The trend toward continued miniaturization of Electronic circuits presents new challenges for resistor design. For example, the increase in electronic functionality in vehicles has resulted in an increase in the number of electronic devices per unit area. This in turn affects passive components in many ways – resistors in particular. These devices need to become smaller while offering higher accuracy and better stability. Higher accuracy is achieved through tighter tolerances and lower temperature coefficients.

Thin-film chip resistor arrays can meet the requirements of reduced size, higher precision, and increased electrical stability by integrating multiple resistors on the same ceramic substrate. By integrating these devices, the resistor array requires less space than the same number of discrete resistors. This allows for higher packing densities of electronic circuits and therefore more electronic functions per unit area. In addition, thin film chip resistor arrays are used in applications where the relative behavior of the resistors is critical, such as voltage dividers and feedback circuits in op amps or DC-to-DC converters.

This article will describe how thin film chip resistor arrays can positively impact the electrical stability of a circuit while reducing the required area. Using a voltage divider as an example, we will explain the relative parameters “tolerance matching” and “TCR tracking” in the article, and discuss the temperature behavior of resistor arrays. In addition, this article will show how to control the tolerance and temperature coefficient of resistors during production.

**Relative tolerance (tolerance matching) using a voltage divider**

Figure 1: Voltage divider consisting of R1 and R2.

Figure 1 depicts an unloaded voltage divider consisting of R1 and R2. At the output pin of the voltage divider, the output voltage VOUT, determined by R1 and R2 and their deviation Δ from the nominal resistance value, can be measured:

The deviation from the nominal resistance is called the absolute tolerance. If the two absolute tolerances Δ1 and Δ2 are equal, the error term (1+Δ1)/(1+Δ2) is equal to 1. Resistor arrays can achieve approximately equal tolerances. Figure 2 shows the tolerance of a thin film chip resistor array integrated with four resistors.

Figure 2: Tolerance of resistor arrays.

In this example, all four resistor values of the array are within ±0.5% of the absolute tolerance. In addition, tolerance matching is specified for precision resistor arrays. It is defined as the span between the minimum and maximum resistance deviation, as an unsigned number. In the example above, the tolerance match value is 0.1%. When compared to a single resistor in a voltage divider, this corresponds to a deviation of ±0.05%.

**Relative Temperature Coefficient (TCR Tracking)**

The absolute temperature coefficient a describes the change in resistance value as the temperature increases or decreases

In the above, J represents the layer temperature in degrees Celsius (°C), RJ is the resistance value at the layer temperature, and R20 is the resistance value at 20°C (reference temperature). At temperature J=20°C, △R/R20=0. According to formula (2), the change of resistance ΔR decreases at lower temperature coefficient α. For this reason, a low temperature coefficient (TCR) is essential to ensure a small resistance variation with temperature. TCR is given in ppm/K. If the ambient temperature J rises to 120°C due to thermal conduction, thermal radiation, or convection from nearby devices, then a 50-ppm/K resistor will change its value by ±0.5%. The temperature coefficient always has a defined temperature range. The typical temperature range is –55°C to +125°C. For automotive applications in harsh environments, such as engine control units or gearbox controls, the temperature range extends up to +155°C. Figure 3 shows the TCR of a thin film chip resistor array.

Figure 3: TCR tracking.

The absolute TCR limit in this example is ± 50 ppm/K. The TCR curves of the 4 integrated resistors R1, R2, R3, and R4 fall within the limits. For precision resistor arrays, in addition to the absolute temperature coefficient, the relative temperature coefficient is also specified. Relative TCR (TCR Tracking) is defined as the difference between the largest and smallest TCR among the 4 integrated resistors. In this example, the TCR tracks a value of 10 ppm/K, which corresponds to a TCR of ± 5 ppm/K over a temperature range of –55 °C to +125 °C for the discrete resistors used in the voltage divider. Similar to the discussion about relative tolerance, for TCR tracking, the four resistors exhibit uniform behavior, yielding the low TCR values we expect.

**Temperature Behavior of a Voltage Divider**

On a printed circuit board, the local ambient temperature is usually different in different areas. This is the result of thermal conduction, thermal radiation, and thermal convection from adjacent devices. If discrete resistors are used, different ambient temperatures will result in different resistance changes. This effect is illustrated in Figure 4.

Figure 4: Left – Different local ambient temperatures when using discrete resistors. Right – same local ambient temperature when using integrated resistors (resistor array).

The output voltage of the fixed regulator is adjusted through a voltage divider (Figure 4, left). The resistance value of the two discrete resistors is R1=R2=1kΩ, and the TCR is ±50ppm/K. One is under the other on a printed circuit board (PCB). The fixed voltage regulator is located near R1, which increases the ambient temperature due to thermal radiation and convection. This causes the temperature of R1 to rise to +120°C. The local ambient temperature of R2 remains almost unchanged at +20°C. The different temperature levels of R1 and R2 cause the voltage divider mismatch, which can be calculated from Equation 2. The effect of a mismatch on adjacent circuits containing voltage regulators can be significant. In the worst case, the fixed-voltage regulator can fail to provide the required voltage regulation, rendering the entire circuit useless.

This effect can be reduced by placing R1 and R2 on an isotherm as much as possible. In doing so, the ambient temperature of R2 will be closer to the temperature level of R1. However, since the discrete resistors are placed at some minimum distance from each other, even the smallest possible distance will result in different temperature levels. If the two resistors have different values (R1≠R2), then things get worse. Due to the different resistance values, the power consumption is also different (P1≠P2), resulting in different temperature levels between the resistors.

Resistor arrays provide a good option for ensuring that all integrated resistors have the same ambient temperature. Due to the integration of the resistors, these arrays exhibit uniform temperature behavior. The ceramic substrate has good thermal conductivity, so all integrated resistors are at roughly the same thermal level. Therefore, the output voltage provided by the fixed regulator can be considered to be temperature independent at first approximation.

**accomplish**

Tolerance The tolerance of thin film chip resistors or thin film chip resistor arrays can be adjusted by a laser processing process. A laser beam cuts, for example, a wire-wound structure into a resistive layer, as shown in Figure 5. During the adjustment process, the resistance value is constantly monitored so that the final resistance value is within the required tolerance.

Figure 5: Wire-wound structure in thin-film chip resistor arrays.

Temperature Coefficient The temperature coefficient of thin film resistors is influenced by several process parameters, including alloy composition, coating process (sputtering process) and subsequent temperature adjustment. In order to obtain a low temperature coefficient, every parameter of all these processes needs to be done with high accuracy. The subsequent heat treatment adjusts the temperature coefficient of the thin metal layer. Depending on the duration and temperature of this heat treatment, the temperature coefficient gradually increases from initially negative to positive, ie the electrical behavior of the thin layer becomes increasingly metallic.

**product**

Thin film chip resistor arrays consist of multiple resistors integrated on the same substrate, with defined relative tolerances and relative temperature coefficients, and the fabrication process allows for uniform or different resistance values on the same ceramic carrier. Therefore, a voltage divider or feedback circuit can be easily implemented, characterized by a resistor ratio ≥ 1. Another advantage of the array is the reduced board space. This is especially beneficial in complex electronic systems where PCB area is limited. In addition, the layout cost is lower than discrete resistors because only one device needs to be placed on the PCB.

Automotive applications such as engine control units or gearbox controls require stable chip arrays designed to handle power, temperature, humidity levels and thermal cycling in harsh environments. Automotive Electronics Council standards, such as AEC-Q200, consider resistors and other passive components used in the automotive industry to be of considerable importance. AEC-Q200 presents a wide variety of electrical and climatic tests and test levels. A large number of test methods and test properties ensure that the quality of the device will be tested in many different aspects. In particular, the test level of the humidity test is very high. Since the tests proposed by AEC-Q200 only require one test without any repetition, some manufacturers conduct these tests regularly to maintain the high quality of their products.

These properties of resistor arrays translate to an advantage when implementing voltage divider, feedback, and analog signal conditioning circuits when automotive applications are in harsh environments that require long-term high stability of the voltage divider ratio.

**Summarize**

Miniaturization has increased the demands on passive components, especially resistors. Thin film resistor arrays reduce the area required on the printed circuit board without sacrificing electrical stability of the resistance values. By integrating 4 resistors on the same ceramic substrate, area requirements are reduced by more than 25%. Also, layout costs are reduced because only one device needs to be processed instead of 4 discrete devices. Relative factors such as relative tolerance and relative temperature coefficient can significantly affect the electrical stability of a resistor network or voltage divider network. These relative sizes are especially beneficial in feedback network applications such as in voltage dividers or op amp resistors. Robust designs in automotive applications require chip arrays. Passing AEC-Q200 qualification is the most desirable method of ensuring device quality, as many different aspects are tested.

The push for smaller technology solutions, especially in automotive and industrial electronics, is calling for smaller designs, but also for passive components. For this reason, resistor arrays will be shrunk into smaller standard packages. In addition, the high distribution ratio provided by the solution will also allow more flexible solutions for analog circuits to emerge.

By: Dr. Carsten Bronskowski

Vishay Draloric Beyschlag Resistor Division

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