The hidden variable: circuit stability as a function of resistor stability

-August 26, 2010

Designers of instruments or control systems often find that component performance limits overall equipment performance in areas such as stability, frequency response, noise, and ESD. This is particularly true of resistors, which must also be able to meet stringent size, bandwidth, accuracy, and tracking requirements.

Selecting the right resistor type from wirewound, thick- or thin-film, or foil components involves tradeoffs due to the interlinked effects of thermal and mechanical forces on resistor electrical characteristics.

Stresses, whether mechanical or thermal, cause a resistor to change its electrical parameters. If such aspects as shape, length, or diameter are changed by mechanical or other means, the electrical parameters also change.

When current passes through a resistor it generates heat, and the thermal reaction causes mechanical changes by differential expansion in the different materials. Ambient conditions have the same effect. The ideal resistor would undergo no mechanical change during manufacturing, eliminating the need to compensate for the effects of heat or stress during use.

Wirewound resistors can be as good as ±0.005% with their initial tolerance, with a TCR (temperature coefficient of resistance) as low as 5 ppm/°C typical but usually about 15 to 25 ppm/°C. Thermal noise is low and tracking to ±2 ppm/°C over a limited temperature range is possible, though it adds considerable cost.

There are certain important manufacturing factors that affect wirewound resistor properties. For example, the wire is wound under tension around a core, which can elongate the wire and alter its diameter. In addition, during formation of the coil, each turn of wire has the inside surface under compression and the outside surface under tension. These deformations are permanent and irreversible. They affect stability and unpredictably shift the TCR from its original value. Over long periods, the wound element tends to change physically as the wire attempts to regain its original shape.

Permanent mechanical changes, which occur randomly and in unpredictable ways, cause equally random and unpredictable changes in the wire’s electrical parameters. Therefore, after winding, resistance elements can have highly variable electrical performance characteristics ranging from excellent to poor.

Wirewound resistors have relatively high inductance values due to their coiled-wire construction. There is also an intercoil capacitance. These units thus exhibit poor high-frequency characteristics, especially above 50 kHz.

It is difficult to make two wirewound resistors of equal value that can accurately track each other over a specified temperature range. Such tracking is of great importance in high-precision circuitry.

Traditional wirewound manufacturing methods do not isolate the resistive element from the various stresses arising out of handling, packaging, insertion pressures, and lead forming, for example. Here, one must consider tension applied to axial leads on mounting and pressure on the package exerted by mechanically induced forces.

Thick-film resistors possess good frequency response but have other characteristics that prevent their use in precision applications. Accuracy is generally in the range of ±5 to 20%, although tolerances of 1% can be attained. The temperature coefficient of thick film can be held through selection to 50 ppm/°C and can be selected to provide ±20-ppm/°C tracking. Shelf-life stabilities are about 2 to 5% of resistance value (20,000 to 50,000 ppm/year), and noise is appreciable.

Thin-metal-film resistors, evenly deposited on various substrates, offer accuracies of ±0.1% at best. The nature of the manufacturing process is such that a TCR better than ±10 ppm/°C is extremely difficult to produce. Moreover, the coefficient change of any two resistors falls randomly into the 20-ppm/°C span of the product.

As with most other resistor types, environmental effects and load-life changes cumulatively add up to, and exceed, their initial tolerances. Resistance changes can reach ±1 to 2% regardless of whether the initial resistor tolerance was ±0.05% or ±1%. When changes amounting to ±2% occur, a total design tolerance span of 6% would have to be considered in a circuit employing ±1% units, or 4.2% for ±0.1% units. This degree of instability prohibits the use of evaporated metal-film resistors as direct replacements for precision wirewound types.

Various and complex factors contribute to the instability of thin-film resistors. These include lattice distortion, discontinuous aggregate formations, occlusion of gas at crystal interfaces, oxidation of the film to form oxide semiconductors, and mechanical strains. The principal virtue of thin-film resistors is that they can be used in high-speed applications where precision and stability are not major factors, and where price is a consideration. In addition, because thin-film devices can be deposited on a single substrate in large resistor arrays, they can require fewer external connections. Thin-film resistors are very sensitive to ESD and can drift above 2500V or can open-circuit.

The hidden variable: circuit stability as a function of resistor stability figure 1The comparative advantages of bulk metal foil resistors begin with how the devices are manufactured (Figure 1). Bulk metal foil resistors are produced by cementing a cold rolled alloy film on a large-area substrate. The film is then photoetched with very fine lines and precise spacing to obtain resistances that are easily adjustable down to 0.001% (10 ppm) with matching of pairs to 0.002% (20 ppm). The standard ±0.05-ppm/°C TCR (between 0 and 60°C) with the new Z-Foil technology is derived from the properties of the alloy and its match with the substrate.

The planar design with a parallel patterned element compensates for inductance effects; maximum total inductance of the resistor is 0.08 µH. Capacitive effects are 0.5 pF (max). A 1-kΩ resistor, for example, has a rise time of less than 1 nsec without ringing. Rise time depends on resistance value, but higher and lower values are only slightly slower than midrange values. The absence of ringing is especially important in high-speed switching: for example, in computer conversion ladder networks.

Foil resistors and networks have been used extensively in precision measurement and control instrumentation, in precision current applications, and in defense and space electronics. They are particularly advantageous in systems exposed to extreme environmental conditions and ambient temperature where only small changes in resistance can be tolerated. They have also proven valuable for use in devices such as analog-to-digital and digital-to-analog converters, where high speed and stability are important factors, along with close tolerances and precise ratios.

For example, one firm designed an energy-absorbing winch that uses a small computer. This controller automatically regulates the braking force during high-stress aerial recovery operations to provide a constant line tension or payload acceleration.

The energy-absorbing controller must reach a level that will not damage the package being retrieved or place undue loads on the aircraft executing the retrieval, and maintain that level throughout the runout.

Because the computer functions in an aircraft, it must operate over a temperature range from –65 to 120°F and in a high-vibration environment. Early models used wirewound resistors and precision thin film, but temperature stability was a problem. The wirewound resistors and precision thin film caused drifting, and at high temperatures, the power rating fell off considerably. Constant adjustments were necessary because the resistors just weren’t stable over the operating temperature range. Acceptable operation could be achieved only by utilizing much larger but derated wirewound resistors. A switch to bulk metal foil resistors based on the Z-Foil technology solved the drift problems, and provided increased board density and lower mass for vibration resistance.

Many air data parameters needed for navigation by high-performance aircraft are a function of static and total air pressures around aircraft during flight. To generate such information requires sophisticated equipment.

Before these parameters can be calculated, the total and static pressures must be precisely transduced from pneumatic to electronic digital signals. Since digital computation is inherently accurate, overall stability of the air data computer depends mainly on the degree of stability of the pneumatic to electrical transducer and related circuits such as A/D and D/A converters, sample and hold amplifiers, and precision power supplies. Stability is of particular concern, with ±0.01 psi per year (±0.07% of full-scale) essential.

By using bulk metal foil resistors in place of military metal film devices, a 30 to 50% increase in the long-term performance of the analog circuits was achieved over a period of 650,000 flight hours. The transducers have an initial accuracy of ±0.04% full-scale maintained over a period of one year.

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