Master Your Circuit Design: Dive into Worst Case Analysis

When designing any circuit, it is essential to ensure its reliable performance under various conditions beyond the controlled environment of a laboratory desk. This involves considering component tolerances and temperature variations. In safety-critical applications, such as aerospace and military, additional factors like component aging and radiation exposure must also be considered. While setting up appropriate tests can be challenging, a thorough analysis can effectively verify the robustness of your design.

This article will guide you through analyzing a differential amplifier, helping you understand the sources of errors and ensuring reliable performance under different conditions.

Differential Amplifier Circuit for Measuring Small Currents

In this example, we examine a differential amplifier configuration designed to measure small currents through a shunt resistor. Our chosen operational amplifier is the ADA4084, which features rail-to-rail output and low offset voltage. Let’s first verify the correct functionality of our circuit.

Figure 1: Differential amplifier configuration for measuring small currents

To verify the circuit, we conduct a DC sweep simulation. The output expression calculates the current from the output voltage by dividing it by the amplification factor (201) and the shunt resistor value (0.2Ω).

Figure 2: Results of DC sweep simulation with parameters

As shown by cursor A, our circuit performs almost perfectly. For instance, with a real load of 30.005mA, we obtain a calculated current of 29.810mA. However, the real world often differs.

Next, we include various parameters, such as resistor tolerances and specific parameters from the ADA4084 datasheet. The most critical parameters to consider are the input offset voltage, input offset current, and input bias current.

Figure 3: Important parameters to include in simulation and its values

Figure 4: Circuit including input offset current, input offset voltage and input current bias

Sensitivity Analysis

Sensitivity analysis allows us to determine which parameter deviations most significantly affect the output. Resistors were set to 1% tolerance (10m in the sensitivity window), while other parameters were set to 100% to assess their impact.

Figure 5: Sensitivity simulation setup

Figure 6: Results of sensitivity analysis. Relative deviation column shows impact on output with changing parameters

As expected, resistor tolerances play the most significant role, whereas input currents (bias and offset) are negligible. For simplicity, these parameters will be ignored later in this particular case.

Worst Case Analysis (WCA)

While sensitivity analysis changes one component value at a time, worst-case analysis examines the combined effect of all parameter variations. The highest values from 1% tolerance do not necessarily yield the worst output; the interaction of these tolerances does.

Monte Carlo analysis is a useful tool for this purpose. It creates random values for components within their tolerances at each algorithm iteration. With enough simulations, we can determine output values with specific probabilities. However, Monte Carlo analysis does not guarantee that extreme values are reached. Therefore, selecting the Worst Case Analysis option within Monte Carlo analysis in Altium and setting the number of runs to 2^5 (considering five components) provides a thorough examination. R10, which does not affect the output, will be excluded.

Figure 7: Monte Carlo analysis parameters. In this particular case we only change resistors

The base tolerance was defined as 1%. To include aging, we could use the Arrhenius law, as detailed in ECSS-Q-HB-30-01A. For simplicity, we will skip the details here and just add an additional 0.17% tolerance. Temperature drift can also be included in the tolerance calculation. For example, a 100 ppm resistor at 50°C adds 0.5%, resulting in a total tolerance of 1.67%.

The offset voltage remains unchanged. Two separate simulation runs were prepared, one with a -300µV offset voltage and one with a +300µV offset voltage. The results of these simulations are shown below.

Figure 8: DC sweep analysis with different variation of component values. Offset voltage: 300u

Figure 9: DC sweep analysis with different variation of component values. Offset voltage: -300u

The cursors illustrate the difference between a 60mA real load and the output, with errors as high as 17%! To explore how this value changes with different resistor tolerances (e.g., 0.1%), you can try it yourself. Give it a go today! Altium offers a free trial for your experiments.

Conclusion

By analyzing and simulating circuits, we can confidently design robust and reliable systems capable of withstanding the challenges of their intended environments. This careful process not only improves the circuit's performance and lifespan but also ensures it functions reliably in critical applications where precision and reliability are crucial.