Workhorse Devices
As one of the most basic of electronic components, resistors are easy to view as unimportant. But they can really cause problems in your design, if they’re not used in ways they’re intended. Here, Stuart dives into the key details you need to know to understand resistors and how to use them.
Resistors—boring and mundane, right? Resistors are the components that, as the comedian Rodney Dangerfield used to say, get no respect. In many applications, they don’t need much respect; they just quietly do their job, restricting current flow and generating a tiny bit of heat.
If the only place you ever use a resistor is as a pull-up on a microcontroller input, you can usually just ignore them. But when you use resistors in ways that push the limits of their capabilities, or ask them to do something for which they aren’t designed, then that tiny bit of heat can become a lot of heat, and the resistor can turn into a smoking piece of carbon. And when it dies, it may take other parts with it. Those end-of-the envelope situations are what I want to look at here.
The two most common schematic symbols for a resistor are shown in Figure 1. The actual resistor element may be composed of carbon, resistance wire, carbon film or other materials. On a schematic, a 1.5kΩ resistor may be noted as 1.5K or 1K5, with the K indicating the decimal point and multiplier.
Schematic symbols for resistors
WHAT IS A RESISTOR
A resistor dissipates electrical current as heat and has a resistance value. The relationship between the resistance value and current is given by Ohm’s law:
I = V/R
where V is the voltage across the resistor, I is the current in amperes, and R is the resistance in ohms. So for a 1K (1kΩ, 1,000Ω) resistor, if the voltage across the resistor is 5V, then the current is 5/1,000 or 5mA. Using Ohm’s power law, the power dissipated in the resistor is VI, or V2/R or I2R. In this example, the power would be 25/1,000 or 0.025W or 25mW. You get the same result if you use the other two methods of calculating it.
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Identifying Resistors—If you’ve ever picked up a soldering iron, you are probably familiar with the resistor color code. It is shown in the Table 1. The color code is in the form of a series of color bands on the resistor body, and is read as AB × M where A is the first color band, B is the second, and M is the multiplier. So the 1kΩ (1K) resistor would be brown, black, red, which is read as 10 × 100. A 1.5kΩ (1.5K) resistor would be brown, green, red, or 15 × 100.
The color code table is for resistor tolerances of 20%, 10%, and 5%. This limits the precision with which the resistor can be identified, since there are only two significant digits. For example, in the standard 5% tolerance values, there are seven values between 1K and 2K (1K, 1.1K, 1.2K, 1.3K, 1.5K, 1.6K and 1.8K). All of these can be represented with two digits and a multiplier. But for 1% resistors there are 29 values in the standard table between 1K and 2K, some of which can’t be represented by two digits. There are values such as 1.37K, for example.
For 1% resistors, the color code is three digits and a multiplier to accommodate the extra precision. So a 1.37K 1% part would be marked as brown, orange, violet, brown (137 × 10).
Some resistors are marked with the actual resistance value instead of color bands. A 1.37K part would be marked “1371.”
Figure 2 shows four different resistors—from top to bottom, a 1K 0805 surface-mount part, a 1K 1/8W resistor, 1K 1/4W, and a 100Ω 5W resistor. Surface-mount resistors don’t use color codes; they are marked with numeric values if they are marked at all.
CHARACTERISTICS OF RESISTORS
Parallel/Serial—Figure 3 shows resistors in parallel and in series. R1 and R2 are in parallel. If you apply 5V across the pair of resistors, then the current in R1 will be 5V/1,000, or 5mA. The current in R2 will be 5V/1,500 or 3.33mA. The total current is the sum of the two, or 8.33mA.
Photos of 0805, 1/8W, 1/4W, and 5W resistors.
Resistor color codes, 5%, 10%, and 20% tolerances
Parallel and series resistors
The value of the two resistors in parallel is:
In fact, you can calculate the value of any number of parallel resistors as:
In the example, you could also calculate the effective parallel resistance by dividing the voltage by the total current; 5V/8.33mA = 600Ω. If both resistors are the same value, the current in each resistor and the power dissipated in each resistor is the same. You can algebraically derive the formula for effective parallel resistance from Ohm’s law if you’re so inclined.
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Also in Figure 3, resistors R3 and R4 are in series. Resistors in series add, so the total resistance of R3 and R4 is 1K + 1.5K = 2.5K. If you apply 5V across the series string, then the current is 5V/2,500 or 2mA. Both resistors have the same current, so the voltage across R3 is 2mA x 1,000, or 2V. Across R4 it is 2mA x 1,500 = 3V. The sum of the two, of course, equals the 5V supply voltage. Series resistors are often used as voltage dividers, but you have to take into account the effect of the load resistance on the series string, which will function as a resistance across one or both of the divider resistors.
With resistors in parallel, each resistor has the same voltage across it, but the current through each resistor depends on the resistance. With series resistors, each resistor has the same current through it, but the voltage across it depends on the resistance. In both cases, the total dissipation is the sum of the dissipation in the individual resistors.
Tolerance—Resistors have a “tolerance” value, the amount that the resistance can vary from the nominal value. If the series string in Figure 3 is using 5% resistors, then R3 can range in value from 950Ω to 1,050Ω (1,000Ω ±5%). R4 can range from 1,425Ω to 1,575Ω. With nominal resistance values of 1K and 1.5K, the voltage across R4 will be 3V. But if you include the tolerance in the calculations, the voltage across R4 can range from 2.87V to 3.12V with one resistor at maximum and the other at minimum. That’s a quarter of a volt difference. It may or may not make a difference in your application, but you will want to calculate the maximum voltage variation (and for parallel resistors, the maximum current variation) in such cases. If your design won’t work with that amount of variation, you will want to use resistors with lower tolerance, such as 1%. Most resistors will be closer to the nominal value than the extreme ends of the tolerance range—but you can’t depend on it, especially if the product is going to be mass produced.
Power Dissipation—Resistors have a specified maximum power dissipation. This means that the 5W resistor in Figure 2 can dissipate 5W, right? Well, sort of. Aside from the fact that you don’t want to operate a resistor right at its maximum dissipation, there is an additional problem of the temperature “derating curve.” All resistors have a derating curve where the allowable dissipation falls off with increasing temperature. For a 5W 100Ω resistor similar to the one in Figure 2, I found a datasheet that indicates the part can dissipate 5W up to about 70°C. After that, the dissipation drops to about 60% (maximum of 3W) at about 155°C, and to zero at 275°C. At the other end of the size scale, a 1K 0805, 0.1W resistor as shown in
Figure 2, also starts derating at about 70°C, but by about 110°C, the allowable dissipation is down to about 50% of the specified value, or about 50mW in this case. At 150°C, the allowable dissipation is zero.
If all your projects or products are going to operate around room temperature, none of this is a concern. But for electronics in certain industries, such as automotive or military, those derating charts may be very important if you don’t want field failures due to excessive dissipation at a high temperature. And even at room temperature, a circuit in a sealed enclosure can generate enough heat to raise the temperature inside the enclosure, just from self-heating.
Temperature Coefficient of Resistance (TCR)—A resistor’s TCR is a number that describes how much the resistance can change with temperature. The 0805, 1K resistor that I described above has a TCR of 200ppm (parts per million) per °C. That translates to a maximum resistance change of about 5Ω as the resistor heats up from 25°C to 50°C. ((50 – 25) x 1,000 x (200/1,000,000)). That’s not much, and few applications would have a problem with resistance change that small. But if the resistor is part of a balanced bridge circuit, it could affect the output. Some resistors have a much larger TCR, on the order of 1,000ppm/°C. Still not an issue for most designs, but be aware of it if your operating temperature range is large.
Maximum Working Voltage—This is the maximum voltage you can apply across the terminals of the resistor before there is a risk of arcing. For most applications, you will exceed the power limit before exceeding the voltage limit. But small surface-mount technology (SMT) parts, such as 0201 or 0405 packages, can have maximum working voltages down around 25V. So a 1/20W 0201 resistor of 22K with 30V across it and a maximum working voltage of 25V is below the maximum power the part can handle, but over the maximum working voltage. Always check the datasheet if working with smaller parts or higher voltages.
POTENTIOMETERS
A potentiometer or “pot” is a resistive element that has a sliding contact that can move from one end of the element to the other. Figure 4 shows the schematic symbols. The center contact physically slides across the resistive element. The total resistance of the resistive element, from end to end, is always the same. But the resistance measured from the center (wiper) contact to one end varies as the wiper moves toward or away from that end.
Potentiometer symbols
A rheostat is a variable resistor with just two contacts, and can be thought of as a potentiometer with just one end and the wiper; it is just a variable resistor. Rheostats are most commonly used in high-current applications, though I’ve seen small trimmer resistors with just two contacts.
Figure 5 shows a panel-mounted pot, which might be used for a volume control on an audio product, next to a PCB-mounted multiturn trimmer potentiometer. Most volume-control-type potentiometers are a single turn, whereas a trimmer may be either a single turn or multiturn part with five or more turns to move the wiper from one end to the other. Multiturn potentiometers usually hace gearing inside and are adjusted by turning the tiny screw at one end or on the top.
Photos of potentiometers
Power Dissipation—Potentiometers have a power dissipation specification the same as fixed resistors. But they have an added complication. A potentiometer, such as the panel-mount part shown in Figure 5, might have a maximum power dissipation of 0.25W. That’s the wattage for the entire part, so the two ends constitute a 1K resistor with 0.25W power, which allows for 15.8mA maximum current. That is the maximum current that can flow through the entire potentiometer. It’s also the maximum current that can flow through any part of the potentiometer.
If you are using a potentiometer for something like a volume control, the current is usually so low that dissipation is not an issue. But at higher currents, you have to be sure that the maximum current through any part of the resistive element doesn’t exceed the maximum allowable current for the entire device. For example, if you use the potentiometer as a variable resistor by just using one end and the wiper, you have to make sure that the current isn’t excessive when the wiper is near the end of rotation.
Cycles of operation—A potentiometer has a rated life in cycles of operation. For a small trimmer pot, it might be a few hundred cycles. For a panel mount volume control, it may be 100,000 or more. The main factor that limits the life of the part is wear on the resistive element. The wiper is literally a wiper that slides across the resistive material. To make that work, the wiper has to apply pressure to the resistive element to maintain contact. So every time the potentiometer is turned, the resistive element wears down a tiny bit, and the contact point of the wiper wears also. Eventually there are gaps where the wiper is no longer making contact. In a volume control, this results in a scratchy sound. On some other type of control, it can result in erratic operation as the contact is interrupted.
Linear vs. logarithmic—Potentiometers come in two basic varieties, linear taper and logarithmic taper. A linear potentiometer has a resistive element that has the resistance evenly spread across the entire range. If the wiper is 20% of the distance between end A and end B, then the resistance between the wiper and end A will be 20% of the total. The resistance between the wiper and end B will be 80% of the total. If the shaft is turned so that the wiper is 80% of the distance between A and B, then those resistance values are reversed. At the midpoint, the resistance between the wiper and either end is the same.
A logarithmic taper follows a logarithmic curve, intended to match the logarithmic response of the human ear. A logarithmic taper is sometimes called an audio taper for that reason. Figure 6 shows a linear vs. log taper. Sometimes inverse log pots are used as well, and have a resistance curve that is the mirror image of the log taper.
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There are other taper configurations, but linear and logarithmic are the most common.
Loading—The voltage divider characteristics of the potentiometer are affected by the resistance connected to the potentiometer wiper. Figure 7 shows a 1K linear taper pot with a 1K resistor from the wiper to the low (ground) end. The 1K resistor is in parallel with the lower portion of the potentiometer, so it affects the voltage division of the part. At 50% rotation, the resistance from the wiper to the V+ signal is half the total resistance, or 500Ω. But the resistance from the wiper to ground is 500Ω in parallel with the 1K fixed resistor, or 333Ω. This makes the wiper voltage not 0.5V but 0.4V, and results in a nonlinear curve.
Graph of linear vs. logarithmic taper
Linear taper potentiometer with load resistor from wiper to ground
Thermistor self-heating
Note that this applies to an AC signal voltage as well, even if the R1 resistor is AC coupled to the wiper through a capacitor. At DC, the wiper voltage would be what you expect, 0.5V. But AC signals will be attenuated by the 1K resistor. A logarithmic potentiometer has the same issue, but the curve will be different.
THERMISTORS
A thermistor is a resistor made from metal oxides and other elements and is sensitive to temperature; as the temperature changes, the resistance changes. A thermistor that has a positive temperature correlation (resistance goes up as temperature goes up) is a positive temperature coefficient (PTC) thermistor. If the thermistor temperature goes down as temperature goes up, it is an negative temperature coefficient (NTC) thermistor. NTC is the most common type.
Thermistors are normally used in circuits to measure temperature or trip something, such as an alarm, when a certain temperature is reached. Thermistors do not have a linear temperature-resistance curve; instead, the curve is logarithmic. The thermistor is characterized at a specific temperature, typically 25°C. A second number is provided at some other temperature, typically 50°C or 100°C. That value essentially defines the curve and lets you calculate the expected resistance at any temperature.
Normally, if you were using a thermistor in an application, you would make a table of resistance to temperature values and look up the temperature from the resistance. But here we’re only going to go over characteristics of the thermistor itself. The calculations for the thermistor I used in the example are shown in the sidebar Thermistor resistance vs. temperature calculation, if you want to go through the messy math.
Self-heating—Since thermistors act as resistors, they turn current into heat. The problem is that the thermistor also measures heat. If you look at Figure 8, NTC thermistor TH1 has a 1K resistor in series with it. I used a small thermistor for this experiment with a tiny thermistor element, about the size of the push button at top of a ballpoint pen. TH1 has a nominal value of 10K at 25°C.
When I measure the voltage across TH1, when V+ is 5V, there isn’t much voltage change. But when I increase V+ to 15V, the current through the thermistor is enough to heat it about 2°C. That changes the resistance, and whatever is using that thermistor would be measuring a temperature that is off by about 10% at room temperature. Not a lot, but the error caused by self-heating is about twice the 5% tolerance of the part. To confirm that self-heating was the cause, I immersed the thermistor in a container of water, which is a reasonably good conductor of heat. In that configuration, the voltage did not drop, indicating that self-heating was unable to heat the thermistor enough to affect any temperature reading.
Going back to Figure 8, resistor R2 and thermistor TH2, this is a 1K NTC thermistor with a 1K series resistor. This will draw significantly more current, and when I tried it with V+ at 5V, the resistance of TH2 dropped enough to represent a 2°C change, which is about the same as the change across TH1 using 15V. At V+ = 15V, the dissipation in TH2 raised its temperature about 12°C, which would be a significant measurement error. This is a bit of an extreme abuse of the thermistor to illustrate the point.
The lesson is probably obvious: when using a thermistor, make sure the current through the thermistor is low enough to prevent self-heating that will affect the measurement. The thermistor can’t indicate whether a lower resistance is due to self-heating or an actual change in ambient temperature. The current limit is dependent on the thermistor characteristics and mounting. A thermistor with a metal tab attached to a heatsink, for example, can handle more current without affecting the reading than can be handled by a bead-type thermistor in open air with characteristics that are otherwise the same.
CONCLUSION
Resistors are the unacclaimed workhorses of all electronic devices. Hopefully this has helped you understand them a little bit better, so you can design electronics that are both reliable and repeatable. CC
THERMISTOR RESISTANCE VS. TEMPERATURE CALCULATION
T1 = Nominal thermistor temperature, in degrees kelvin. 25°C for the
example, is 273.15°K
T2 = Temperature where B is specified for part, in degrees kelvin, 50°C
for the example, 323.15°K.
R1 = Resistance at T1, 10K for the example.
R2 = Resistance at T2, the value we want
B = B value from thermistor datasheet, 3470 for the thermistor used in
the example here.
Reworking this algebraically, to find the resistance at a specific
temperature:
PUBLISHED IN CIRCUIT CELLAR MAGAZINE • MAY 2022 #382 – Get a PDF of the issue
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Stuart Ball recently retired from a 40+ year career as an electrical engineer and engineering manager. His most recent position was as a Principal Engineer at Seagate Technologies.
