A New Ratiometric Data Acquisition Circuit for Unequal Supply and Reference Voltages

Ratiometric data acquisition of remote or offboard sensors is a technique that improves overall system accuracy. Designers normally think that an acquisition system ADC’s reference voltage (V_ref) must be very precise. This isn’t necessarily the case in a ratiometric data-acquisition system, at least as long as the supply voltage is equal to the reference voltage (V_supply = V_ref).

However, many systems are forced to use supply voltages that aren’t equal to the reference voltage (V_supply ≠ V_ref). This can introduce a significant error into a ratiometric measurement system. This article proposes a modified system that remedies this problem, maintaining the ratiometric measurement with excellent tolerance.

 

A Basic Ratiometric System Review

Figure 1 shows a typical ratiometric system, in which the sensor supply voltage is equal to the V_ref used to create it.

 

Figure 1. A ratiometric data-acquisition system where V_supply = V_ref.

 

The sensor outputs a voltage (V_sensor) that is proportional to V_supply by a factor of K:

$$V_{sensor} ~=~ KV_{supply}~=~K V_{ref}$$

Equation 1.

 

where 0 ≤ K ≤ 1.

V_sensor is digitized by a single-ended, unipolar-input ADC having N bits and supplied with V_ref:

$$ADC~output~=~\frac{V_{sensor}}{V_{ref}}(2^N~-~1)$$

Equation 2.

 

Because V_supply = V_ref, the resulting calculation shows that K is independent of V_supply or V_ref:

$$ADC~output~=~K\frac{V_{ref}}{V_{ref}}(2^N~-~1)~=~K(2^N~-~1)$$

Equation 3.

 

Tracker LDOs

Intrinsic to a ratiometric data-acquisition system is a tracker low-dropout linear regulator (LDO), which provides V_supply. A tracker LDO differs from a standard LDO in that it doesn’t have an internal V_ref. Instead, the tracker LDO output tracks an externally supplied V_ref. The supply voltage to the sensor is often 5 V, which—as shown in Figure 1—then necessitates that the ADC V_ref also be 5 V.

The circuit in Figure 1 uses the TPS7B4255-Q1 tracker LDO from Texas Instruments (TI), which is often used to power remote offboard sensors. It also includes features to protect against faults such as short-circuit to ground or supply, blocking of reverse current, overtemperature, and reverse polarity of supply. The tracker LDO can be disabled by pulling its ADJ/EN pin low using Q1.

Tracker LDOs do have a tracking error, which is an offset voltage (V_os) between the ADJ pin and the FB node. This output offset is 6 mV maximum for the TPS7B4255-Q1. Even in ratiometric systems like the one shown in Figure 1, V_os is not removed and remains as an error. This is because V_os changes V_supply and therefore V_sensor, but it doesn’t change V_ref. In a 5 V system, the error is only 6 mV (0.12%).

 

Systems Where V_supply Doesn’t Equal V_ref

As we stated previously, offboard remote sensors often have a supply voltage requirement of 5 V. In a traditional ratiometric system, this also necessitates making V_ref = 5 V. However, many modern ADCs typically have a V_ref of 1.8, 2.5, or 3.3 V.

If V_ref and V_supply are different voltages, then you must use resistor dividers. In Figure 2, for example, V_supply = 5 V and V_ref = 1.8 V.

 

Figure 2. Schematic of a ratiometric data-acquisition system where V_supply ≠ V_ref.

 

A resistor divider composed of R1 and R2 in the feedback path of the Tracking LDO is used to scale V_ref up to V_supply as follows:

$$V_{supply}~=~V_{ref}\frac{R_1~+~R_2}{R_2}~=~V_{ref}(1~+~\frac{R_1}{R_2})$$

Equation 4.

 

Another divider must scale V_sensor down to fit within the ADC’s V_ref range:

$$V_{sensor\text{_}div}~=~V_{sensor}\frac{R_4}{R_3~+~R_4}$$

Equation 5.

 

The resistor dividers aren’t perfect. For example, resistors with a 0.1% initial tolerance also have other error terms, as listed in Table 1. Summing all terms in Table 1 gives an absolute worst-case resistor tolerance of ± 0.65%.

 

Table 1. Example error terms of a 0.1% headline tolerance resistor. Data used courtesy of Texas Instruments

Error term	Tolerance (±%)	Test conditions
Initial tolerance	0.10
Temperature drift	0.15	±15 ppm/°C resistor over a 100 °C span
Cold temperature	0.05	–55 °C for 2 hours
Endurance	0.10	70 °C for 1,000 hours of operation
Humidity	0.10	40 °C at 93% relative humidity for 56 days
Temperature cycling	0.05	–10 °C (30 minutes) to +85°C (30 minutes) × 5 cycles
Vibration	0.05	Swept from 10 to 2,000 Hz for 7.5 hours
Soldering	0.05	260 °C for 10 seconds

 

The list in Table 1 is not exhaustive and is highly application-dependent, making the question, “What is the true accuracy of a 0.1% tolerance resistor?” surprisingly tricky to answer.

 

A Ratiometric Data-Acquisition System With V_supply ≠ V_ref

In Figure 2, the errors introduced into the system by the two resistor dividers aren’t cancelled. This limits the accuracy of the measurement.

One source of error is the output offset voltage of the LDO. The V_os of the tracker LDO is multiplied by (R₁ + R₂)/R₂ and appears on the output. For example, in a system where V_supply = 5 V and V_ref = 1.8 V, the output V_os maximum is:

$$V_{os,max}~=~6~\text{mV}~\times~\frac{5~\text{V}}{1.8~\text{V}}~=~16.7~\text{mV}$$

Equation 6.

 

This error is divided back down again by R₃ and R₄ so that the V_os at the ADC is 6 mV. However, the V_ref is only 1.8 V. The error from V_os at the ADC is therefore 6 mV/1.8 V = 0.33%, which is larger than when V_ref was equal to 5 V.

To address this, Figure 3 shows a proposed ratiometric data-acquisition system where V_supply ≠ V_ref. In this example, V_supply = 5 V and V_ref = 1.8 V. However, this approach will also work with other common ADC reference voltages.

 

Figure 3. Schematic of proposed data-acquisition system where V_supply ≠ V_ref.

 

Comparing Figure 3 to Figure 2, there is now a resistor divider (D1) that scales V_supply down so that it can also be captured by the ADC. Resistive dividers D1 and D2 are a matched pair integrated into the same package. As we’ll see later, divider D3 can be made on the OUT-to-FB of the tracker LDO using standard 1% tolerance resistors.

Using three dividers allows us to choose D3 so that it scales the 1.8 V reference voltage exactly to the 5 V supply voltage. If you were to use one of the matched pair of dividers instead, the ratios available wouldn’t allow for exact scaling of 1.8 V to 5 V. This is important because the sensor has a requirement for the accuracy of its V_supply, and you want V_supply to sit right at the nominal supply voltage of 5 V.

 

Matched Resistor Divider Networks

Figure 4 shows an example of a matched resistor divider network. The TI RES11A consists of two independent resistor dividers. The RES11A is available with different resistor divider ratios and versions qualified for automotive applications (the RES11A-Q1).

 

Figure 4. The RES11A or RES11A-Q1.

 

For all dividers, R_INx = 1 kΩ. While the absolute tolerance of an individual resistor in the RES11A is quite loose (12% maximum), the fact that the four resistors are integrated into a monolithic package and are interdigitated with each other gives them excellent matching characteristics of ± 0.05% maximum.

The matching of the first divider to the second divider within the RES11A is also excellent, at ± 0.1% maximum. Furthermore, other errors, such as temperature drift, are also well matched. This results in a very low divider temperature drift of Δt_Dx/ΔT_a = ±2 ppm/°C drift mismatch maximum.

The resistor dividers, composed of R_INx and R_Gx, can be connected in either direction to provide two different scaling voltages: R_IN/(R_IN + R_G) or R_G/(R_IN + R_G). Table 2 shows versions of the RES11A devices with different divider ratios and how each can be used to scale the 5 V V_supply and V_sensor voltages to the target V_ref voltage.

 

Table 2. Versions of the RES11A with different resistor divider ratios.

Vref (V)	Device variant	Usage of RINx and RGx	Scales 5 V to … (V)
1.8	RES11A20	RIN/(RIN + RG)	1.67
1.8	RES11A25	RIN/(RIN + RG)	1.43
2.5	RES11A10	RIN/(RIN + RG)	2.5
2.5	RES11A15	RIN/(RIN + RG)	2.0
3.3	RES11A15	RG/(RIN + RG)	3.0
3.3	RES11A16	RG/(RIN + RG)	3.12

 

The ADC that you use can be integrated into a microcontroller, as with the TI MSPM0L1306. Alternatively, it can be a stand-alone ADC such as TI’s ADS7142-Q1, ADS7138-Q1 (I²C), or ADS7038-Q1 (SPI). The ADS7142-Q1 has two input channels, while the other two ADCs have more analog inputs.

 

Analyzing the System’s Effectiveness

Let’s analyze the effectiveness of the measurement scheme in Figure 3. We’ll start by evaluating the resistor divider ratios (D₁, D₂, and D₃). Dividers D1 and D2 are attenuators that scale down the voltage:

$$D_1~=~\frac{R_{IN1}}{R_{G1}~+~R_{IN1}}$$

Equation 7.

 

$$D_2~=~\frac{R_{IN2}}{R_{G2}~+~R_{IN2}}$$

Equation 8.

 

D3 is a multiplier that scales up a voltage:

$$D_3~=~\frac{R_1~+~R_2}{R_2}~=~1~+~\frac{R_1}{R_2}$$

Equation 9.

 

The output from the tracker LDO, including the V_os, is expressed by:

$$V_{supply}~=~D_3(V_{ref}~+~V_{os})$$

Equation 10.

 

V_supply is measured by the ADC through resistor divider D1 to give V_{supply_div}:

$$V_{supply \text{_} div}~=~D_1D_3(V_{ref}~+~V_{os})$$

Equation 11.

 

The sensor has a gain of K (0 ≤ K ≤ 1) and its output is proportional to its supply voltage. The sensor output is measured by the ADC through divider D2 as shown in Equation 12:

$$V_{sensor \text{_} div}~=~K D_2 V_{supply}~=~K D_2 D_3(V_{ref}~+~V_{os})$$

Equation 12.

 

The ADC has N bits and uses V_ref. It performs a single-ended, unipolar measurement with an output expressed as:

$$ADC~output~=~\frac{V_{input}}{V_{ref}}(2^N~-~1)$$

Equation 13.

 

where V_input is the voltage input to the ADC.

Equations 14 and 15 calculate the digitized V_{supply_div} and V_{sensor_div} voltages as:

$$V_{supply\text{_}div\text{_}digitized}~=~D_1D_3\frac{V_{ref}~+~V_{os}}{V_{ref}}(2^N~-~1)$$

Equation 14.

 

$$V_{sensor\text{_}div\text{_}digitized}~=~KD_2D_3\frac{V_{ref}~+~V_{os}}{V_{ref}}(2^N~-~1)$$

Equation 15.

 

The microcontroller takes the digitized ADC readings of V_{supply_div_digitized} and V_{sensor_div_digitized} and computes the ratio:

$$Computed~ratio~=~\frac{V_{sensor\text{_}div\text{_}digitized}}{V_{supply\text{_}div\text{_}digitized}}~=~K\frac{D_2}{D_1}$$

Equation 16.

 

The computed ratio value is independent of V_ref, V_supply, V_os, and D₃. That’s why it’s possible, as we mentioned earlier, to make divider D3 using standard 1% tolerance resistors.

If the two resistor dividers in the RES11A (D1, D2) are perfectly matched, then D₁ = D₂ and the resulting computed ratio = K. The acquisition system is measuring only K, which is the output of the sensor from 0 to 100% of full scale.

In practice, dividers D1 and D2 are not error-free. Let’s analyze that in the next section.

 

Matched Resistor Divider Networks vs. Discrete Resistors

You could make dividers D1 and D2 from discrete 0.1% resistors instead of the RES11A matched resistor divider networks. However, the discrete resistors aren’t matched, and their errors don’t track each other. This would negatively impact the accuracy of the system.

 

Errors When Using Discrete Resistors

In any resistor divider, the tolerance of each resistor does not simply add together to create the tolerance of the divider output. The divider output tolerance also depends on the ratio of the divider (D). Equation 17 gives the relative divider error as:

$$\frac{\Delta D}{D}~=~\pm~2T(1~-~D)$$

Equation 17.

 

where:

ΔD is the absolute error

T is the tolerance of each resistor in the divider.

 

Let’s examine the limits. As D → 1, then ΔD/D → 0. As D → 0, ΔD/D → ±2T, which is the worst-case error. In other words, the higher the attenuation of the divider, the larger the error from the resistor tolerances.

By applying these results, we can evaluate the effect of using discrete resistors in the proposed system (Figure 3). We know from Equation 16 that the computed ratio from its two ADC readings is proportional to D₂/D₁. Equation 18 calculates the computed ratio when divider errors ΔD₁ and ΔD₂ are included:

$$Computed~ratio~with~error~=~\frac{D_2~+~\Delta D_2}{D_1~+~\Delta D_1}$$

Equation 18.

 

The resistor divider ratios are designed to be identical: D₁ = D₂ = D. Therefore, Equation 19 gives the error of the computed ratio as:

$$Computed~ratio~error~(\%)~=~\pm \left[\frac{1~+~2T(1~-~D)}{1~-~2T(1~-~D)}~-~1 \right]~100 \%$$

Equation 19.

 

As D approaches 1, the computed error ratio approaches 0. On the other hand, as D approaches 0, the computed ratio error approaches ±4T. This is the worst case.

Equation 19 also applies when considering the other errors, such as temperature drift, that we described in Table 1.

 

Errors When Using Matched Resistor Divider Networks

For the RES11A, the analysis is different. The matching tolerance (t_M) between the two dividers has a maximum value of ±1,000 ppm, or ± 0.1%.

The temperature coefficient of each divider has a maximum value of Δt_Dx/ΔTa = ±2 ppm/°C drift mismatch. Thus, a very conservative value of the temperature drift of D₂/D₁ is ±4 ppm/°C. The data sheet, which is linked to earlier in the article, does specify the typical matching temperature coefficient of resistance between the two dividers (Δt_M/ΔTa = ±0.05ppm/°C). However, it doesn’t give the maximum value.

Table 3 compares the errors for matched resistor divider networks with discrete 0.1% tolerance resistors. The table compares the initial accuracies and temperature drift. The use case is for the RES11A20 to make D₁ and D₂. For that reason, D = 0.333.

 

Table 3. Comparison of errors of D₂/D₁ when using discrete 0.1% resistors vs. the RES11A.

Parameter	RES11A tolerance (±%)	Discrete 0.1% resistor-divider tolerance (±%)
Initial tolerance	0.10	0.267
Drift with temperature	0.04	0.401

 

The total error from the RES11A is ± 0.104%, compared to ± 0.668% for the discrete resistor solution. As previously discussed, there are other error terms to consider for both cases. You can expect that the matching of the dividers in the RES11A will outperform the discrete 0.1% resistor dividers.

 

Simulation of the New Ratiometric Data-Acquisition System

Using the TINA-TI™ software, we’ve developed a behavioral model of the proposed ratiometric data-acquisition system. Figure 5 shows this system set up to run a DC simulation.

 

Figure 5. TINA-TI software DC analysis of a ratiometric data-acquisition system where V_supply ≠ V_ref. [click to enlarge]

 

The TPS7B4256-Q1 tracker LDO is modeled as a gain equal to D₃. The RES11A20, with R_INx = 1 kΩ and R_Gx = 2 kΩ, is used to scale 5 V to 1.67 V. The output of the sensor is set to K = 0.15.

To see how the system reacts in the presence of errors, D₃ is increased by 3% to 2.86, V_os = –6 mV, and V_ref is increased by 1% to 1.818 V. In Figure 5, the computed ratio remains at the ideal value of 0.15, which is K.

 

Wrapping Up

When a ratiometric data acquisition system uses a topology where V_ref ≠ V_supply, additional errors are typically introduced that impact the accuracy. We have demonstrated a new ratiometric data-acquisition system that allows these errors to be canceled.

Using a matched pair of resistor dividers such as the RES11A restores the accuracy of the acquisition system and is superior to using individual precision resistors. When compared to using 0.1% discrete resistors, the RES11A reduces the error by 6.4×.

 

Featured image used courtesy of Adobe Stock; all other images used courtesy of Texas Instruments