Keywords: sensors, ratiometric sensors, sensor interface, analog to digital converters
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APPLICATION NOTE 3775

Abstract: Most sensors are inherently analog and must have their signals digitized before they can be used in today's electronic systems. This application note will cover the basics of ratiometric sensors and how they interact with analog-to-digital converters (ADCs). In particular, it will show how the ratiometric characteristics of sensors and ADCs can be exploited to improve accuracy while simultaneously reducing component count, lowering cost, and reducing board space.

Note: For the purposes of this article ratiometric means that the output of the device is dependent on the ratio of the property being measured and some other voltage or current.

Resistive elements are ratiometric because resistance is not measured directly. It is determined by the ratio of the voltage across the resistor to the current through the resistor.

R = V/I Eq. 1 (Ohms law)

Sensors using resistive elements typically send a current through the resistor and measure the resulting voltage. This voltage can be amplified and level shifted before reaching the sensor's output, but it is still dependent on the current through the resistor. If that current is derived from the supply voltage, then the sensor's output will be ratiometric to the supply voltage. Equation 2 describes the output of a generic ratiometric sensor (

Vs = Ve (P x S + C) Eq. 2

The Honeywell™

Needing to know the excitation voltage in order to use the output signal is very inconvenient in many applications. To solve this problem manufacturers add a voltage reference to the circuit. These devices provide a very accurate voltage independent of temperature and the supply voltage. If the current flowing through the sensing resistor is derived from a voltage reference, then Ve in Equation 2 is replaced by a constant. This gives rise to Equation 3, where the new constant is incorporated in S

Vs = P x S

Equation 3 is not ratiometric because the output signal is only a function of the property being measured. Honeywell's MLxxx-R5 series of pressure transducers is an example of nonratiometric sensors. The offset is 1V and the full-scale output is 6V when operated with any supply voltage between 7V and 35V.

D = (Vs/Vref)FS x K Eq. 4

The source of the reference voltage depends on the design of the ADC. In some ADCs the reference is the supply voltage, in others it comes from an internal voltage reference, and with others the user must connect a reference voltage to the Vref input on the ADC. If the reference voltage has been made constant through the use of an internal or external voltage reference, then Equation 4 can be simplified to Equation 5, where K

D = Vs x K

D = P x S

Equation 6 provides exactly what is needed. The digital value (D) is proportional to changes in P and is only affected by changes in P. D is not affected by changes in temperature or supply voltage.

The remainder of this article will show how creative use of an ADC's reference voltage input can eliminate the voltage references and current sources used in many sensor circuits. This design saves component cost, board space, and overhead voltage. Small improvements in accuracy can also be achieved, as eliminating the voltage reference eliminates the errors associated with an imperfect reference. The automotive industry has taken advantage of these techniques for years. By specifying both sensors and ADC that are ratiometric to the supply voltage, the need for accurate voltages references is eliminated.

The use of similar techniques with current-driven sensors and single-element resistive sensors such as RTDs is less common. With all these circuits the ADC's sensitivity will vary with temperature or supply voltage. The combination of the ADC and sensor input is, nonetheless, quite stable.

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

At first glance the approach in Equation 7 appears undesirable because the output (D) is a function of three variables, not just P. A closer look, however, shows that it is the ratio of Ve/Vref that is important, not the individual values. The ratio of Ve/Vref can inexpensively be made constant by deriving both voltages from the same source. Once this is done, D will be proportional to changes in P, and only changes in P. Setting Ve/Vref to a constant allows Equation 7 to be simplified to a form that matches Equation 6. This shows, therefore, that equivalent performance can be achieved without using voltage references.

From a practical standpoint, Ve and Vref must be large enough that noise is not a problem; they must also lie within the specified limits of the ADC and the sensor. Using the positive supply voltage as the source of both Ve and Vref usually satisfies all these conditions and allows numerous sensors to be powered in parallel, as shown in

The MAX1238 shown in Figure 3 has a 12-input multiplexer on the front-end and a built-in voltage reference. In this case, there would be no additional cost to add a reference to the ADC, but there would be a significant cost to add a reference to each of the ten sensors. The MAX1238 also allows the AN11 input to be used as the reference voltage. Using AN11 as the reference input and connecting it to the 5V supply sets the full-scale input of the ADC to 5V and allows it to be used with the ratiometric sensors. In Figure 3, the MAX1238's internal voltage reference is not wasted. Through software control the internal voltage reference can be selected and used for diagnostic purposes, such as measuring the supply voltage. This is done through a voltage-divider connected to input AN10.

The topology of Figure 3 works well in automotive applications and other applications where power is provided by a single voltage source and voltage drops along the power lines are small. It is not appropriate for applications where the sensor must operate with very long lead wires or applications where the ADC and sensors are powered by different supplies.

Vs= Ie (S x P+C) Eq. 8

An alternate approach to Figure 4 is shown in the circuit of

The derivation for Figure 5 follows with Equation 9:

Vref = Ie x R1 Eq. 9

Starting with the ADC Equation 4 above and substituting Equation 9 for Vref and Equation 8 for Vs, yields Equation 10.

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

The excitation current (Ie) drops out because it is common to both the numerator and denominator. This yields Equation 11, which shows that the output is independent of the excitation current. If the constants in Equation 11 are combined, the result is once again equivalent to Equation 6: the system using voltage references.

D = P(S x FS x K/R1)+C(FS x K/R1) Eq. 11

R1 must have a low temperature coefficient if it is to behave as a constant. Requiring R1 to have good temperature stability is not a drawback of Figure 5 when compared to Figure 4, because the resistor in Figure 4 must also have good temperature stability.

R2 does not appear in Equation 11 and is not needed for this circuit. R2 is, nonetheless, included in this analysis to show that it does not affect the ADC reading. R2 can be replaced by another current-driven pressure sensor, an RTD, or the resistance of a solid-state switch without affecting the ADC reading.

Theoretically it is possible to use a multiple-input ADC with several current-driven sensors powered in series. However, placing sensors in series lowers the excitation current (Ie), the sensor signal (Vs), and the reference voltage (Vref). When placing sensors in series, special attention must be paid to the ADC's Vref requirements as well as system noise.

The circuit in

The derivation of the circuit in Figure 6 follows:

Vs = (V+) x Rt/(R1+R2+Rt) Eq. 12

Vref = (V+) x R1/(R1+R2+Rt) Eq. 13

Starting with Equation 4 and substituting Equation 12 for Vs and Equation 13 for Vref, gives the output of the ADC in Figure 6. The results of this substitution can be simplified to yield Equation 14. Equation 14 shows that if R1 is stable, changes in D will be directly proportional to, and only dependent on, changes in Rt, which is the desired result.

D = FS x K x (Rt/R1) Eq. 14

As can be seen from Equation 14, R2 does not affect the reading; R2 reduces the power dissipated by Rt. If R2 did not have this effect, the self-heating of Rt could cause significant errors in the temperature reading. R2 also lowers the common-mode input voltage to the ADC. This is necessary for some ADCs where the common-mode input-voltage range is less than the supply voltage.

ADCs like the MAX1403 include current sources for driving RTDs. These are not, however, precision current sources and require some type of calibration. Calibration is frequently accomplished by using an additional ADC input to measure a reference resistor driven by the same current source. Software is then used to scale the measurement of the unknown resistor to the measurement of the known resistance. While this technique works quite well, using R1 as the reference resistor is simpler and does not require an additional ADC input. The onboard current source can still be used to excite the RTD and reference resistor. Replacing R2 in Figure 6 with a current source will not affect Equation 14.

Two matched current sources are provided on some ADCs for accurately measuring remote RTDs. The resistance of the long lead wires used in these applications adds to the resistance of the RTD, thus creating an error that must be removed. The lowest cost solution is to use a three-wire RTD. As shown in

Vo = Vb(Rc/(Rc+Ru) - Rb/(Ra+Rb)) Eq. 15

If Vo = 0, then Ru = Rc x Ra/Rb Eq. 16

Today balanced bridge circuits are seldom used to measure resistance, but it is quite common to use an unbalanced bridge in a sensor. During factory calibration the bridge is usually balanced at a well-defined point; deviations from that point are measured by measuring the imbalance in the bridge. The benefits of using a bridge in this manner are easily seen in the following example.

Assume that a silicon strain gauge has been bonded to a diaphragm to make a pressure sensor and that a pressure resolution of 0.1% is desired. The value of the resistor is 5000Ω at 0psi and 25°C. At 100psi (full-scale pressure) and 25°C the value of the resistor has increased by 2% to 5100Ω. Besides being sensitive to strain, the resistor is sensitive to temperature and has a Temperature Coefficient of Resistance(TCR) of 2000ppm/°C.

Because the resistor changes 100Ω over the pressure range, it will be necessary to resolve 0.1Ω of resistance to achieve 0.1psi (0.1%) pressure resolution. Measuring 0.1Ω out of 5000Ω is 1 part in 50,000 or about 15.6 bits of resolution. A bigger problem than the resolution requirement is the affect of temperature changes. Due to a resistor's high TCR, a temperature change of 1°C will create the same change in resistance as a 10psi pressure change. That translates to 10% of full-scale per °C.

Now consider the same resistor used in a bridge circuit that has two volts of excitation. The other three resistors are 5000Ω each and have the same TCR as the sensing resistor. The resistors are mounted isothermally. There are two significant benefits to this approach.

The greatest benefit of the bridge in this application is that it rejects changes due to temperature. Examining Equation 15 shows that TCR no longer matters. The bridge resistors could double in value and the output would remain the same. As long as all the resistors change by the same percentage, the output does not change!

The second benefit of the bridge is that it reduces resolution requirements. The bridge's output is 0mV at 0psi and 10mV at 100psi. To resolve 0.1psi it will be necessary to resolve 10µV out of 10mV. This only requires 10 bits of resolution, compared to the 15.6 bits required if the resistance is measured directly.

From a practical standpoint, 10-bit ADCs cannot measure 10µV directly. The signal must be amplified. The cost of amplification can make it more attractive to use a higher resolution ADC that does not need an external amplifier. The big benefit of lower resolution comes from the reference requirements. It is generally impractical to design in a voltage reference, current source, or reference resistor that is stable to 16-bits over time and temperature.

The values in this example were not chosen to exaggerate the importance of the bridge. Rather, these values are typical of many piezoresistive pressure sensors (See

Vs = (Vb)(R3/(R2+R3) - (R1/(R1+Rt)) Eq. 17

Vfer = (Vb)(R1/(R1+Rt) Eq. 18

The ADC's output, Equation 19, is obtained by starting with Equation 4 and substituting Equations 17 and 18 for Vs and Vref, respectively. Equation 19 shows that by using this reference voltage, the ADC output becomes a linear function of Rt, minus the desired offset term.

D = Rt(R3/(R1(R2+R3)) - R2/(R2+R3) Eq. 19

In Figure 10 R3b and R1b adjust offset and sensitivity respectively. When this is done the display will directly show the temperature in °C or °F. The only significant errors will come from the nonlinearity of the RTD its self. This error will be a few tenths of a degree between 0°C and 100°C.

The circuit in Figure 10 can also be calibrated digitally by using the serial interface on the MAX1492 ADC to correct the displayed reading for offset and sensitivity errors. This method of calibration not only eliminates the need for R1a and R3a, but it also provides an opportunity to correct for linearity errors in the RTD. If higher resolution measurements are needed, the MAX1492 can be replaced with the MAX1494, which provides an additional digit of resolution.

According to Equation 19, the value of R4 will not affect the reading. R4 has been added to the circuit to reduce the self-heating of the RTD. This also reduces the signal from the bridge and reduces the reference voltage. Although the MAX1492 does not have an internal PGA, it does allow for small reference voltages. Using a small reference voltage eliminates the need for additional amplification.

A similar article appeared in the July, 2005 edition of

Silicon also has an undesirable characteristic that causes the sensitivity of these sensors to decrease with temperature, typically at rate greater than 2000ppm/°C. Fortunately it is possible to create bridge resistors whose resistance increases at the same rate as sensitivity decreases. When these sensors are powered by a current source, the bridge voltage will increase at the same rate that the sensitivity decreases. This provides an output signal that, over a limited temperature range, is temperature independent.

For the bridge circuit to reject changes in resistance due to temperature, it is critical that all four resistors have the same Temperature Coefficient of Resistance (TCR) and are at the same temperature. The silicon sensors easily meet these requirements. The small size of the sensor ensures uniform temperature, and fabricating all four resistors at the same time results in TCRs that are virtually identical.

It is also customary to have all four resistors respond to pressure. Two resistors will increase in value as the pressure increases and two resistors will decrease in value. This not only increases the output of the bridge by a factor of four, but it also eliminates the nonlinearity error seen in unbalanced bridges with a single active element.

Device | Function | Max Load | Accuracy @ 25°C | Temperature Coefficient | Line Regulation | Load Regulation |

MAX8510 | Regulator | 120mA | 1.0% | 12ppm/°C, typ | 10ppm/V, typ | 30ppm/mA, typ |

MAX6126A | Reference | 10mA | 0.02% | 0.5ppm/°C, typ | 1.2ppm/V, typ | 0.4ppm/mA, typ |

²For more information on the Melexis sensors, visit their website

³For more information on the Nova Sensor products, visit their website