# Variables of resistor heating: many variables affect resistor heating, but most of them relate to the design and construction of the PCB.

LAST MONTH MY coauthor Mike Jouppi covered conductor heating of embedded resistors. This month I explore material, process and design variables that affect resistor heating. These variables can be counted on four fingers: 1) material set, 2) related PCB manufacturing process, 3) PCB construction, and 4) current applied to the resistor.

Briefly, within these variables, we have several choices:

Material sets. Currently there are only two commercial resistor material set types: metal thin-films (MTF) and polymer thick-films (PTF). A third type--ceramic thick films (CTF)--is emerging but is not quite there, according to its developer.

PCB manufacturing processes. Each material set has its own manufacturing process flow. For a given material set there are several suppliers of materials, and although the basic processes are the same, there are slight differences in chemistry and operating parameters, depending on the supplier.

PCB construction. The design establishes and controls the construction; e.g., dielectric material, dielectric and copper thickness and orientation, traces, planes and via structures. The ability of the board to dissipate power is related to the construction.

Current. The design of resistors depends on the current, which in turn determines their power requirements and the size and shape, all of which relates back to the board construction.

Since there is such a tight relationship between the PCB construction (design) and the resistor power requirements (also design), one of the first things that we should be considering is a guideline for the designer. To begin, the designer knows the required resistance in ohms and the current or voltage drop across the resistor and the material that he wants to use. With this information, one can calculate the power dissipation using P=[I.sup.2]R, where P is power (watts), I is current (amps) and R is resistance (ohms). Resistance, R=[rho]L/A, where [rho]=resistivity which is expressed in ohms cross-sectional area/length; i.e., [ohms] [in.sup.2]/in, or [ohms] [cm.sup.2]/cm. Since resistors allow us to keep the thickness relatively constant or uniform, if we hold length and width as equal, then the numeric value of p equals the numeric value of R for the resistance being described in ohms/square. With this relationship the resistance (R) will vary with the ratio of L/W, which we call the aspect ratio. Regardless of the size of the square, the resistance is the same. Placing two squares end to end (an aspect ratio of 2), the resistance doubles; two squares side by side (aspect ratio of 1/2) halves the resistance.

The dissipation of this power and the construction of the board local to the resistor are the primary factors that will determine the temperature of the resistor. Ohmega Industries (1) has published test results for a 25[ohms] resistor material at 100 mW power dissipation, showing that by increasing the size of the resistor from 0.031" x 0.031" (power density = 104,058 mW/[in.sup.2]) to 0.5" x 0.5" (an area factor of 250x and power density = 400 mW/[in.sup.2]), we can decrease the temperature rise of the resistor by 125[degrees]C. Similarly, for a 250[ohms] material at a power density of 100 mW/[in.sup.2], they show that adding copper cladding to a 0.0025" core decreases the resistor temperature rise by 100[degrees]C. Increasing the core thickness from 0.0025" to 0.025" decreases the temperature rise by 50[degrees]C.

We have modeled three conditions to illustrate the influence of board construction and we will add more in future articles. For example, FIGURES 1, 2, and 3 show the effect of adding copper above and below a single resistor in a 0.06" thick FR-4 board. We are taking into account trace heating, which has a 10[degrees]C rise above the ambient (25[degrees]C) and is at 35[degrees]C. The resistor is 0.04" x 0.04" and dissipates 50 mW (31,250 mW/[in.sup.2]). The board is suspended in still air at 25[degrees]C. As shown, simply adding copper reduces the temperature rise by 50[degrees]C.

[FIGURES 1-3 OMITTED]

Design affects resistor heating. We know this; it is logical. It is easy to see that if you design a larger area resistor it will run cooler for a given current. It's also easy to see that if you put a resistor close to a plane of copper it will run cooler. It is also easy to see that depending on how cool you want to keep the resistor you can play with its size and location in the board stackup. But where are the specifics? How big, how small, how close, how far, how many, where? How do you make an informed decision during board layout? At the moment, the best published design guidelines that we've found are on the Web site listed in the references at the end of this column. These are the best such guidelines, but they do not give you specifics. These specifics simply do not exist. Yet.

Our goal over time is to develop these specifics and provide them to you through publications and ultimately, IPC standards.

We are currently finishing the design of a temperature-measurement sensor that will be built right into the PCB test composite. The sensor will utilize the measurement of the voltage drop in a very fine copper conductor positioned above or below the resistor. Initial tests will also include conventional thermal couples to characterize and verify the technique. By the time we write our next column, we should have preliminary data on the feasibility of this measurement technique. In parallel, we are developing a resistor size and board composition matrix that can be used with any of the commercial resistor material sets. Although the variables affecting resistor heating are numerous, as shown in TABLE 1, we will initially be looking at relatively standard constructions and basic FR-4 dielectric materials.

The test patterns will enable us to characterize a broad range of materials and constructions, developing supporting data. With the supporting data, we can then use models to assist in the actual design details. In other words, we will characterize power and power density vs. temperature and then manage the temperature rise by using the elements that you can control in the PCB design. Having design guidelines that ensure both a reliable and efficient design enable us to optimize the application of embedded resistors.

We are giving you, the reader, an assignment. First, we would like your comments and ideas on test sensors for measuring resistor temperature. Second, should other variables or influences be added to those given in Table 1? Please e-mail responses to rsnogren@coretec-inc.com.
```TABLE 1. Temperature influencing factors

# SIGNIFICANCE VARIABLE

1 High Current
2 High Power budget
3 High Power density
4 High Resistor size constraints
5 High Copper weight
6 High Copper orientation (planes, signals,
splits, location)
7 High Number of layers
8 High Location of resistors (relation to copper)
9 High Other heat sources (conductors, hot
components)
10 High Other heat sinking/cooling elements
11 High Mounting configuration (bolt, card guide,
wedge lack, connector)
12 High Environment (vacuum, air, harsh,
ambient temperature)
13 High Board thickness
14 Medium Board material, thermal conductivity
```

REFERENCES

(1.) www.ohmega.com/Design Resistor.html

RICHARD SNOGREN is a member of the technical staff at Coretec Inc. (coretec-inc.com). He is scheduled to speak at PCB Design Conference East in October. He can be reached at rsnogren@coretec-denver.com.
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