  # How to Use the Ratiometric Characteristics of Sensors and ADCs to Improve Accuracy

Most sensors are analog in nature and therefore must be digitized before they can be used in current Electronic systems. This application note covers the fundamentals of ratiometric sensors and their use with analog-to-digital converters (ADCs). In particular, this article will show how the ratiometric nature of the sensor and ADC can be used to improve accuracy while reducing component count, reducing cost, and saving board space.

Most sensors are analog in nature and therefore must be digitized before they can be used in current electronic systems. This application note covers the fundamentals of ratiometric sensors and their use with analog-to-digital converters (ADCs). In particular, this article will show how the ratiometric nature of the sensor and ADC can be used to improve accuracy while reducing component count, reducing cost, and saving board space.

Note: The ratiometric characteristic mentioned in this article refers to the ratio of the device output to the other voltage or current to be measured.

Sensors and Resistive Sensing Elements

The output of many sensors is proportional to their supply voltage. This is usually because the sensing element that produces the output is a ratiometric device. The most common ratiometric element is the resistor, whose resistance varies as the measurand changes. Resistance temperature detectors (RTDs) and strain gauges are typical resistive sensitive components.

The ratiometric nature of resistive elements is due to the fact that their impedance cannot be measured directly. Its value is determined by the ratio of the voltage across the resistor to the current through the resistor.
R = V/I Equation 1 (Ohm’s Law)

Sensors that use resistive elements typically pass a current through a resistor and measure its voltage. This voltage can be amplified or level shifted before output to the sensor, but its magnitude is still related to the current flowing through the resistor. If this current comes from the supply voltage, then the output of the sensor is proportional to the supply voltage. Equation 2 describes the output of this type of proportional sensor (Figure 1), where Vs is the output signal, Ve is the excitation voltage, S is the sensitivity of the sensor, P is the magnitude of the parameter being measured, and C is the offset of the sensor.

Vs = Ve (P x S + C) Equation 2 Figure 1. Ratiometric Sensor

Honeywell? MLxxx-C series pressure sensors are representative devices among many automotive proportional sensors. When operating from a nominal 5V supply voltage, the offset voltage is 0.5V and the full-scale output is 4.5V. If the excitation voltage is changed, the offset voltage and full-scale output will change proportionally.

The excitation voltage needs to be known to use the output signal, which is inconvenient in many applications. To address this, manufacturers add a voltage reference to the circuit. This device provides very precise voltage independent of temperature and supply voltage. If the current flowing through the sense resistor is from the reference voltage, then Ve in Equation 2 can be replaced with a constant. This results in Equation 3, where the new constant is contained in S2 and C2.
Vs = P x S2 + C2 Equation 3

Because the output signal is only a function of the parameter being measured, Equation 3 is not proportional. Honeywell’s MLxxx-R5 series pressure sensors are non-proportional sensors. When operating from any supply voltage between 7V and 35V, the offset is 1V and the full-scale output is 6V.

Analog-to-Digital Converters (ADCs) and Resistive Devices

ADCs used to digitize sensor signals are also ratiometric devices. Regardless of their internal architecture, all ADCs operate by comparing an unknown input voltage to a known reference voltage. The digitized output of the converter is the ratio of the input voltage to the reference voltage multiplied by the full-scale reading of the ADC. A scaling factor K is also required to account for the variety of internal scale-ups and designs. Regardless of the value of K, as long as the configuration of the ADC has not changed, the value of K remains fixed. Equation 4 describes the relationship between the digital reading (D) of a general ADC (Figure 2) and the input signal (Vs), reference voltage (Vref), full-scale reading (FS), and scale factor (K).

D = (Vs/Vref)FS x K Equation 4 Figure 2. Analog-to-digital converter in general

The reference voltage is related to the specific design of the ADC. In some ADCs the reference voltage is the supply voltage, in others the reference voltage is derived from an internal reference source, in other designs the user must connect the reference voltage to the ADC’s Vref input. If an internal or external voltage reference is used, making the reference a constant value, Equation 4 can be simplified to Equation 5, where K2 is a new constant with the value FS x K/Vref.

D = Vs x K2 Equation 5

sensor measurement

The output of a small system consisting of a non-ratiometric sensor and an ADC with a fixed reference voltage can be obtained by substituting Vs (input of the ADC) from Equation 3 (the output of the sensor) into Equation 5. as shown in Equation 6.
D = P x S2K2 + C2K2 Equation 6

Equation 6 gives the exact relationship required. The magnitude of the digital value (D) is proportional to changes in P and is only affected by changes in P. D is not affected by temperature and supply voltage variations.

omit voltage reference

Stabilizing sensors and ADCs with a voltage reference is an effective and necessary technique. However, it’s not always the best technology.

The remainder of this article will discuss how the ADC’s reference voltage input can be used creatively, thereby eliminating the need for voltage references and current sources in many sensor circuits. This design saves component cost, board space, and voltage “headroom.” Since the voltage reference is eliminated, the errors associated with non-ideal references are also eliminated, resulting in improved accuracy. This technology has been used in the automotive industry for many years. Once the sensor and ADC are proportional to the supply voltage, an accurate voltage reference is not required.

Similar techniques using current-driven sensors and single-element resistive sensors such as RTDs are not commonly used. The sensitivity of ADCs in these circuits can vary with temperature or supply voltage. Nonetheless, the combination of ADC and sensor input is fairly stable.

Sensor proportional to supply voltage

Substituting the input signal (Vs) in Equation 2 into Equation 4 yields the output of the ADC when measuring the ratiometric sensor. Equation 7 results, which says: D is a function of P, Ve, and Vref.

D = P(S x FS x K x Ve/Vref) + C(FS x K x Ve/Vref) Equation 7

At first glance, the approach in Equation 7 does not seem ideal, since the output (D) is a function of three variables, not just P. However, a closer look reveals that the ratio of Ve/Vref is very important, and the value alone does not mean much. If the Ve and Vref voltages come from the same source, it is easy to get a constant Ve/Vref ratio. Once this is the case, D will be proportional to changes in P, and only related to changes in P. Assuming the Ve/Vref ratio to be a constant, Equation 7 can be simplified to a form similar to Equation 6. Therefore, this means that the same performance can be achieved without a voltage reference.

From a practical application point of view, Ve and Vref must be large enough to avoid noise interference; at the same time, Ve and Vref must also be within the range specified by the ADC and sensor. Using a positive supply voltage as the voltage source for Ve and Vref usually satisfies the above requirements and allows powering a large number of sensors in parallel, as shown in Figure 3shown. The front end of the MAX1238 in Figure 3 has a 12-input multiplexer with a built-in voltage reference. In this case, there is no additional cost associated with the ADC reference, but adding a reference to each of the 10 sensors would add significantly to the cost. The MAX1238 also allows the AN11 input to be used as a voltage reference. Using AN11 as a reference input and connecting it to a 5V supply sets the ADC’s full-scale input to 5V and facilitates use with ratiometric sensors. In Figure 3, the MAX1238’s internal voltage reference is not idle. The internal voltage reference can be controlled by software and used for diagnostics, such as measuring supply voltage. This can be achieved by a voltage divider connected to input AN10.

Figure 3. The MAX1238 ADC allows the AN11 input as a reference voltage, so the ADC can be used with a ratiometric sensor.

The topology of Figure 3 is ideal for automotive applications and those that operate from a single supply with minimal voltage drop across the supply line. Not suitable for sensors that must operate with long wires or applications where the ADC and sensor are powered by different power supplies.

current driven bridge

In low noise environments or systems where the pressure sensor is placed next to the ADC, it may not be necessary to use a sensor with signal amplification. In these applications, low-cost bridge output sensors are more suitable.To reduce sensor cost while providing good performance over the entire temperature range, many of these pressure sensors, such as the NPI-19 series from Nova SensorBoth are powered by a current source rather than a voltage source. (See Appendix 1 for a more detailed discussion). Equation 8 gives the output of such a current-driven sensor, where Ie is the excitation current.

Vs= Ie (S x P+C) Equation 8 Figure 4 shows a current source commonly used in bridge output sensors. The current source consists of a low temperature coefficient resistor, an op amp, and a voltage reference. If the ADC and pressure sensor are integrated into one component, the voltage reference of the current source can also provide the reference voltage for the ADC. In the circuit of Figure 4, a voltage reference is used to stabilize both the sensor and the ADC against changing temperature and supply voltage.

Figure 4. The current source for the current-driven sensor in this design consists of a resistor, an op amp, and a voltage reference.

Another approach similar to Figure 4 is the circuit shown in Figure 5, without the need for a current source or voltage reference. One caveat: While the sensor and ADC combination is stable over temperature, both the ADC and the sensor have large temperature drifts. If measured alone, the sensitivity of the sensor will decrease with increasing temperature, while the sensitivity of the ADC will increase. Since the ADC output is not stable over temperature, special care must be taken when applying this method to circuits where the ADC has multiple inputs.

Figure 5. An alternative design approach for a sensor and ADC combination that does not require a separate current source or voltage reference. Equation 9 can be derived from Figure 5:

Vref = Ie x R1 Equation 9

Substituting Vref in Equation 9 and Vs in Equation 8 into Equation 4 of the ADC above yields Equation 10.

D = [Ie (S x P+C)/(Ie x R1)](FS x K) Equation 10

Since the excitation current (Ie) is contained in the numerator and denominator, it can be eliminated. This results in Equation 11, indicating that the output is independent of the excitation current. If the constant terms in Equation 11 are combined, the equivalent of Equation 6 is again obtained: a system with a voltage reference.

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