Resistor Network Matching Design

A resistor network is several resistive elements on one substrate in one package. It is bought not for its absolute accuracy but for the match between its elements, and understanding that distinction is what makes the part worth its price.

Absolute Tolerance and Ratio Tolerance

absolute tolerance is the error of a single element against its nominal value, and it is often one percent or worse. ratio matching is the error of the ratio of two elements against the nominal ratio, and it can be a few parts per million.

That difference of three or four orders of magnitude is the reason a network exists. A circuit that depends on a ratio, such as a difference amplifier or a divider, gains almost nothing from a precise absolute value and a great deal from a precise ratio.

The two specifications are quoted separately in the datasheet and they are frequently confused. A part described as a precision network with a ratio tolerance of zero point zero one percent may still have elements that are one percent from their nominal values.

Why the Substrate Matters

Elements on the same substrate share a temperature, a manufacturing process and a mechanical stress. The first gives tracking, the second gives a low ratio tolerance, and the third gives stability over the life of the product.

tracking is the change in the ratio as the temperature changes, and it is much better than the individual temperature coefficients. Two elements with a coefficient of fifty parts per million per degree that track to within one part per million give a ratio that moves by one part per million per degree.

A discrete pair from the same batch tracks reasonably well and never as well as a network. Where a ratio of a few parts per million over temperature is required, the network is the only practical answer.

Configurations Available

Networks are available as isolated elements, as a common bus with several resistors, and as complete functional blocks such as a divider, a difference amplifier pair or an R-2R ladder.

A complete block is designed for one job and its internal matching is achieved by trimming. It saves board area and it removes the layout errors that arise when discrete parts are placed at different distances from an amplifier.

A ladder for a converter is the extreme case, where the matching of many elements determines the linearity of the converter. The network is the converter and it is treated as a single component in the design.

Layout and Thermal Behaviour

Place the network so that its pins see the same thermal environment. Two elements at opposite ends of a package can differ by a fraction of a degree, which is enough to matter at a ratio tolerance of one part per million.

Keep the network away from heat sources and from air movement. A gradient across the package changes the ratio, and the effect appears as a drift that follows the duty cycle of the product.

The network should be connected to the board with short traces, and the traces should be matched where the circuit depends on the ratio. A difference in trace resistance between two elements is a ratio error, and it is easy to introduce without noticing.

Where Networks Are Used

A difference amplifier built from a network has a common mode rejection that depends entirely on the ratio matching of the four resistors. A discrete implementation with one percent parts has a rejection of about forty decibels, and a network improves it by thirty decibels.

A precision divider for a reference or a feedback network is the second common use. The ratio tolerance becomes the accuracy of the output, and the tracking becomes its temperature stability.

Instrumentation amplifier gain setting is the third. The gain depends on the ratio of one external resistor to the internal network, and the external part is the one that limits the accuracy.

Cost and Availability

A network costs more than the equivalent discrete resistors, and the difference is justified whenever the ratio matters. In a circuit where the absolute value sets the accuracy, the network buys nothing.

The availability of a particular configuration matters in production. A functional block that is made by one supplier is a risk, and where a second source exists, the specifications may not be identical.

Sizes and packages range from a small surface mount network to a hermetic metal can. The can offers the best stability against humidity and mechanical stress and it is used in instruments rather than in volume products.

Alternative Approaches

Trimming a discrete pair with a potentiometer achieves a good ratio at a single temperature and it does not track. The adjustment also drifts with vibration and it can be moved accidentally.

Software calibration with a multiplexed measurement of the two legs achieves the ratio at production and does not remove the tracking error. It is useful where a network is not available.

Ratios built from the same physical element, such as a tapped resistor, are the ultimate in matching because the two parts are literally the same piece of material. They are used in the most demanding dividers.

Manufacturing and Trimming

A network is made by depositing a resistive film on a substrate and etching the pattern. The ratio accuracy comes from the geometry rather than from the absolute sheet resistance, which is why the ratio is far better than the absolute value.

Trimming with a laser adjusts individual elements to bring the ratio within tolerance. The trim removes a small part of the element, and the trimmed area is a place where the film is thinner and more prone to drift over time.

The absolute value can also be trimmed when the application needs it, at the cost of a longer test and a higher price. Most networks are trimmed for ratio alone, because the ratio is what the customer measures.

Packaging affects stability. A moulded plastic package transmits mechanical stress to the substrate, while a ceramic or a metal package isolates it from the board, and the choice follows from the stability that the application requires.

Verification and Faults

Verify a network by measuring the ratio rather than the absolute values. The measurement requires an instrument with a ratio accuracy better than the specification of the part, which usually means a calibrated bridge or a precision multimeter.

Check the drift by measuring the ratio at two temperatures inside an oven. That measurement is the only way to confirm the tracking figure of the assembled board.

A ratio that has changed after assembly usually indicates mechanical stress from the board or the mounting. The release checks that keep such networks consistent are collected in our PCB design release checklist, the assembly points in judging PCB quality, and the thermal measures in our guide to PCB thermal management design.

FAQ

Should I choose a network by absolute tolerance? Only if the absolute value sets the accuracy. For a ratio, the ratio tolerance and the tracking are the specifications that matter.

What is tracking? The change in the ratio with temperature. It is much better than the individual temperature coefficients of the elements.

Can I match discrete resistors instead? For a moderate ratio, yes. For a few parts per million over temperature, only a network will do.