Diode (Advanced)

The diode model with piecewise linear BAC is similar to the model Diode, with the addition of a fixed junction capacitance and the ability to account for charge dynamics. If the direct voltage across the diode exceeds the value specified in the parameter Forward voltage, the diode behaves like a linear resistor with the resistance specified in the parameter On resistance. Otherwise, the diode behaves as a linear resistor with the small conductance specified in the parameters Off conductance. At zero voltage, zero current flows through the diode.

The exponential EAC is the following relationship between diode current and diode voltage :

, at ,

, at ,

where

When , the block replaces with , which corresponds to the diode current gradient at and is extrapolated linearly.

When , the block replaces with , which also corresponds to the gradient and is extrapolated linearly.

Conventional electrical circuits do not reach such extremes. The block provides this linear extrapolation to facilitate convergence when solving constraints during the modelling process.

If the parameters Parameterization are chosen to be Use parameters IS and N, the diode is specified as parameters Saturation current, IS and Emission coefficient, N.

If the parameters Parameterization are set to , , the diode is specified as parameters and . `Use two I-V curve data points`then two voltage and current measurement points on the diode’s VAC are set, and the block determines the values and . It calculates and as follows:

,

,

where

If for the parameters Parameterization is selected. Use an I-V data point and IS, the block calculates as follows:

.

If the parameters Parameterization are set to . Use an I-V data point and N, the block calculates as follows:

.

To simulate a diode with a tabulated BAC, set the parameters Diode model to Tabulated I-V curve. This figure shows the realisation of the diode variant with tabulated BAC:

You only provide tabulated data for forward bias. The block uses modified Akim interpolation to find intermediate values. If the voltage or current is outside the range of the tabular data, the block uses linear extrapolation after the last voltage and current data point.

For reverse bias:

If a thermal port is used in the block, the junction capacitance can only be modelled if the parameters Fidelity level are set to . Include capacitance and charge dynamics.

There are three ways to enable junction capacitance modelling:

where

The reverse bias voltages (defined as positive values) must satisfy the condition . This means that the capacitances must satisfy the condition , since reverse bias expands the depletion region and therefore reduces the capacitance. Violation of these inequalities leads to an error. The voltages and must be sufficiently distant from the transition potential . The voltage must be less than the junction potential , with the typical value of being 0.1 V.

The voltage-dependent junction capacitance is defined in terms of capacitor charge accumulation as:

Where

These equations are similar to those given in [2], except that the temperature dependence for and is not modelled.

If a thermal port is used in the block, the junction capacitance can only be modelled if the parameters Fidelity level are set to Include capacitance and charge dynamics.

For applications such as diodes for switching circuits, it can be important to model the charge dynamics of the diode. When a reverse voltage is applied to a direct-input diode, it takes time for the charge to dissipate and hence for the diode to switch off. The time required to switch off the diode is mainly determined by the span time parameter. After switching off the diode, the remaining charge is dissipated, the rate of this process being determined by the carrier lifetime.

To account for these effects, the model of Lauritzen and Ma [3] is used in the block. The defining equations are given below:

, (1)

, (2)

, (3)

where

This graph shows a typical reverse current characteristic for a diode.

Where

The diode data sheets provide values of peak reverse current for initial forward current and constant rate of change of current. The data sheet may also provide values of reverse recovery time and full recovery charge.

How the unit calculates and

The block calculates the span time, , and carrier lifetime, , based on the values entered for the Charge Dynamics parameters. The block uses and to solve the charge dynamics equations (1), (2), and (3).

During the initial current decay in reverse mode, the diode remains on and the rate of current change is determined by an external test circuit.

The block first uses equation (1) to perform this calculation:

. (4)

Then it substitutes equation (4) into equation (2):

. (5)

Then equation (5) is solved for :

, (6)

where is a constant value.

When , and , since the system is in steady state.

Substituting these relations into equation (6) and solving it, we obtain .

Thus,

. (7)

At time , the current is , and the junction charge is zero. The block substitutes these values into equation (1).

. (8)

The block expresses from equation (8) and substitutes the obtained result into equation (7).

. (9)

The block then expresses the time through , and .

. (10)

Consider the diode recovery process, i.e., when . The diode is reverse biased, and the junction current and charge are effectively zero.

The current is determined by Eq:

, (11)

where

. (12)

The block now relates the expression in equation (12) to the backward recovery time .

When current is .

Therefore

(13)

и

. (14)

The block uses equations (9) and (14) to calculate the values of and . The calculation uses an iterative scheme because there is an exponential term in equation (9).

Alternatives to directly specifying

In addition to allowing the block to specify the inverse recovery time directly, it supports three alternative parameterizations. The block can define from any of the parameters:

The relationship between the recovery time stretch factor and is expressed by the equation

.

The reverse recovery time should be greater than . Its typical value is .

Therefore, the typical value of is 3. The value of must be greater than 1.

The reverse recovery charge is the integral over the reverse current time from the moment the current goes negative to the moment it falls back to zero.

The initial charge by the time is expressed by the following equation:

. (15)

Integration of equation (11) gives the charge between the time instants and inf. This charge is equal to .

Thus, the total charge of the reverse recovery is determined by Eq.

. (16)

Rearranging equation 16 to solve for and substituting the result into equation 14 gives an equation expressing in terms of :

.

Alternatively, the block calculates , using the reverse recovery energy . This equation determines the voltage curve across the diode:

, (17)

where is the maximum reverse voltage of the diode.

If , which is the usual condition for a reverse recovery check circuit, the block calculates the maximum reverse voltage of the diode as:

.

Since the value of the decay time is small, the block assumes that the diode current decay is linear:

. (18)

Equation (18) is then substituted into equation (5):

. (19)

Equation (19) is solved to obtain the total accumulated charge:

, (20),

where is the current gradient.

When , the peak reverse current is:

. (21)

The block now substitutes equation (21) into equation (20):

. (22)

Finally, the block solves equation (22) to obtain the reverse recovery energy:

. (23)

By default, for the Diode (Advanced) block the temperature dependence is not modelled and the device is modelled at the temperature for which the block parameters are set. Diode with exponential VAC contains several options for modelling the temperature dependence of diode current and voltage during simulation. The temperature dependence of the junction capacitance is not modelled because its influence is much smaller.

When the temperature dependence is included, the diode’s defining equation remains the same. The value of the measurement temperature, , is replaced by the modelling temperature, . The saturation current, , becomes a function of temperature according to the following equation:

,

where

The respective values of and depend on the type of diode and the semiconductor material used. By default values for specific material types and diodes reflect approximate behaviour with temperature changes. By default values for common diode types are given in the block.

In practice, to simulate the exact behaviour of a particular diode requires adjusting the values and . Some manufacturers specify these adjusted values in the data sheets, where you can view the corresponding values. Otherwise, you can determine improved estimates for , using a specific current-voltage data point at a higher temperature in the data sheet. For this purpose, the block includes a parameterization option. It also allows the saturation current at higher temperature to be set directly .

If the final reverse breakdown voltage , is set, the value of the reverse is modulated by the reverse breakdown temperature coefficient (set with the parameters Reverse breakdown voltage temperature coefficient dBV/dT):

. (24)

You can use the perfect switching option with blocks for switching circuits:

The diode in these blocks can be modelled internally, or using a separate block Diode (Advanced).

To use the perfect switching option, set the parameters Fidelity level to Ideal switching.

Reverse recovery losses are one of the main sources of thermal losses in diodes. The diode dissipates energy each time it switches off, going from a conducting state to an open circuit state.

In ideal switching, the block does not use a physical charge model. The block represents the losses created by charge during reverse recovery as instantaneous losses.

The block applies the reverse recovery loss by raising the transition temperature by an amount equal to the reverse recovery loss divided by the total heat capacity of the transition.

If the Reverse recovery loss model parameters are set to a value of Tabulated loss, the value of the parameter Reverse recovery loss table, Erec(Tj, If) determines the energy dissipated as a function of junction temperature and forward current just prior to the switching event. The turn-off voltage linearly scales the loss with respect to Turn-off voltage when measuring recovery loss, Vrec. The table uses delayed current and voltage values. To use a near instantaneous value in the lookup table, set the parameters Filter time constant for voltage and current values to a value less than the fastest switching period.

If the parameter Reverse recovery loss model is set to a value lower than the fastest switching period. Fixed loss, the value of the Reverse recovery loss parameter determines the energy dissipated during each shutdown event. If the parameter Scale reverse recovery loss with current and voltage, is selected, the unit scales this loss value linearly in terms of turn-on current and turn-off voltage. For usage of scaling values close to instantaneous values, set Filter time constant for voltage and current values to a value smaller than the fastest switching period.

A thermal port can be used to model the effects of the heat generated and the temperature of the device:

To simulate a Zener diode (semiconductor stabilitron) that conducts in the forward and reverse biased directions, select the checkbox Model Zener diode and specify a value for the parameters Reverse breakdown voltage.

If you select this option, you can model the reverse VAC for the diode block by specifying values for the parameters Reverse voltages, Vr(Tj,Ir), Reverse currents, Ir(Tj,Vr), Reverse voltages, Vr and Reverse currents, Ir.