Unlike most calls that are short on some critical data my caller last week had more numbers than he knew what to do with. His goal was to be able to adjust for any voltage offset in his op amp application. To do this he needed to understand the various components of voltage offset.
In order to keep the various components straight we decided to assign each one a number as we defined it, and then combine them at the end. The first component was the initial offset. This is the input referred voltage offset under the standard conditions that are usually stated at the top of the table of specifications. We called this V1. V1 is usually the largest of the DC error components and the one read directly from the data sheet.
The next component of the total offset, V2 is usually the offset drift with temperature. This term may be shown as Vos/ΔT, or the change in Vos for a change in temperature. To evaluate this term we needed the maximum temperature variation from the standard condition, which is usually 25°C.
For example, for service from -40°C to +85°C the change in temperature is -65°C and +60°C. Worst case is the cold excursion, which is 65°C. For a 1.5 μV/C specified op amp this would result in a voltage offset shift of 97.5 μV.
V3 was assigned to the change in offset for a change in power supply voltage. The value of V3 was given for a known voltage across the power supply pins. When that voltage changes the offset voltage may change. The amount of change is given by the power supply rejection ratio or PSRR. This may be expressed in terms of μV/V or in dB.
Notice that the value of V3 is determined by the PSRR and the change in voltage across the supply pins of the device. If this change is not symmetric it may also cause a change in the error due to common mode voltage.
The last contribution to the total effect is that due to change in common mode voltage. The common mode rejection (CMR) is usually expressed in dB so the conversion is given by:
The initial offset, V1, for op amps and instrumentation amps is usually specified with the CMV equal to Vsupply/2. Therefore, if one supply changes then there are changes in two terms,
You can add up these errors to get a worst-case offset but that may be more stringent than required for most applications. With several error sources, it's unlikely that they will all add in one direction. One commonly used alternative is to root-sum-square the various error components:
I'll let the real statisticians argue about this point, lapsing into discussions about confidence intervals and such. Let's just say that there is judgment involved that may depend on whether you are making toys or airplanes.
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Editor's Note: Op amp guru will be hosting a series of web seminars on op amp design issues. The first one, co-hosted by Texas Instruments and Memec Insight on September 8th, looks at "The Pitfalls of Single Supply Op Amps." By all means check it out.