What is LTspice?

LTspice is a SPICE simulator provided free of charge by Analog Devices, Inc.
It offers a variety of dot commands, including those for parametric analysis and tolerance analysis, making it useful for selecting circuit constants.

How to Check Dot Commands

LTspice Help provides explanations of dot commands.
To open LTspice Help, select "Help" and then "LTspice Help" from the LTspice toolbar.
In LTspice Help, go to "LTspice Simulator" and select "Dot Commands."
The ".PARAM — User-Defined Parameters" section also includes a list of functions registered in LTspice.

Parametric Analysis

You can use the ".step" command to change the parameters of your choosing and run a simulation.

How to Run Simulations Using the .step Command

1. Enter the variable {x} for the parameter you want to change.
2. Open "SPICE Directive(.)" -> Edit Text on the Schematic from the LTspice toolbar and enter the .step command syntax.

The syntax in the figure above changes the x variable to 1kΩ, 2kΩ, and 3kΩ.

3. Run the simulation for the analysis you wish to perform.

The image of a non-inverting amplifier circuit.

Variables can be varied by List, Linear, or Logarithmic methods. List: .step param ...
Linear: .step param
Example: .step param x 1k 10k 1k: Changes parameter x from 1k to 10k in 1k intervals.
Logarithmic: .step oct(dec) param
Example: .step dec param x 1k 10k 10: Changes parameter x from 1k to 10k in 10 divisions per decade (10 times).

You can also run simulations with multiple parameters as variables.

The above runs simulations for all combinations (9 cases) of the two variables.

See here for more information on the .step command.

• LTspice: How to use the .STEP command to perform repeated analyses | Analog Devices

Tolerance Analysis

LTspice tolerance analysis methods include using Gaussian distribution and Monte Carlo distribution.
Gaussian distribution (gauss(x) function): Normal distribution
Monte Carlo distribution (mc(x,y) function): Uniform distribution

Procedure for LTspice tolerance analysis using the gauss(x) function (Gaussian distribution)

1. Enter {[center value]+gauss([standard deviation])} for the component.
2. From the LTspice toolbar, open "SPICE Directive (.)" and select "Edit Text on the Schematic". Use the .step command to specify the number of simulations.
3. Run the simulation for the analysis you wish to perform.

The image of a non-inverting amplifier circuit.

Center value: 1kΩ
Standard deviation: 42.6Ω (calculated as σ = FWHM / 2.35, assuming 10% as full width at half maximum)
Number of simulations: 1001
For a uniform distribution: Use {mc(1k,tol)} to represent 1kΩ ±100Ω, where tol is set to 0.1 for the ±100Ω range.
For a normal distribution: Use {1k+gauss(42.6)} with a standard deviation of 42.6Ω, utilizing the sigma value derived from the full width at half maximum.
The standard deviation of 42.6Ω is calculated by taking half of the ±100Ω range, which is ±50Ω (total width of 100Ω), considering this as the full width at half maximum, and applying the relationship σ = FWHM / 2.35, resulting in σ = 100Ω / 2.35 = 42.6Ω.
This calculation assumes 10% as the full width at half maximum.

Create a histogram in Excel from the graph data

How to perform an LTspice tolerance analysis using the mc(x,y) function (Monte Carlo distribution)

1. Enter {mc([average value],[tolerance])} for the desired component.
2. From the LTspice toolbar, open "SPICE Directive (.)" and select "Edit Text on the Schematic". Use the .step command to specify the number of simulations.
3. Run the simulation for the analysis you wish to perform.

Example: Non-inverting amplifier circuit

Average value: 1kΩ
Tolerance: 10%
Number of simulations: 1001

Create a histogram in Excel from the graph data

For more information on tolerance analysis, refer to the official page on the Analog Devices website.

• Using LTspice to Build Models for Statistical Tolerance Analysis of Complex Circuits | Analog Devices