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Voltage-dependent resistor

**Library:**Simscape / Electrical / Passive

The Varistor block represents a voltage-dependent resistor (VDR). This component is also commonly known as a metal-oxide varistor (MOV). The block exhibits high resistance at low voltages and low resistance at high voltages.

You can protect parts of an electrical circuit from high-voltage surges by placing this block in parallel with them. When a surge occurs, the resistance of the varistor drops significantly, causing the current to be shunted through the varistor rather than through the circuit.

Use the **Parameterization** parameter to choose between two
different behaviors for this block. The `Linear`

option focuses
on the on- and off-states of the varistor and uses a linear relationship between current
and voltage in both regions. The `Power-law`

option uses an
exponential relationship between current and voltage in the initial on-state. This
option also adds a third, linear region at higher voltages.

This parameterization option separates the voltage-current relationship into two linear regions:

Off-region — resistance is high and current increases slowly with increasing voltage.

On-region — resistance is low and current increases rapidly with increasing voltage.

This figure shows the voltage-current relationship across the on- and off-regions.

Use linear parameterization in one of these scenarios:

You are modeling voltage surges close to the threshold voltage

You expect your varistor to behave linearly in all regions

The voltage-current relationship for the linear varistor is:

$${i}_{varistor}=\{\begin{array}{cc}\frac{{v}_{varistor}}{{R}_{off}}& \left|{v}_{varistor}\right|<{v}_{clamp}\\ \frac{{v}_{varistor}}{{R}_{on}}+{c}_{1}\mathrm{sgn}({v}_{varistor})& \left|{v}_{varistor}\right|\ge {v}_{clamp}\end{array}.$$

where:

*v*and_{varistor}*i*are the varistor voltage and current, respectively._{varistor}*v*is the threshold voltage that separates the two regions of operation. Set this value using the_{clamp}**Clamping voltage**parameter.*R*and_{on}*R*are the resistances in the on- and off-regions. Set these values using the_{off}**On resistance**and**Off resistance**, respectively.*c*is a constant used to enforce current continuity between the two regions:_{1}$${c}_{1}={v}_{clamp}\left(\frac{1}{{R}_{off}}-\frac{1}{{R}_{on}}\right).$$

This parameterization option separates the voltage-current relationship into three regions:

Leakage region — Resistance is high and current increases slowly with increasing voltage.

Normal region — Resistance decreases exponentially with increasing voltage.

Upturn region — Resistance is low and current increases rapidly with increasing voltage.

This figure shows the three regions of operation in log-log-scale.

Use power-law parameterization in one of these scenarios:

You are modeling voltage surges across a large range of voltages

You expect your varistor to behave exponentially in the first on-region

The voltage-current relationship for the power-law varistor is:

$${i}_{varistor}=\{\begin{array}{cc}\frac{{v}_{varistor}}{{R}_{L}}& \left|{v}_{varistor}\right|<{v}_{LN}\\ k{\left({v}_{varistor}\right)}^{\alpha}+{c}_{1}& {v}_{LN}\le \left|{v}_{varistor}\right|\le {v}_{NU}\\ \frac{{v}_{varistor}}{{R}_{U}}+{c}_{2}& \left|{v}_{varistor}\right|>{v}_{NU}\end{array}$$

where:

*v*and_{varistor}*i*are the varistor voltage and current, respectively._{varistor}*α*is the power-law exponent which determines the rate of current increase with voltage increase in the normal region. Set this value using the**Normal-mode power-law exponent**parameter.*v*and the_{LN}*v*are the threshold voltages corresponding to the leakage-normal and normal-upturn transition points. Set these values using the_{NU}**Leakage to normal voltage transition**and**Normal to upturn voltage transition**parameters, respectively.*R*and_{L}*R*are the resistances in the leakage- and upturn-regions. Set these values using the_{U}**Leakage-mode resistance**and**Upturn-mode resistance**parameters, respectively.*k*,*c*, and_{1}*c*are constants used to enforce current continuity between the regions:_{2}$$k=\frac{1}{\alpha {R}_{U}{v}_{NU}^{\alpha -1}},$$

$${c}_{1}=\frac{{v}_{LN}}{{R}_{L}}-\frac{{v}_{LN}^{\alpha}}{\alpha {R}_{U}{v}_{NU}^{\alpha -1}},$$

and

$${c}_{2}=\frac{1}{\alpha {R}_{U}{v}_{NU}^{\alpha -1}}({v}_{NU}^{\alpha}-{v}_{LN}^{\alpha})-\frac{{v}_{NU}}{{R}_{U}}+\frac{{v}_{LN}}{{R}_{L}}.$$

In addition to the varistor equations, you can also specify a constant terminal
resistance *R _{t}* and device capacitance