible. If the ADC has a low input impedance, the signal should be fed to a buffer before connecting to the ADC.

As mentioned earlier, there will be an offset in the system which will vary with temperature. Offset/offset drift with temperature and low frequency noise can be removed using correlated double sampling (CDS). With CDS, first the zero referenced offset is measured (to measure it, both inputs are shorted) and then the voltage across the sensor is measured. In Figures 3 and 4, to measure the zero referenced signal, the ADC is connected to channel 1.

When the voltage across the sensor is measured, it will include the actual thermocouple voltage, offset, and noise (**Equation 1** ). In Figures 3 and 4, it is the voltage measured on channel 0.

V_{R_Signal } = V_{RTD} + V_{N } + V_{offset } (Eq. 1)

The zero referenced reading is given by **Equation 2** .

V_{Zero_Ref } = V_{N} + V_{offset} (Eq. 2)

The previous zero referenced sample with respect to the current zero referenced measurement is given by **Equation 3** .

V_{Zero_ref_Prev } = (V_{N} + V_{offset} ) × Z^{-1} (Eq. 3)

The difference, then, between the current voltage measurement across the sensor and previous zero referenced signal is given by **Equation 4** .

V_{signal } = (V_{RTD} + V_{N} + V_{offset} ) – (V_{N} + V_{offset} ) × Z^{-1} (Eq. 4)

V_{signal} = V_{RTD} – (V_{N } + V_{offset} ) × (1-1/Z)(Eq.5)

As an offset is fairly constant for consecutive samples, **Equation 5** will result in **Equation 6** .

V_{signal} = V_{RTD} – V_{N} ×(1-1/Z)(Eq. 6)

Using the bilinear transform, Z = (1 + sT/2)/(1-sT) where T is 1/fsample, equation 6 can be written as **Equation 7** .

V_{signal } = V_{RTD} – V_{N} × (2s/(s+ 2f_{sample} )(Eq. 7)

If we analyze equation 7, it is a high-pass response. On the other hand, ADCs have a low-pass response. This helps to reduce overall noise of the system. Also, looking at the topology shown in Figure 4, it is evident that the accuracy of the system is dependent entirely on the accuracy of the IDAC. If the IDAC deviates by 5%, then the calculation is also going to deviate by 5%.

This is a gain error term in the measurement and is not be acceptable for most systems. There are other contributors to gain error as well, ADC and its reference accuracy being the first reason. If the ADC had a reference that is accurate to just 1%, all the measurements made using the ADC suffer from this 1% gain error. Since we are measuring temperature here, the issue of drift can pose an even deeper issue.

The best way to avoid the effect of these different gain errors is by referencing all measurements against a more accurate parameter. A 0.1% accurate resistance can be used for this purpose. Figure 5 shows the topology in which the calibration resistance is connected.

*Figure 5: 4-wire RTD measurement with gain error compensation*

The current is first passed through the reference resistor and the voltage is measured, thus giving a measure of its resistance. This measurement is prone to the gain errors discussed earlier. However, in the next step the same current is passed through the RTD and the voltage across it is measured using the same setup. The ratio of the two ADC measurements eliminates any gain error that is present since the RTD’s resistance measurement is made with reference to the reference resistor. The accuracy of the system is now based on the accuracy/tolerance of the reference resistor used.

(** Part 2 ** will look at considerations for measurements in the millivolt range such as from load cells, and digital filtering.)

**About the authors **

** Kannan Sadasivam ** is a Staff Applications Engineer with Cypress Semiconductor Corp. He has spent a considerable amount of his past career designing and integrating Satellite subsystems. He loves working on different types of analog circuits and applications. He can be reached at .

**is a Senior Applications Engineer with Cypress Semiconductor. He loves working on different types of analog and digital circuits, as well as synthesizable codes. He can be reached at .**

*Sachin Gupta*

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