SLPT058 January   2023

## What are matched resistor pairs?

A resistor pair is made up of two resistors connected in series making up a resistor divider. With matched pairs, each pair functions independently and is made up of an RIN and an RG with RIN1 = RIN2 and RG1 = RG2. A tap point can be found between the resistors of each divider, labeled RMID1 and RMID2 in the Functional Block Diagram. Additionally, one of the two GND pins can be used to bias the substrate for best AC performance.

Functional Block Diagram

To determine the value of the resistors, consider the ratio of the RES11Axx device in question. The divider ratio for a resistor pair is RIN divided by RG, where RIN is fixed to 1kΩ for all RES11A-Q1 and RG is the variable gain resistor that sets the dividing ratio. Each orderable part number (OPN) is associated with a different ratio, as noted in the Table 1 table. For example, a RES11A20 has a 1:2 ratio, thus the resistor has a 1kΩ RIN and a 2kΩ RG. For additional specifications see the RES11A-Q1 Automotive, Matched, Thin-Film Resistor Dividers With 1-kΩ Inputs data sheet.

RES11A-Q1 Ratios
OPNRIN (Nominal)RG (Nominal)Maximum Differential Divider Voltage
(RINX Pin to RGX Pin)(1)
RES11A001kΩ10kΩ44.7V
RES11A101kΩ1kΩ24.4V
RES11A151kΩ1.5kΩ20.3V
RES11A161kΩ1.667kΩ19.9V
RES11A201kΩ2kΩ18.3V
RES11A251kΩ2.5kΩ28.4V
RES11A301kΩ3kΩ32.5V
RES11A401kΩ4kΩ30.5V
RES11A501kΩ5kΩ29.9V
RES11A901kΩ9kΩ40.7V

## Ratio Tolerance vs Initial Tolerance

The RES11A-Q1 features a ±0.05% maximum ratio tolerance (tD1 and tD2) meaning that the ratio of RIN1:RG1 and RIN2:RG2 are at most 0.05% off of the specified ratio values at a room temperature of 25°C. The initial tolerance (tabs) of 14% refers to the part-to-part variation of the individual resistors to the nominal or printed resistance. The four resistors within the device track each other much more closely, with a typical absolute error span of 235 ppm. This means a RES11A-Q1 (which has a nominal RIN1 of 1kΩ) can have an RIN1 value as high as 1140Ω; however, because of the maximum ratio tolerance specification this means all other resistors (RIN2, RG1, RG2) have values approximately 14% above the nominal values of these resistors.

Figure 1 Resistor Ratio Matching

## Considerations for use

• Connect only one of the two GND pins to a low-impedance ground or bias point. Float the other pin to avoid the formation of current return paths through the device substrate. See the RES11A-Q1 data sheet for more information.
• The RES11A-Q1 is AEC-Q200 Grade 1 qualified and has an operating temperature range of –40°C to 125°C, desirable for industrial and automotive applications. AEC-Q200 is the worldwide standard for stress and temperature resistance that all passive electric components must meet to be qualified for use in the automotive industry. Pair the RES11A-Q1 with AEC-Q100 active components (amplifiers, comparators, ADC, DAC, and so forth) for a full automotive qualified design.
• Though labeled RINX and RGX there is no requirement for the direction of current flow. The RES11A can be rotated 180° for an attenuating gain configuration. With RGX used as the input and RINX as the output the divider ratio becomes inverted. For example, a RES11A-Q1 with a nominal resistance ratio of 1:2 has a 1:0.5 ratio when RGX is used as the input.

Figure 2 Attenuating Gain Configuration

## Importance of Matched Resistors For Maximizing CMRR in Discrete Amplifier Implementations

Consider a standard differential amplifier as Figure 3 shows. When simplified to R1 = R2, and R3 = R4, CMRR can be expressed as CMRR(dB) = 20×log[(1+R3 / R1) / (4T / 100)] where T is resistor tolerance in percent. This means CMRR is expected to be only 54dB in a unity gain configuration (R1 = R3) with unmatched 0.1% tolerance resistors. If both divider ratios are matched to a 0.05% ratio tolerance then the value for T in this formula is 0.025% resulting in an improved CMRR of 66dB. See the application information section in the RES11A-Q1 data sheet to learn more about how this number is calculated. An operational amplifier has infinite CMRR, which is a specification pertaining to the amount of the common mode signal present at the output of an amplifier. Ultimately, CMRR is a factor impacting the output signal noise. Learn more about CMRR with the Common-mode rejection ratio TI Precision Labs video on this topic.

Figure 3 Standard Differential Amplifier

## Discrete Implementations of Difference and Instrumentation Amplifiers

Difference Amplifier

Utilizing an operational amplifier such as the OPA392 and a single RES11A-Q1 in the Difference Amplifier Configuration yields a differential amplifier topology including differential inputs and a single-ended output. The gain of the amplifier can be calculated by the formula in Equation 1.

Equation 1. G = RG / RIN
Figure 4 Difference Amplifier Configuration

Instrumentation Amplifier

Utilizing two operational amplifiers such as OPA392 and a single RES11A-Q1 in the Instrumentation Amplifier Configuration yields an instrumentation amplifier topology with two high-impedance inputs and differential output. In some cases, a weak path for input bias current is needed(1). The gain of the amplifier is calculated using Equation 2.

Equation 2. G = 1 + RG / RIN
Figure 5 Instrumentation Amplifier Configuration With Differential Output

Utilizing two operational amplifiers such as OPA392 and a single RES11A-Q1 as illustrated in Figure 6 yields an instrumentation amplifier topology with two high-impedance differential inputs, one single-ended output, and a reference input. is important to simulate the design to check that the input common mode ranges and output swings meet the requirements of the desired application. The gain of the amplifier is calculated with Equation 3.

Equation 3. G = 1 + RIN / RG
Figure 6 Instrumentation Amplifier Configuration With Reference Input

Fully-Differential Amplifier

A fully-differential amplifier requires resistors to set the gain as Figure 7 illustrates. The ratio between these resistors determines the gain, thus matching is important to make sure the circuit behaves as intended. Equation 4 shows the formula for gain in this configuration.

Equation 4. G = RG / RIN
Figure 7 Fully-Differential Amplifier Configuration

The maximum sustained differential voltage rating per divider is determined by a number of factors, including the maximum junction temperature and the self-heating associated with a given voltage and divider impedance. See the specifications section of the RES11A-Q1 Automotive, Matched, Thin-Film Resistor Dividers With 1-kΩ Inputs data sheet for more details.

See the Importance of Input Bias Current Return Paths in Instrumentation Amplifier Applications application note for applications such as AC-coupled measurements or thermocouple measurements.