# So We Just Consider the Resistor's Tolerance, Right?

**Adam Taylor, Director, Adiuvo Engineering & Training**

12/9/2013 02:55 PM EST

24 comments post a comment

In reality, the tolerance of a resistor is just the starting point that doesn't fully define the maximum or minimum value the resistor could be within your circuit.

When designing precision electronics or performing a detailed worst-case analysis, one quickly learns to consider parameters that may not be so important in other applications. One of the more interesting things to learn is that the tolerance of a resistor is just the starting point. It does *not* actually define the maximum or minimum value the resistor could be within your circuit.

The key parameters associated with a resistor are as follows.

**Tolerance:**This defines how close to the nominal value is allowable for the resistor when it is manufactured. A nominal 1,000Ω resistor with a tolerance of ±5% will have a value ranging between 950 and 1,050Ω. This value will be fixed; the value of the resistor will not vary during its life due to the tolerance. However, the engineer has to consider the tolerance in design calculations and ensure the circuit will function across the entire potential value range.**Temperature coefficient:**This describes how the value of the resistor changes as a function of temperature. It is defined as parts per million/Kelvin; common values are 5, 10, 20, and 100 PPM/K. Actually, the best way to think of this is parts per million per ohm/Kelvin. A 1,000Ω resistor with a temperature coefficient of 100 PPM experiencing a ±60K temperature change over the operating temperature range (240-360K, based on an ambient room temperature of 300K) will experience a resistance change of ±6Ω based on its nominal value. Obviously, the lower the temperature coefficient, the more expensive the resistor will be. (This is the same for low-tolerance resistors.)

**Resistor self-heating:**For really high-precision circuits, it is sometimes necessary to consider the power dissipation within the resistor. The resistor will have a specified thermal resistance from the case to ambient, and this will be specified in °C/W. The engineer will know the power dissipation within the resistor; this can be used to determine the temperature rise and hence the effect on the resistance.

To determine the maximum and minimum resistance applicable to your resistor, you must consider the tolerance, the temperature coefficient, and the self-heating effect. As you perform your analysis, you may notice some of the parameters are negligible and can be discounted, but you have to consider them first to know whether or not you can discount them.

For some precision circuits (gain stages in amplifiers, for example) it may be necessary to match resistors to ensure their values are within a specified tolerance of each other and have the same temperature coefficients.

In certain circuits, it is also important to make sure that critical resistors are positioned correctly to ensure both terminal ends of the resistor are subjected to the same heating or cooling effects. Otherwise, the Seebeck effect may need to be considered. When using forced airflow, for example, it may be necessary to ensure that both resistor terminals are perpendicular to the airflow, so the component is of uniform temperature.

To what level do you consider these effects in your own designs? Also, are there any other factors you take into consideration when selecting a resistor?

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Author

Robert.Groh 12/11/2013 10:31:47 AM

And, yes, the wood working went well.

Author

Adam-Taylor 12/11/2013 3:01:41 AM

However, the article was mainly looking at worse case analysis, which typically covers such things as tolerance and drift and the effects upon the peformance of the circuit.

There is another blog which Max will hopefully be pulling across from the old programmeable logic design line which addresses the reliability and part stress anaylsis.

Typically the reliability analysis would look at the component failure rate, however this could be either a parts count or stressed reliability in which case the voltage, current and power rating of the resistor would be considered from the part stress analysis.

I should do a blog showing how all these are interconnected and analysed to demonstrate a reliable system.

I hope the wood work was fun ;)

Author

seaEE 12/11/2013 12:23:37 AM

Author

Robert.Groh 12/10/2013 10:25:24 PM

Resistor tolerance (which you covered nicely although the statiscal distribution may be of importance - I usually just assume a square distribution - i.e. it is equally likely that the resistor value will be anywhere within it's specified range).

Power Rating (including the derating factors for high temperature - some resistor types start to derate at 25 degC and are rated at zero dissipation at 100 degC). You need to do a check on the in circuit power dissipation of ALL your resistors.

Temperature range

Voltage rating (some resistor types are only good for 50 V or so - might not be a problem but you need to be aware of it).

Reliability (and the impact of all the stress factors on the reliability).

Current ratings - short impulse as well as long term (e.g. heating) (a 10A, 100 ns wide pulse may not exceed the power rating of a small resistor but it might very well blow it to bits).

Changes in value to stuff like the thermal shock of being soldered into your circuit.

Noise effects

Non-linearity (e.g. variations in resistance with applied voltage).

Effects of shock (on reliability, etc).

Probably more but it is late at night and I have some wood working to do.

Author

MeasurementBlues 12/10/2013 9:21:18 AM

I'll stick with a baseball cap.

Author

Adam-Taylor 12/10/2013 6:47:05 AM

Author

Adam-Taylor 12/10/2013 3:25:52 AM

Author

Adam-Taylor 12/10/2013 3:21:35 AM

You are correct this does assume we are working at DC, I was going to follow it up with one looking at AC but this would look at other discretes as well as once frequency is introduced you need to consider the parasitics

Author

MeasurementBlues 12/9/2013 10:39:26 PM

Thermocouples: Simple but misunderstood

Author

MeasurementBlues 12/9/2013 10:36:54 PM