Professional Circuit Design: Statistical Analysis

Explore Mathcad Prime basics, including worksheets, text blocks, operators, functions, vectors, matrices, and calculations with units, with examples on resistors, plots, and color-coded inputs, results, and assumptions.

Set and use origin and tolerances, define min and max, and index-based vector values to analyze worst-case scenarios in circuit design.

Define a reusable function for the ADC voltage from a voltage divider, parameterized by sensor voltage, pull-up and pull-down resistances, enabling symbolic then real-value calculations across equations.

Apply partial derivatives to a dc voltage function, compute derivatives with respect to pull-down and sensor inputs, and use symbolic calculation for the statistical analysis.

Plot and visualize dependencies using the ADC function, showing how pull-up and pull-down values affect the ADC voltage and the resulting voltage divider, via an xy plot.

Apply linear interpolation to estimate resistance across temperature points for a temperature dependent resistor. Explore supporting points between 10 and 30 degrees to predict values in calculations.

Explore min and max functions to find the minimum in a defined temp vector and the maximum across multiple vectors or matrices, such as temperature and resistance.

Learn basic programming concepts, including a for loop from 1 to 5, function definitions, and matrix indexing, to compute powers and build a result vector.

Explore statistical basics for circuit design, including calculating the mean, comparing uniform and normal distributions, understanding standard deviation, and applying the process capability index CPK to specification limits.

Analyze a simple voltage divider with three independent statistical values: pull-up resistor, pull-down resistor, and Vref, and derive six-sigma statistical worst-case for Vdiv alongside analytic worst-case.

Define the goal of the analysis by calculating a six sigma voltage deviation for a simple voltage divider circuit, using the color information and worksheet settings described in prior chapters.

Analyze a circuit diagram featuring a voltage divider with reference, pull-up, and pull-down resistors, and calculate the minimum, typical, and maximum divider voltages considering component tolerances.

Define the reference voltage with its min, typical, and max values from the datasheet, and compute worst-case pull-up resistance using three tolerances—min 43 kΩ, typical 47 kΩ, max 50 kΩ.

apply gaussian propagation of uncertainty to a three-parameter voltage divider, deriving the divider voltage and its one-sigma error from reference voltage and pull-up/down resistors.

Compare standard deviation in uniform and normal distributions, apply CPK and six-sigma to resistor tolerances, and derive partial derivatives of the V divider with respect to vref and pull-up/pull-down resistors.

Use gaussian error functions and six-sigma thresholds to assess a 5-volt divider with normally distributed components. Compare normal and uniform distributions and discuss when statistical results align with analytic worst-case.

Compute six sigma statistical error for a voltage divider by propagating uncertainties in reference voltage and pull resistors, comparing normal and uniform distributions to estimate a 2.09-2.91 V worst-case range.

Analyze a temperature sensor circuit used in control units to determine the ADC voltage at the microcontroller pin. Assess its components, including reference voltage, supply voltage, NTC thermistor, and capacitors.

Calculate the six sigma temperature error across the full -40 to 150°C range for the temperature sensor circuit using statistical analysis and color-coded input and results.

Identify customer requirements for temperature sensors, including a minus forty to one hundred five degrees Celsius range and minus five to plus five Kelvin accuracy, and illustrate sensor applicability constraints.

Explore a typical temperature sensor circuit with an NTC thermistor, pull-up resistors, and a voltage divider, plus ESD protection and an RC low-pass filter to safeguard a microcontroller ADC.

Define circuit parameters including reference voltage, adc clamping voltages, and leakage; model resistor, capacitor, diode, and ntc thermistor tolerances with min/typ/max vectors, and note adc resolution.

Explain gaussian propagation of uncertainty for two equations, deriving the ADC value from voltage and incorporating six parameters pull-up, filter, ntc, ADC accuracy, leakage current, vref to estimate temperature error.

Explore how to define standard deviation for independent circuit values, using linear interpolation for NTC thermistors, and compare normal and uniform distributions for pull-up resistors, ADC, and reference voltages.

Define partial derivations for six parameters using the adc gauss function, like the voltage divider method. Fill values for vref, leakage current, and 16-bit adc; ntc independency from theta ambient.

Explore Gaussian propagation of uncertainty in ADC calculations across -40 to 150 C, incorporating theta ambient, temperature coefficients, and interpolation to estimate temperature error in kelvin under six sigma conditions.

Plot temperature error function across -40 to 105°C, compare normal versus uniform distributions, and show that only normal assumptions meet the ±5 requirement, stressing realistic data such as CPK.

Explore a statistical analysis of six sigma temperature error across -40 to 105 °C, using adc, ntc thermistor, and resistor models, with gaussian and uniform distribution error functions.