# Diffusion Resistor

Resistor model with velocity saturation and optional tolerance, operational limits, fault behavior, and noise

• Library:
• Simscape / Electrical / Passive

• ## Description

The Diffusion Resistor block represents a resistor with velocity saturation, while letting you model the following effects:

You can turn these modeling options on and off independently of each other.

In its simplest form, the resistance of the Diffusion Resistor block is:

`$R={R}_{0}\left(1-{p}_{2}-{p}_{3}+{p}_{2}\sqrt{1+{\left({\theta }_{2}{v}_{pn}\right)}^{2}}+{p}_{3}\sqrt{1+{|{\theta }_{3}{v}_{pn}|}^{3}}\right)$`

where:

• R0 is zero-bias resistance.

• p2 and p3 are the quadratic and linear voltage coefficients, respectively.

• θ2 and θ3 are inverse voltages for quadratic and linear voltage activation, respectively.

• vpn is applied voltage across the resistor.

At low bias,

`$R\approx {R}_{0}\left(1+\frac{{p}_{2}{\theta }_{2}^{2}{v}_{pn}^{2}}{2}\right)$`

and therefore p2 and θ2 determine the low-bias quadratic behavior of the resistor.

At high bias,

`$R\approx {R}_{0}\left(1-{p}_{2}-{p}_{3}+|{v}_{pn}|\left({p}_{2}{\theta }_{2}+{p}_{3}{\theta }_{3}\right)\right)$`

and therefore p3 and θ3 impact only the high-bias linear behavior of the resistor.

You can use the voltage-dependence of the resistance to model velocity saturation in a diffused resistor. For sufficiently high voltage,

`${i}_{sat}=\frac{1}{{R}_{0}\left({p}_{2}{\theta }_{2}+{p}_{3}{\theta }_{3}\right)}$`

where isat is saturation current.

### Simplified Parameterization

The simplified parameterization model assumes that the quadratic and linear coefficients are the same. This is one of the recommended assumptions for the r2_cmc model provided by the Compact Model Coalition, as a reasonable initial guess when performing parameter extraction. With this assumption, it is possible to define two new parameters, Critical voltage and Corner voltage, which provide a simpler means for parameterizing models:

`$\begin{array}{l}{p}_{2}={p}_{3}=\frac{{v}_{co}}{2{v}_{crit}}\\ {\theta }_{2}={\theta }_{3}=\frac{1}{2{v}_{co}}\end{array}$`

where:

• vcrit is critical voltage.

• vco is corner voltage.

At high voltage,

`$\frac{dR}{d{v}_{pn}}\approx \frac{{R}_{0}}{{v}_{crit}}$`

and therefore, critical voltage is the reciprocal of the slope of the increase of R/R0 with voltage.

With this parameterization, the saturation current is

`${i}_{sat}=\frac{{v}_{crit}}{{R}_{0}}$`

### Tolerances

You can apply tolerances to the nominal value you provide for the Resistance parameter. Datasheets typically provide a tolerance percentage for a given resistor type. The table shows how the block applies tolerances and calculates resistance based on the selected Tolerance application option.

OptionResistance Value

`None — use nominal value`

R0

`Random tolerance`

Uniform distribution: R0 · (1 – tol + 2· tol· `rand`)

Gaussian distribution: R0 · (1 + tol · `randn` / nSigma)

`Apply maximum tolerance value`

R0 · (1 + tol )

`Apply minimum tolerance value`

R0 · (1 – tol )

In the table,

• R0 is the Resistance parameter value, nominal zero-bias resistance.

• tol is fractional tolerance, Tolerance (%) /100.

• nSigma is the value you provide for the Number of standard deviations for quoted tolerance parameter.

• `rand` and `randn` are standard MATLAB® functions for generating uniform and normal distribution random numbers.

Note

If you choose the `Random tolerance` option and you are in "Fast Restart" mode, the random tolerance value is updated on every simulation if at least one between the fractional tolerance, tol, or the Number of standard deviations for quoted tolerance, nSigma, is set to Run-time and is defined with a variable (even if you do not modify that variable).

### Operating Limits

You can specify operating limits in terms of power and maximum working voltage. For the thermal variant of the block (see Thermal Port), you can also specify operating limits in terms of temperature.

When an operating limit is exceeded, the block can either generate a warning or stop the simulation with an error. For more information, see the Operating Limits parameters section.

### Faults

The Diffusion Resistor block allows you to model an electrical fault as an instantaneous change in resistance. The block can trigger fault events:

• At a specific time

• When a current limit is exceeded for longer than a specific time interval

You can enable or disable these trigger mechanisms separately, or use them together if more than one trigger mechanism is required in a simulation. When more than one mechanism is enabled, the first mechanism to trigger the fault takes precedence. In other words, component fails no more than once per simulation.

When the resistor fails, its resistance is changed to the value you specify for the Faulted zero-voltage resistance parameter. You can also choose whether to issue an assertion when a fault occurs, by using the Reporting when a fault occurs parameter. The assertion can take the form of a warning or an error. By default, the block does not issue an assertion.

### Thermal Noise

The Diffusion Resistor block can generate thermal noise current. If you set the Noise mode parameter to `Enabled`, then the block includes a noise current source connected in parallel to the diffusion resistor.

If the sampling time is h, then the thermal noise is given by:

`${i}_{N}=\sqrt{2kT/R}\frac{N\left(0,1\right)}{\sqrt{h}}$`

where:

• k is the Boltzmann constant, 1.3806504e-23 J/K.

• T is temperature.

• R is resistance.

• N is a Gaussian random number with zero mean and standard deviation of one.

• 2kT/R is the double-sided thermal noise power distribution (the single-sided equivalent is 4kT/R).

The block generates Gaussian noise by using the PS Random Number source in the Simscape™ Foundation library. You can control the random number seed by setting the Repeatability parameter:

• `Not repeatable` — Every time you simulate your model, the block resets the random seed using the MATLAB random number generator:

`seed = randi(2^32-1);`
• `Repeatable` — The block automatically generates a seed value and stores it inside the block, to always start the simulation with the same random number. This auto-generated seed value is set when you add a Diffusion Resistor block from the block library to the model. When you make a new copy of the Diffusion Resistor block from an existing one in a model, a new seed value is generated. The block sets the value using the MATLAB random number generator command shown above.

• `Specify seed` — If you select this option, the additional Seed parameter lets you directly specify the random number seed value.

### Thermal Port

The block has an optional thermal port, hidden by default. To expose the thermal port, right-click the block in your model, and then from the context menu select Simscape > Block choices > Show thermal port. This action displays the thermal port H on the block icon, and adds the Thermal tab and the Variables tab to the block dialog box.

Use the Thermal tab to specify how the resistance value changes with temperature and to set the thermal mass. Use the Variables tab to set the initial temperature target.

For the thermal variant, the defining equation for the resistance is augmented with additional temperature scaling:

`$R={R}_{0}\left(1+{T}_{C1}^{eff}\Delta T+{T}_{C2}^{eff}{\left(\Delta T\right)}^{2}\right)\left(1-{p}_{2}-{p}_{3}+{p}_{2}\sqrt{1+{\left({\theta }_{2}{v}_{pn}\right)}^{2}}+{p}_{3}\sqrt{1+{|{\theta }_{3}{v}_{pn}|}^{3}}\right)$`

where ${T}_{C1}^{eff}$ and ${T}_{C2}^{eff}$ are the linear and quadratic temperature scaling coefficients, respectively.

`$\Delta T={T}_{sim}-{T}_{meas}$`

where:

• Tsim is simulation temperature.

• Tmeas is measurement temperature.

With the thermal port exposed, the generated noise uses the temperature at the thermal port when determining the instantaneous noise value. Exposing the thermal port also extends the options on the Operating Limits tab as follows:

• The Power rating parameter becomes temperature dependent. You define a temperature up to which the full power rating is available, plus a higher temperature for which the power rating is reduced to zero. It is assumed that the power rating decreases linearly with temperature between these two values.

• An additional parameter, Operating temperature range, [Tmin Tmax], lets you define the valid temperature range for block operation.

### Variables

Use the Variables section of the block interface to set the priority and initial target values for the block variables prior to simulation. For more information, see Set Priority and Initial Target for Block Variables.

This section appears only for the blocks with exposed thermal port. The Temperature variable lets you specify a high-priority target for the temperature at the start of simulation.

### Basic Assumptions and Limitations

Simulating with noise enabled slows down simulation. Choose the sample time (h) so that noise is generated only at frequencies of interest, and not higher.

## Ports

### Conserving

expand all

Electrical conserving port associated with the resistor positive terminal.

Electrical conserving port associated with the resistor negative terminal.

Thermal conserving port that represents the resistor thermal mass.

#### Dependencies

Enabled for the thermal variant of the block. For more information, see Thermal Port.

## Parameters

expand all

### Main

The zero-bias resistance, used as the nominal resistance value. Resistance value must be greater than zero. For the thermal variant of the block, this is the zero-bias resistance at a temperature equal to the Measurement temperature parameter in the Thermal section.

The resistor tolerance as defined on the manufacturer datasheet.

Select how to apply tolerance during simulation:

• `None — use nominal value` — The block does not apply tolerance, uses the nominal resistance value. This is the default.

• `Random tolerance` — The block applies random offset to the resistance value, within the tolerance value limit. You can choose Uniform or Gaussian distribution for calculating the random number by using the Tolerance distribution parameter.

• `Apply maximum tolerance value` — The resistance is increased by the specified tolerance percent value.

• `Apply minimum tolerance value` — The resistance is decreased by the specified tolerance percent value.

Select the distribution type for random tolerance:

• `Uniform` — Uniform distribution

• `Gaussian` — Gaussian distribution

#### Dependencies

Enabled when the Tolerance application parameter is set to `Random tolerance`.

Number of standard deviations for calculating the Gaussian random number.

#### Dependencies

Enabled when the Tolerance distribution parameter is set to `Gaussian`.

Select how to apply tolerance during simulation:

• `Simplified` — Assume that the quadratic and linear coefficients are the same, and define block behavior using the Critical voltage and Corner voltage parameters.

• `Advanced` — Explicitly specify values for the quadratic and linear voltage coefficients and for the inverse voltages for quadratic and linear voltage activation.

Critical voltage for the saturation mechanism. You can determine this parameter value by taking the reciprocal of the slope of the increase of R/R0 with voltage.

#### Dependencies

Enabled when the Parameterization parameter is set to `Simplified`.

Corner voltage, at which the resistance increase starts to occur. The Corner voltage must be less than the Critical voltage.

#### Dependencies

Enabled when the Parameterization parameter is set to `Simplified`.

Coefficient p2 from the defining equation.

#### Dependencies

Enabled when the Parameterization parameter is set to `Advanced`.

Coefficient θ2 from the defining equation.

#### Dependencies

Enabled when the Parameterization parameter is set to `Advanced`.

Coefficient p3 from the defining equation.

#### Dependencies

Enabled when the Parameterization parameter is set to `Advanced`.

Coefficient θ3 from the defining equation.

#### Dependencies

Enabled when the Parameterization parameter is set to `Advanced`.

### Operating Limits

Select `Yes` to enable reporting when the operational limits are exceeded. The associated parameters in the Operating Limits section become visible to let you select the reporting method and specify the operating limits in terms of power and maximum working voltage. Parameters that specify operating limits in terms of temperature are visible only for blocks with exposed thermal port (see Thermal Port). The default value is `No`.

Select what happens when an operating limit is exceeded:

• `Warn` — The block issues a warning.

• `Error` — Simulation stops with an error.

#### Dependencies

Enabled when the Enable operating limits parameter is set to `Yes`.

Maximum voltage magnitude allowed for normal block operation.

#### Dependencies

Enabled when the Enable operating limits parameter is set to `Yes`.

Maximum power allowed for normal block operation.

If you expose the thermal port of the block, this parameter becomes temperature dependent. The value you specify for the Power rating parameter applies up to the temperature specified by the Temperature below which full power rating is available parameter value. Then the power rating decreases linearly with temperature, until it becomes 0 at temperature specified by the Temperature above which power rating is reduced to zero parameter value.

#### Dependencies

Enabled when the Enable operating limits parameter is set to `Yes`.

Maximum temperature where full power rating, specified by the Power rating parameter value, still applies.

#### Dependencies

Enabled for the thermal variant of the block. For more information, see Thermal Port.

Temperature where power rating becomes 0. Above this temperature, the simulation always issues an assertion regardless of dissipated power. This parameter value must be higher than Temperature below which full power rating is available.

#### Dependencies

Enabled for the thermal variant of the block. For more information, see Thermal Port.

A row vector of length 2 specifying minimum and maximum temperature values allowed for normal block operation. The first element is the lowest allowable operating temperature, and the second element is the largest allowable operating temperature.

#### Dependencies

Enabled for the thermal variant of the block. For more information, see Thermal Port.

### Faults

Select `Yes` to enable faults modeling. The associated parameters in the Faults section become visible to let you select the reporting method and specify the trigger mechanism (temporal or behavioral). You can enable these trigger mechanisms separately or use them together.

Choose whether to issue an assertion when a fault occurs:

• `None` — The block does not issue an assertion.

• `Warn` — The block issues a warning.

• `Error` — Simulation stops with an error.

#### Dependencies

Enabled when the Enable faults parameter is set to `Yes`.

Zero-voltage resistance between the + and – ports when the block is in the faulted state.

#### Dependencies

Enabled when the Enable faults parameter is set to `Yes`.

Select `Yes` to enable time-based fault triggering. You can enable the temporal and behavioral trigger mechanisms separately or use them together.

#### Dependencies

Enabled when the Enable faults parameter is set to `Yes`.

Set the simulation time at which you want the block to enter the faulted state.

#### Dependencies

Enabled when the Enable temporal fault trigger parameter is set to `Yes`.

Select `Yes` to enable behavioral fault triggering. You can enable the temporal and behavioral trigger mechanisms separately or use them together.

#### Dependencies

Enabled when the Enable faults parameter is set to `Yes`.

Specify the maximum permissible current value. If the current exceeds this value for longer than the Time to fail when exceeding maximum permissible current parameter value, then the block enters the faulted state.

#### Dependencies

Enabled when the Enable behavioral fault trigger parameter is set to `Yes`.

Set the maximum length of time that the current can exceed the maximum permissible value without triggering the fault.

#### Dependencies

Enabled when the Enable behavioral fault trigger parameter is set to `Yes`.

### Noise

Select whether to model thermal noise current:

• `Disabled` — No noise is produced by the resistor.

• `Enabled` — Resistor generates thermal noise current, and the associated parameters become visible in the Noise section.

Defines the rate at which the noise source is sampled. Choose it to reflect the frequencies of interest in your model. Making the sample time too small will unnecessarily slow down your simulation.

#### Dependencies

Enabled when the Noise mode parameter is set to `Enabled`.

Select the noise control option:

• `Not repeatable` — The random sequence used for noise generation is not repeatable.

• `Repeatable` — The random sequence used for noise generation is repeatable, with a system-generated seed.

• `Specify seed` — The random sequence used for noise generation is repeatable, and you control the seed by using the Seed parameter.

#### Dependencies

Enabled when the Noise mode parameter is set to `Enabled`.

Random number seed stored inside the block to make the random sequence repeatable. The parameter value is automatically generated using the MATLAB random number generator command. You can modify this parameter value, but it gets overwritten by a new random value if you copy the block to another block in the model. Therefore, if you want to control the seed of the random sequence, use the ```Specify seed``` option for the Repeatability parameter and specify the desired seed value using the Seed parameter.

#### Dependencies

Enabled when the Repeatability parameter is set to `Repeatable`.

Seed used by the noise random number generator.

#### Dependencies

Enabled when the Repeatability parameter is set to `Specify seed`.

The temperature of the resistor at the start of the simulation.

#### Dependencies

Enabled when the Noise mode parameter is set to `Enabled`.

For blocks with an exposed thermal port, this parameter is disabled. Instead, use the Variables tab to set the initial temperature target. For more information, see Variables.

### Thermal

This section appears only for blocks with exposed thermal port. For more information, see Thermal Port.

The coefficient ${T}_{C1}^{eff}$ in the equation that describes resistance as a function of temperature. See Thermal Port for details.

The coefficient ${T}_{C2}^{eff}$ in the equation that describes resistance as a function of temperature. See Thermal Port for details.

The temperature T0, for which the nominal resistance R is specified.

Thermal mass associated with the thermal port H. It represents the energy required to raise the temperature of the thermal port by one degree.