# Commutation Diode

Piecewise linear diode with charge dynamics and junction capacitance

## Library

Semiconductors / Fundamental Components

## Description

The Commutation Diode block augments the Diode block with a model of charge dynamics. For a description of the piecewise linear diode operation that the Commutation Diode block uses, see Diode.

Use the Commutation Diode block in place of the Diode block when you want to specify precisely the charge dynamics of the device as it operates in reverse mode. For example, suppose that your model uses the diode to divert inductive currents from a motor drive or inverter. In this case, precise reverse-mode operation is important and an appropriate time to use the Commutation Diode block.

The Commutation Diode uses a charge model proposed by Lauritzen and Ma [1]. The defining expressions for this charge model are:

 $i=\frac{{q}_{E}-{q}_{M}}{{T}_{M}}$ (1-1)
 $\frac{d{q}_{M}}{dt}+\frac{{q}_{M}}{\tau }-\frac{{q}_{E}-{q}_{M}}{{T}_{M}}=0$ (1-2)
 (1-3)
where:

• i is the diode current.

• qE is the junction charge.

• qM is the total stored charge.

• TM is the transit time.

• τ is the carrier lifetime.

• vD is the voltage across the diode.

• vF is the diode forward voltage.

• R is the diode on resistance.

• G is the diode off conductance.

This graphic shows a typical reverse-mode current characteristic for a diode device.

where:

• iRM is the peak reverse current.

• iF is the starting forward current when measuring iRM.

• a is the rate of change of current when measuring iRM.

• trr is the reverse recovery time.

On the Charge Dynamics tab of the block, you specify characteristics of your diode device. The block uses these values to calculate the diode charge dynamics expressed in equations 1–1, 1–2, and 1–3.

Data sheets for diodes quote values for peak reverse current for an initial forward current and a steady rate of change of current. The data sheet might also provide values for reverse recovery time and total recovery charge.

### How the Block Calculates TM and Tau

The block calculates transit time TM and carrier lifetime τ based on the values you enter on the Charge Dynamics tab of the block dialog box. The block uses TM and τ to solve the charge dynamics equations 1–1, 1–2, and 1–3.

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

Using Equation 1–1,

 ${i}_{F}+at=\frac{{q}_{E}-{q}_{M}}{{T}_{M}}.$ (1-4)

Substituting Equation 1–4 into Equation 1–2,

 $\frac{d{q}_{M}}{dt}+\frac{{q}_{M}}{\tau }={i}_{F}+at.$ (1-5)

Solving Equation 1–5 for qM,

 ${q}_{M}={i}_{F}\tau -a{\tau }^{2}+\frac{k}{\mathrm{exp}\left(\frac{t}{\tau }\right)}+a\tau t,$ (1-6)
where k is a constant.

When t is zero, i = iF and qM = τiF because the system is in steady state.

Substituting these relationships into Equation 1–6 and solving the equation gives k = 2.

Therefore,

 ${q}_{M}={i}_{F}\tau +a{\tau }^{2}\left(\frac{1}{\mathrm{exp}\left(\frac{t}{\tau }\right)}-1\right)+a\tau t.$ (1-7)
At time t = ts, the current is iRM and the junction charge qE is zero.

Substituting these values into Equation 1–1,

 ${i}_{RM}=\frac{-{q}_{M}}{{T}_{M}}.$ (1-8)
Rearranging Equation 1–8 to solve for qM and substituting the result into Equation 1–7,
 $-{T}_{M}{i}_{RM}={i}_{F}\tau +a{\tau }^{2}\left(\frac{1}{\mathrm{exp}\left(\frac{{t}_{s}}{\tau }\right)}-1\right)+a\tau {t}_{s}.$ (1-9)

Expressing time ts in terms of iRM, iF, and a,

 ${t}_{s}=\frac{{i}_{RM}-{i}_{F}}{a}.$ (1-10)

Consider the diode recovery, that is, when t > ts. The diode is reverse biased, and current and junction charge are effectively zero.

The current is defined by

 $i={i}_{RM}\text{exp[}\frac{-\left(t-{t}_{s}\right)}{{\tau }_{rr}}\right],$ (1-11)

where

 $\frac{1}{{\tau }_{rr}}=\frac{1}{\tau }+\frac{1}{{T}_{M}}.$ (1-12)

The block now relates the expression in Equation 1–12 to the reverse recovery time trr.

When $t=\frac{{i}_{RM}}{a}+{t}_{rr},$ the current is $\frac{{i}_{RM}}{10}.$

Therefore,

 $\mathrm{exp}\left(-\frac{t-{t}_{s}}{{\tau }_{rr}}\right)=0.1$ (1-13)
and
 ${t}_{rr}={\tau }_{rr}\mathrm{log}\left(10\right)+\frac{{i}_{RM}}{a}.$ (1-14)

The block uses equations 1–9 and 1–14 to calculate values for TM and τ. The calculation uses an iterative scheme because of the exponential term in Equation 1–9.

### Alternatives to Specifying trr Directly

In addition to allowing you to specify reverse recovery time trr directly, the block supports two alternative parameterizations. The block can derive trr from either of these parameters:

• Reverse recovery time stretch factor λ

• Reverse recovery charge Qrr, when the data sheet specifies this value instead of the reverse recovery time.

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

`$\lambda =\frac{{t}_{rr}a}{{i}_{RM}}.$`
Reverse recovery time must be greater than $\frac{{i}_{RM}}{a}$ and a typical value is $3\left(\frac{{i}_{RM}}{a}\right).$

Therefore, a typical value for λ is 3. λ must be greater than 1.

Reverse recovery charge Qrr is the integral over time of the reverse current from the point where the current goes negative until it decays back to zero.

The initial charge, to time ts (as shown in the figure), is expressed by the equation

 ${Q}_{s}=\frac{1}{2}\left(-{i}_{RM}\right)\frac{{i}_{RM}}{a}.$ (1-15)

Integrating Equation 1–11 gives the charge between times ts and inf. This charge is equal to

`${\tau }_{rr}{i}_{RM}.$`

Therefore, total reverse recovery charge is given by the equation

 ${Q}_{rr}=-\frac{{i}_{RM}^{2}}{2a}+{\tau }_{rr}{i}_{RM}.$ (1-16)

Rearranging Equation 1–16 to solve for τrr and substituting the result into Equation 1–14 gives an equation that expresses trr in terms of Qrr:

`${t}_{rr}=\left(\frac{{Q}_{rr}}{{i}_{RM}}+\frac{{i}_{RM}}{2a}\right)\mathrm{log}\left(10\right)+\frac{{i}_{RM}}{a}.$`

### Modeling Variants

The block provides a thermal modeling variant. To select a variant, right-click the block in your model. From the context menu, select Simscape > Block choices, and then one of these variants:

• No thermal port — This variant does not simulate heat generation in the device. This variant is the default.

• Show thermal port — This variant contains a thermal port that allows you to model the heat that conduction losses generate. For numerical efficiency, the thermal state does not affect the electrical behavior of the block. The thermal port is hidden by default. When you select a thermal variant of the block, the thermal port appears.

## Ports

`+`

Electrical conserving port associated with the diode positive terminal

`-`

Electrical conserving port associated with the diode negative terminal

`H`

Thermal conserving port. The thermal port is optional and is hidden by default. To enable this port, select a variant that includes a thermal port.

## Parameters

### Main Tab

Forward voltage

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 On resistance. The default value is `0.8` `V`.

On resistance

Rate of change of voltage versus current above the Forward voltage. The default value is `0.001` `Ohm`.

Off conductance

Conductance of the reverse-biased diode. The default value is `1e-5` `1/Ohm`.

Number of series diodes

The number of diodes connected in series between the `+` and `-` block ports. Each diode has the Forward voltage, On resistance, and Off conductance that you specify. The default value is `1`.

Number of parallel diodes

The number of parallel diodes, or number of parallel paths formed by series-connected diodes, between the `+` and `-` block ports. Each diode has the Forward voltage, On resistance, and Off conductance that you specify. The default value is `1`.

### Charge Dynamics Tab

Junction capacitance

Diode junction capacitance. The default value is `50` `nF`.

Peak reverse current, iRM

Peak reverse current measured by an external test circuit. This value must be less than zero. The default value is `-235` `A`.

Initial forward current when measuring iRM

Initial forward current when measuring peak reverse current. This value must be greater than zero. The default value is `300` `A`.

Rate of change of current when measuring iRM

Rate of change of current when measuring peak reverse current. This value must be less than zero. The default value is `-50` `A/μs`.

Reverse recovery time parameterization

Determines how you specify reverse recovery time in the block. The default value is `Specify reverse recovery time directly`.

If you select `Specify stretch factor` or ```Specify reverse recovery charge```, you specify a value that the block uses to derive the reverse recovery time. For more information on these options, see Alternatives to Specifying trr Directly.

Reverse recovery time, trr

Interval between the time when the current initially goes to zero (when the diode turns off) and the time when the current falls to less than 10% of the peak reverse current. The default value is `15` `μs`.

This parameter is visible only if you set Reverse recovery time parameterization to ```Specify reverse recovery time directly```.

The value of the Reverse recovery time, trr parameter must be greater than the value of the Peak reverse current, iRM parameter divided by the value of the Rate of change of current when measuring iRM parameter.

Reverse recovery time stretch factor

Value that the block uses to calculate Reverse recovery time, trr. This value must be greater than `1`. The default value is `3`.

This parameter is visible only if you set Reverse recovery time parameterization to ```Specify stretch factor```.

Specifying the stretch factor is an easier way to parameterize the reverse recovery time than specifying the reverse recovery charge. The larger the value of the stretch factor, the longer it takes for the reverse recovery current to dissipate.

Reverse recovery charge, Qrr

Value that the block uses to calculate Reverse recovery time, trr. Use this parameter if the data sheet for your diode device specifies a value for the reverse recovery charge instead of a value for the reverse recovery time.

The reverse recovery charge is the total charge that continues to dissipate when the diode turns off. The value must be less than $-\frac{{i}^{2}{}_{RM}}{2a},$

where:

• iRM is the value specified for Peak reverse current, iRM.

• a is the value specified for Rate of change of current when measuring iRM.

The default value is `1500` `μAs`.

The parameter is visible only if you set Reverse recovery time parameterization to ```Specify reverse recovery charge```.

## References

[1] Lauritzen, P.O. & C.L. Ma, “A Simple Diode Model with Reverse Recovery.” IEEE® Transactions on Power Electronics. Vol. 6, No. 2, 1991, pp. 188–191.

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