7 Normal Distributions in Offset Voltage

In reality, an op amp’s Vosi will not always be the typical value given in the data sheet. The actual values are part of a Gaussian distribution that is limited between the min/max of the device specifications. Figure 7-1 shows a Gaussian distribution of offset voltages sampled from a large batch of OPA2210 units.

As shown in Table 7-1, it is possible for an op amp’s Vosi to have a positive or negative polarity. This means it’s possible for the offsets of various stages to either combine (same polarity) or cancel (opposite polarities).

To understand the effects of these distributions, a Monte Carlo analysis was performed on four different gain implementations of two-stage amplifier circuit, using the OPA2210 for the first stage and the OPA1656 for the second stage. The OPA1656 is a low-noise, low-distortion, precision amplifier optimized for high-performance audio applications where DC precision is not typically required. The typical Vosi of the OPA1656 is still very good at 500µV, but significantly higher than the exceptional 5µV of the OPA2210.

Ten-thousand iterations of the Monte Carlo simulation were performed for each of the four gain implementations. The four designs highlight the differences in offset and bandwidth when different amounts of gain are applied across the stages. Each design has a total gain of 1000 V/V. Results of the Monte Carlo simulation are shown in Table 7-1.

The standard deviation of the analysis is comparable to the results of a DC simulation using the typical offset value. However, it is always necessary to consider the max/min offsets that are likely to occur in large-scale production of multi-stage amplifiers due to probability distributions.