Designers often have questions about a typical specification of an amplifier to design a more robust circuit. Due to natural variation in process technology and manufacturing procedures, every specification of an amplifier exhibits some amount of deviation from the ideal value, like an amplifier's offset voltage. These deviations often follow Gaussian (bell curve), or normal distributions, and circuit designers can leverage this information to guard band their system, even when there is not a minimum or maximum specification in the Electrical Characteristics table.

Figure 7-6 Ideal Gaussian Distribution

Figure 7-6 shows an example distribution, where µ, or mu, is the mean of the distribution, and where σ, or sigma, is the standard deviation of a system. For a specification that exhibits this kind of distribution, approximately two-thirds (68.26%) of all units can be expected to have a value within one standard deviation, or one sigma, of the mean (from µ – σ to µ + σ).

Depending on the specification, values listed in the typical column of the Electrical Characteristics table are represented in different ways. As a general rule, if a specification naturally has a nonzero mean (for example, like gain bandwidth), then the typical value is equal to the mean (µ). However, if a specification naturally has a mean near zero (like offset voltage), then the typical value is equal to the mean plus one standard deviation (µ + σ) to most accurately represent the typical value.

This chart can be used to calculate approximate probability of a specification in a unit; for example, the INA500A typical offset voltage is 700µV, so 68.2% of all INA500A devices are expected to have an offset from –700µV to +700µV. At 4 σ (±2800µV), 99.9937% of the distribution has an offset voltage less than ±2800µV, which means 0.0063% of the population is outside of these limits, which corresponds to about 1 in 15,873 units.

Specifications with a value in the minimum or maximum column are verified by TI, and units outside these limits are removed from production material. For example, the INA500A family has a maximum offset voltage of ±3.5mV at 25°C, and even though this corresponds to 5σ (equals approximately 1 in 3.5 million units), which is extremely unlikely, TI verifies that any unit with larger offset than ±3.5mV are removed from production material.

For specifications with no value in the minimum or maximum column, consider selecting a sigma value of sufficient guard band for the application, and design worst-case conditions using this value. A 6σ value corresponds to about 1 in 500 million units, which is an extremely unlikely chance, and can be an option as a wide guard band to design a system around. Histograms for some of the important specifications like offset, offset drift, CMRR, gain error are shown in the Typical Characteristics section.

In the case of gain error, the INA500 family does not specify a maximum value based on final test but based on characterization as mentioned in the Electrical Characteristics table. The corresponding distribution mentioned in Figure 6-10 has a mean of 0.01% and sigma of 0.003%. Hence, the mean plus 6σ value for gain error can be calculated to be approximately 0.03%. When designing for system conditions with 6σ guardband, this method and value can be used to estimate the worst possible gain error.

However, process variation and adjustments over time can shift typical means and standard deviations, and unless there is a value in the minimum or maximum specification column that is specified based on final test, TI cannot verify the performance of a device. Hence, the maximum gain error spec in the Electrical Characteristics table is relaxed beyond 6σ guardband to be ±0.05%.