How to choose a suitable resistor voltage divider

Whether your application is a precision voltage reference or an instrumentation amplifier, voltage dividers play a large role in high-precision resistor applications. Although resistor- type voltage dividers are simple circuits , problems and misunderstandings still arise when discussing their design:

● If my system is specified to operate in the temperature range of -55 to 125°C, how much will my output voltage deviate from the ideal value?

● What effect does temperature range have on the output of a voltage divider?

● If I use resistors with an accuracy of ±0.1%, then my output voltage accuracy will be within ±0.1%, right?

Selection Method
There are two main ways to implement a resistive voltage divider: by connecting two discrete chip resistors to a common terminal, or by using a resistor network inside the voltage divider package. The type you choose can have a big impact on the performance of the voltage divider.

A common resistive voltage divider consists of two resistors in series, as shown in Figure 1. The voltage is input at the top of the divider and output at the node between the two resistors, while the reference voltage (usually ground) is connected at the bottom of the divider.

Figure 1. Common dual resistor voltage divider

The voltage divider works according to Ohm's law: V=IR. When voltage (input voltage) is applied to the input of the voltage divider, current (I) flows through both resistors. Therefore, according to Ohm's law, the voltage developed across each resistor will be a fraction of the input voltage. V1=I(R1), VOUT=I(R2), and VIN=V1+VOUT. In this way, the input voltage is "divided" into two voltages.

The output voltage divided by the input voltage gives us the transfer function of the voltage divider:

VOUT/VIN=IR2/(I(R1+R2))=R2/(R1+R2)

The transfer function shows that the output voltage depends on the input voltage and the resistance values ​​of R1 and R2. In this ideal situation, the output voltage is exactly calculated as R2/(R1+R2), and this ratio depends on the input voltage and the full temperature at which the resistor element can operate. But resistors are not ideal. Real resistors have inherent tolerances and temperature coefficients that can introduce large errors into electronic systems.

How do these effects affect the error of a voltage divider in a non-ideal state? Let's look at the effect of inherent tolerance on the output voltage of a voltage divider. If the voltage divider is constructed with two discrete resistors (as shown in Figure 2), the output error depends not only on the inherent tolerance of the discrete resistors, but also on the ratio of the voltage divider. If R1=R2, then the maximum error in the output voltage due to the resistor tolerance is equal to the inherent tolerance of the resistors. But what if R1≠R2?

Figure 2: Voltage divider using discrete chip resistors

If R1 and R2 have different values, the error in the voltage output will be approximately twice the inherent resistor tolerance, as shown in Figure 3. The worst case for a voltage divider design occurs when the tolerances of the two resistors are opposite. If the voltage divider is designed using resistors with a ±0.1% tolerance, the output error can be as bad as ±0.2% at this ratio.

Figure 3: The voltage divider output error increases as the ratio increases.

Balanced tolerance

Figure 4 illustrates one way to reduce this doubling tolerance error. By depositing and growing precision thin-film resistors on a monolithic substrate, the resistor elements have very similar electrical characteristics. Because the “divided” output voltage we’re interested in is determined by the ratio of R1 to R2, it’s independent of the absolute tolerance of each resistor element. By purchasing a thin-film resistor divider with a ratio tolerance of ±0.1%, we can be sure that the maximum output error introduced by the inherent tolerance is ±0.1%, regardless of the tolerance of each individual resistor—an improvement of twice that of a discrete solution.

Figure 4 Voltage divider using thin film on a monolithic substrate

The idea of ​​using a monolithic thin-film voltage divider can be used not only to reduce the output error introduced by tolerance effects, but also has the same benefit in reducing the error introduced by temperature. Common high-precision chips have a temperature coefficient (TCR) of ±25×10-6/°C. This means that when the resistor temperature reaches 125°C (100°C higher than room temperature), the resistance value of each resistor may change by as much as ±0.25%. If the temperature coefficients of R1 and R2 change in opposite directions, the output voltage error can be as much as twice (or ±0.5%).

A conventional thin film voltage divider has a TCR tracking of ±5×10-6/°C between the two resistor elements. Again, because the thin film resistor elements are deposited and processed in exactly the same way on a monolithic substrate, they vary in the same direction as temperature. Also, again, because the ratio of the two resistor elements is important to the output voltage, the absolute temperature coefficient of each resistor element is irrelevant to the accuracy of the voltage divider. By purchasing a thin film voltage divider with a TCR tracking specification of ±5×10-6/°C, the output voltage error introduced by temperature effects over a 100°C variation can be reduced from ±0.5% to ±0.05%; a 10-fold improvement.

Table 1 summarizes the two approaches. When designing a voltage divider using 0.1% discrete resistors, the maximum output error introduced by tolerance and TCR is 0.7%. When using precision thin-film resistors, the maximum output error is ±0.15%—more than a 4x improvement in performance.

Further investigation showed that the expected output voltage is affected by the ratio of the resistors in the voltage divider and their inherent tolerances and temperature coefficients.

By choosing a high-precision thin-film voltage divider on a monolithic substrate, designers can ensure that the resistor elements in the voltage divider have very similar electrical characteristics and track well over temperature and time. The similarity of materials and processes on a common substrate ensures that the voltage divider is more stable and performs better over all ratios and environments.