# Half-Bridge (Ideal, Switching)

Half-bridge with ideal switches and thermal port

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• Simscape / Electrical / Semiconductors & Converters

## Description

The Half-Bridge (Ideal, Switching) block models a half-bridge with ideal switches and a thermal port. To choose the ideal switching device, set the Switching device parameter to either `MOSFET`, `IGBT`, or `GTO`.

You can specify an integral protection diode for each switching device. An integral diode protects the semiconductor device by providing a conduction path for a reverse current. An inductive load can produce a high reverse-voltage spike when the semiconductor device suddenly switches off the voltage supply to the load.

### Equations

The protection diodes inside the half-bridge use the Lauritzen and Ma model to capture the charge dynamics effects. The defining equations are:

 ${i}_{RM}=\frac{{q}_{E}-{q}_{M}}{{T}_{M}}$ (1)
 $\frac{d{q}_{M}}{dt}+\frac{{q}_{M}}{\tau }-\frac{{q}_{E}-{q}_{M}}{{T}_{M}}=0$ (2)
where:

• iRM is the diode peak reverse current.

• qE is the junction charge.

• qM is the total stored charge.

• TM is the transit time.

• τ is the carrier lifetime.

The block solves equation 2 at `t = 0` and qM in steady-state:

 ${q}_{M}={i}_{RM}\tau -\tau \left({i}_{RM}-{i}_{F}\right)\mathrm{exp}\left(-\frac{t}{\tau }\right)=\tau {i}_{F}.$ (3)

At `t = 0` and `qE = 0`, equation 1 is equal to:

 ${i}_{RM}=\frac{-{q}_{M}}{{T}_{M}}.$ (4)
The block then substitutes equation 3 into equation 4:
 ${i}_{RM}=\frac{-\tau }{{T}_{M}}{i}_{F},$ (5)
where iF is the starting forward current when measuring iRM.

Finally, the block calculates the reverse recovery energy, Erec, as:

 ${E}_{rec}={\int }_{{t}_{1}}^{{t}_{2}}{i}_{d}{v}_{d}dt={\int }_{n}^{{t}_{2}}{i}_{RM}exp\left(-\frac{t-{t}_{1}}{{\tau }_{rr}}\right){v}_{R}dt,$ (6)
where:

• id is the current through the diode.

• vd is the voltage across the diode.

• τrr is the reverse recovery time.

Given `t2=τrrln(10)`, the total reverse recovery energy is:

 ${E}_{rec}=-0.9{\tau }_{rr}\frac{\tau }{{T}_{M}}{i}_{F}{v}_{R}=-0.9\frac{{\tau }^{2}}{\tau +{T}_{M}}{i}_{F}{v}_{R}.$ (7)

## Assumptions and Limitations

• The current change in the load is negligible. The inductance or the switching frequency are large enough so that the load current is constant between the switches.

• The stray inductance of the circuit is negligible.

## Ports

### Input

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Physical signal conserving port associated with the gate terminals of the two switching devices, specified as a vector of two physical signals.

The first element of the vector controls the upper side switch. The second element of the vector controls the lower side switch. If, in the Diode settings, you set the Integral protection diode parameter to `Yes`, the first and second element of the vector also controls the lower and upper diode, respectively.

#### Dependencies

To enable this port, set Gate-control port to `PS`.

### Conserving

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Electrical conserving port associated with the positive terminal.

Electrical conserving port associated with the negative terminal.

Electrical conserving port associated with the output node.

Electrical conserving port associated with the gate terminal for the first switching device.

#### Dependencies

To enable this port, set Gate-control port to `Electrical`.

Electrical conserving port associated with the gate terminal for the second switching device.

#### Dependencies

To enable this port, set Gate-control port to `Electrical`.

Thermal conserving port.

## Parameters

expand all

### Main

The visibility of the Main parameters depends on the Switching device and On-state behavior and losses parameters. To learn how to read this table, see Parameter Dependencies.

Main Parameter Dependencies

Parameters and Options
Gate-control port
Switching Device
`MOSFET``IGBT``GTO`
Threshold voltage, VthThreshold voltage, VthGate trigger voltage, Vgt
Gate turn-off voltage, Vgt_off
Holding current
On-state behaviour and losses
```Specify constant values``````Tabulate with temperature and current``````Specify constant values``````Tabulate with temperature and current``````Specify constant values``````Tabulate with temperature and current```
Drain-source on resistance, R_DS(on)On-state voltage, Vds(Tj,Ids)Forward voltage, VfOn-state voltage, Vds(Tj,Ice)Forward voltage, VfOn-state voltage, Vak(Tj,Iak)
Temperature vector, TjOn-state resistanceTemperature vector, TjOn-state resistanceTemperature vector, Tj
Drain-source current vector, IdsCollector-emitter current vector, IceAnode-cathode current vector, Iak
Off-state conductance

Whether to use the physical signal input port, G, or the electrical conserving ports G1 and G2, as the gate control ports.

Switching device to use for the half-bridge.

Threshold voltage at which the device turns on. The default value depends on the Switching device setting.

#### Dependencies

See the Main Parameter Dependencies table.

Gate-cathode voltage threshold. The device turns on when the gate-cathode voltage is above this value.

#### Dependencies

See the Main Parameter Dependencies table.

Gate-cathode voltage threshold. The device turns off when the gate-cathode voltage is below this value.

#### Dependencies

See the Main Parameter Dependencies table.

Current threshold. The device stays on when the current is above this value, even when the gate-cathode voltage falls below the gate trigger voltage.

#### Dependencies

See the Main Parameter Dependencies table.

Parameterization method, specified as either:

• `Specify constant values` — Use scalar values to specify the output current, switch-on loss, and switch-off loss data.

• ```Tabulate with temperature and current``` — Use vectors to specify the output current, switch-on loss, switch-off loss, and temperature data.

#### Dependencies

See the Main Parameter Dependencies table.

Drain-source resistance when the device is on.

#### Dependencies

See the Main Parameter Dependencies table.

Voltage drop across the device when the device is in a triggered conductive state. This parameter is a function of temperature and the final on-state output current.

#### Dependencies

See the Main Parameter Dependencies table.

Drain-source currents for which the on-state voltage is defined. The first element must be zero. Specify this parameter using a vector quantity.

#### Dependencies

See the Main Parameter Dependencies table.

Minimum voltage required across the collector and emitter block ports for the gradient of the diode I-V characteristic to be 1/Ron, where Ron is the value of the On-state resistance parameter.

#### Dependencies

See the Main Parameter Dependencies table.

Collector-emitter resistance when the device is on.

#### Dependencies

See the Main Parameter Dependencies table.

Voltage drop across the device when the device is in a triggered conductive state. This parameter is a function of temperature and the final on-state output current.

#### Dependencies

See the Main Parameter Dependencies table.

Collector-emitter currents for the on-state voltage. The first element must be zero. Specify this parameter using a vector quantity.

#### Dependencies

See the Main Parameter Dependencies table.

Voltage drop across the device when the device is in a triggered conductive state. This parameter is a function of temperature and the final on-state output current.

#### Dependencies

See the Main Parameter Dependencies table.

Anode-cathode currents for which the on-state voltage is defined. The first element must be zero.

#### Dependencies

See the Main Parameter Dependencies table.

Temperature values at which the on-state voltage is specified.

#### Dependencies

See the Main Parameter Dependencies table.

Conductance when the device is off. The value must be less than 1/R, where R is the value of the On-state resistance parameter.

#### Dependencies

See the Main Parameter Dependencies table.

### Losses

The visibility of the Losses parameters depends on the Switching device and On-state behavior and losses parameters in the Main tab. To learn how to read this table, see Parameter Dependencies.

Losses Parameter Dependencies

Parameters and Options
Switching Device
`MOSFET``IGBT``GTO`
On-state behaviour and losses
```Specify constant values``````Tabulate with temperature and current``````Specify constant values``````Tabulate with temperature and current``````Specify constant values``````Tabulate with temperature and current```
Switch-on lossSwitch-on loss, Eon(Tj,Ids)Switch-on lossSwitch-on loss, Eon(Tj,Ice)Switch-on lossSwitch-on loss, Eon(Tj,Iak)
Switch-off lossSwitch-off loss, Eoff(Tj,Ids)Switch-off lossSwitch-off loss, Eoff(Tj,Ice)Forced commutation switch-off lossSwitch-off loss, Eoff(Tj,Iak)
Diode reverse recovery lossDiode reverse recovery loss, Erec(Tj,Ids)Diode reverse recovery lossDiode reverse recovery loss, Erec(Tj,Ice)Diode reverse recovery lossDiode reverse recovery loss, Erec(Tj,Iak)
On-state current for loss dataTemperature vector for losses, TjOn-state current for loss dataTemperature vector for losses, TjOn-state current for loss dataTemperature vector for losses, Tj
Drain-source current vector for losses, IdsCollector-emitter current vector for losses, IceNatural commutation rectification lossAnode-cathode current vector for losses, Iak
Natural commutation rectification loss
Off-state voltage for loss data

Energy dissipated during a single switch-on event. This parameter is a function of temperature and the final on-state output current.

#### Dependencies

See the Losses Parameter Dependencies table.

Energy dissipated during a single switch-off event. This parameter is a function of temperature and the final on-state output current.

#### Dependencies

See the Losses Parameter Dependencies table.

Energy dissipated during a diode-reverse recovery event.

#### Dependencies

See the Losses Parameter Dependencies table.

Output voltage when the device is off. The loss data define the blocking voltage at this value.

#### Dependencies

See the Losses Parameter Dependencies table.

Output current for which the switch-on loss, switch-off loss, and on-state voltage are defined.

#### Dependencies

See the Losses Parameter Dependencies table.

Energy dissipated during a single switch-on event. This parameter is a function of temperature and the final on-state output current.

#### Dependencies

See the Losses Parameter Dependencies table.

Energy dissipated during a single switch-off event. This parameter is defined as a function of temperature and the final on-state output current.

#### Dependencies

See the Losses Parameter Dependencies table.

Energy dissipated during a diode-reverse recovery event. This parameter is a function of temperature and the final on-state output current.

#### Dependencies

See the Losses Parameter Dependencies table.

Drain-source currents for which the losses are defined. The first element must be zero.

#### Dependencies

See the Losses Parameter Dependencies table.

Energy dissipated during a single switch-on event. This parameter is a function of temperature and the final on-state output current.

#### Dependencies

See the Losses Parameter Dependencies table.

Energy dissipated during a single switch-off event. This parameter is a function of temperature and final on-state output current.

#### Dependencies

See the Losses Parameter Dependencies table.

Energy dissipated during a diode-reverse recovery event. This parameter is a function of temperature and the final on-state output current.

#### Dependencies

See the Losses Parameter Dependencies table.

Collector-emitter currents for which the losses are defined. The first element must be zero.

#### Dependencies

See the Losses Parameter Dependencies table.

Energy dissipated during a forced commutation switch-off event. This parameter is a function of temperature and final on-state output current.

#### Dependencies

See the Losses Parameter Dependencies table.

Rectification loss applied when the block switches off because the current falls below the value of the Holding current parameter.

#### Dependencies

See the Losses Parameter Dependencies table.

Energy dissipated during a single switch-on event. This parameter is a function of temperature and the final on-state output current.

#### Dependencies

See the Losses Parameter Dependencies table.

Energy dissipated during a single switch-off event. This parameter is a function of temperature and the final on-state output current.

#### Dependencies

See the Losses Parameter Dependencies table.

Energy dissipated during a diode-reverse recovery event. This parameter is a function of temperature and the final on-state output current.

#### Dependencies

See the Losses Parameter Dependencies table.

Anode-cathode currents for which the losses are defined. The first element must be zero.

#### Dependencies

See the Losses Parameter Dependencies table.

Temperature values at which the losses are specified. Specify this parameter using a vector quantity.

#### Dependencies

See the Losses Parameter Dependencies table.

Temperature values at which the losses are specified. Specify this parameter using a vector quantity.

#### Dependencies

See the Losses Parameter Dependencies table.

Output voltage when the device is off. The loss data define the blocking voltage at this value.

#### Dependencies

See the Losses Parameter Dependencies table.

### Integral Diode

Whether to model the block integral protection diode.

Diode model, specified as either:

• `Piecewise Linear` — Use a piecewise linear model for the diode, as described in Piecewise Linear Diode.

• `Tabulated I-V curve` — Use tabulated forward bias I-V data and fixed reverse bias off conductance.

#### Dependencies

To enable this parameter, set Integral protection diode to `Yes`.

Minimum voltage required across the `+` and `-` block ports for the gradient of the diode I-V characteristic to be 1/Ron, where Ron is the value of the On resistance parameter.

#### Dependencies

To enable this parameter, set Integral protection diode to `Yes` and Diode model to `Piecewise linear`.

Rate of change of the voltage versus the current above the value of the Forward voltage parameter.

#### Dependencies

To enable this parameter, set Integral protection diode to `Yes` and Diode model to `Piecewise linear`.

Conductance of the reverse-biased diode.

#### Dependencies

To enable this parameter, set Integral protection diode to `Yes` and Diode model to `Piecewise linear`.

Whether to tabulate the current as a function of temperature and voltage or the voltage as a function of temperature and current.

#### Dependencies

To enable this parameter, set Integral protection diode to `Yes` and Diode model to ```Tabulated I-V curve```.

Forward currents. This parameter must be a vector of at least three nonnegative elements.

#### Dependencies

To enable this parameter, set Integral protection diode to `Yes`, Diode model to ```Tabulated I-V curve```, and Table type to `Table in If(Tj,Vf) form`.

Vector of junction temperatures. This parameter must be a vector of at least two elements.

#### Dependencies

To enable this parameter, set Integral protection diode to `Yes`, and Diode model to ```Tabulated I-V curve```.

Vector of forward voltages. This parameter must be a vector of at least three nonnegative values.

#### Dependencies

To enable this parameter, set Integral protection diode to `Yes`, Diode model to ```Tabulated I-V curve```, and Table type to `Table in If(Tj,Vf) form`.

Forward voltages. This parameter must be a vector of at least three nonnegative elements.

#### Dependencies

To enable this parameter, set Integral protection diode to `Yes`, Diode model to ```Tabulated I-V curve```, and Table type to `Table in Vf(Tj,If) form`.

Vector of forward currents. This parameter must be a vector of at least three nonnegative values.

#### Dependencies

To enable this parameter, set Integral protection diode to `Yes`, Diode model to ```Tabulated I-V curve```, and Table type to `Table in Vf(Tj,If) form`.

### Thermal Port

Use the thermal port to simulate the effects of generated heat and device temperature. For more information about using thermal ports and the Thermal Port parameters, see Simulating Thermal Effects in Semiconductors.

## Version History

Introduced in R2021b