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Model light-emitting diode as exponential diode and current sensor in series
Sensors
The Light-Emitting Diode block represents a light-emitting diode as an exponential diode in series with a current sensor. The optical power presented at the signal port W is equal to the product of the current flowing through the diode and the Optical power per unit current parameter value.
The exponential diode model provides the following relationship between the diode current I and the diode voltage V:
where:
q is the elementary charge on an electron (1.602176e–19 Coulombs).
k is the Boltzmann constant (1.3806503e–23 J/K).
Vz is the Reverse breakdown voltage BV parameter value.
N is the emission coefficient.
IS is the saturation current.
T is the temperature at which the diode parameters are specified, as defined by the Measurement temperature parameter value.
When
, the block replaces
with
, which matches the gradient
of the diode current at
and extrapolates
linearly. When
, the block replaces
with
, which also matches the gradient
and extrapolates linearly. Typical electrical circuits do not reach
these extreme values. The block provides this linear extrapolation
to help convergence when solving for the constraints during simulation.
When you select Use parameters IS and N for the Parameterization parameter, you specify the diode in terms of the Saturation current IS and Emission coefficient N parameters. When you select Use I-V curve data points for the Parameterization parameter, you specify two voltage and current measurement points on the diode I-V curve and the block derives the IS and N values. When you specify current and voltage measurements, the block calculates IS and N as follows:
where:
V1 and V2 are the values in the Voltages [V1 V2] vector.
I1 and I2 are the values in the Currents [I1 I2] vector.
The exponential diode model provides the option to include a junction capacitance:
When you select Fixed or zero junction capacitance for the Junction capacitance parameter, the capacitance is fixed.
When you select Use parameters CJO, VJ, M & FC for the Junction capacitance parameter, the block uses the coefficients CJO, VJ, M, and FC to calculate a junction capacitance that depends on the junction voltage.
When you select Use C-V curve data points for the Junction capacitance parameter, the block uses three capacitance values on the C-V capacitance curve to estimate CJO, VJ, and M and uses these values with the specified value of FC to calculate a junction capacitance that depends on the junction voltage. The block calculates CJO, VJ, and M as follows:
where:
VR1, VR2, and VR3 are the values in the Reverse bias voltages [VR1 VR2 VR3] vector.
C1, C2, and C3 are the values in the Corresponding capacitances [C1 C2 C3] vector.
It is not possible to estimate FC reliably from tabulated data, so you must specify its value using the Capacitance coefficient FC parameter. In the absence of suitable data for this parameter, use a typical value of 0.5.
The reverse bias voltages (defined as positive values) should satisfy VR3 > VR2 > VR1. This means that the capacitances should satisfy C1 > C2 > C3 as reverse bias widens the depletion region and hence reduces capacitance. Violating these inequalities results in an error. Voltages VR2 and VR3 should be well away from the Junction potential VJ. Voltage VR1 should be less than the Junction potential VJ, with a typical value for VR1 being 0.1 V.
The voltage-dependent junction capacitance is defined in terms of the capacitor charge storage Qj as:
For
:
For
:
where:
These equations are the same as used in [2], except that the temperature dependence of VJ and FC is not modeled. This model does not include the diffusion capacitance term that affects performance for high frequency switching applications.
The Light-Emitting Diode block has the following limitations:
When you select Use I-V curve data points for the Parameterization parameter, choose a pair of voltages near the diode turn-on voltage. Typically this is in the range from 0.05 to 1 Volt. Using values outside of this region may lead to numerical problems and poor estimates for IS and N.
This block does not model temperature-dependent effects. SimElectronics™ simulates the block at the temperature at which the component behavior was measured, as specified by the Measurement temperature parameter value.
You may need to use nonzero ohmic resistance and junction capacitance values to prevent numerical simulation problems, but the simulation may run faster with these values set to zero.
The amount of optical power the light-emitting diode generates per unit of current flowing through the diode. The default value is 0.005 W/A.
Select one of the following methods for model parameterization:
Use I-V curve data points — Specify measured data at two points on the diode I-V curve. This is the default method.
Use parameters IS and N — Specify saturation current and emission coefficient.
A vector of the current values at the two points on the diode I-V curve that the block uses to calculate IS and N. This parameter is only visible when you select Use I-V curve data points for the Parameterization parameter. The default value is [ 0.0017 0.003 ] A.
A vector of the voltage values at the two points on the diode I-V curve that the block uses to calculate IS and N. This parameter is only visible when you select Use I-V curve data points for the Parameterization parameter. The default value is [ 0.9 1.05 ] V.
The magnitude of the current that the ideal diode equation approaches asymptotically for very large reverse bias levels. This parameter is only visible when you select Use parameters IS and N for the Parameterization parameter. The default value is 5e-05 A.
The temperature at which IS or the I-V curve was measured. The default value is 25 °C.
The diode emission coefficient or ideality factor. This parameter is only visible when you select Use parameters IS and N for the Parameterization parameter. The default value is 10.
The series diode connection resistance. The default value is 0.1 Ω.
Select one of the following options for modeling the junction capacitance:
Fixed or zero junction capacitance — Model the junction capacitance as a fixed value.
Use C-V curve data points — Specify measured data at three points on the diode C-V curve.
Use parameters CJ0, VJ, M & FC — Specify zero-bias junction capacitance, junction potential, grading coefficient, and forward-bias depletion capacitance coefficient.
The value of the capacitance placed in parallel with the exponential diode term. This parameter is only visible when you select Fixed or zero junction capacitance or Use parameters CJ0, VJ, M & FC for the Junction capacitance parameter. The default value is 20 pF.
A vector of the reverse bias voltage values at the three points on the diode C-V curve that the block uses to calculate CJ0, VJ, and M. This parameter is only visible when you select Use C-V curve data points for the Junction capacitance parameter. The default value is [ 0.1 10 100 ] V.
A vector of the capacitance values at the three points on the diode C-V curve that the block uses to calculate CJ0, VJ, and M. This parameter is only visible when you select Use C-V curve data points for the Junction capacitance parameter. The default value is [ 15 10 2 ] pF.
The junction potential. This parameter is only visible when you select Use parameters CJ0, VJ, M & FC for the Junction capacitance parameter. The default value is 1 V.
The grading coefficient. This parameter is only visible when you select Use parameters CJ0, VJ, M & FC for the Junction capacitance parameter. The default value is 0.5.
Fitting coefficient that quantifies the decrease of the depletion capacitance with applied voltage. This parameter is only visible when you select Use C-V curve data points or Use parameters CJ0, VJ, M & FC for the Junction capacitance parameter. The default value is 0.5.
The block has the following ports:
Optical output power.
Electrical conserving port associated with the diode positive terminal.
Electrical conserving port associated with the diode negative terminal.
[1] H. Ahmed and P.J. Spreadbury. Analogue and digital electronics for engineers. 2nd Edition, Cambridge University Press, 1984.
[2] G. Massobrio and P. Antognetti. Semiconductor Device Modeling with SPICE. 2nd Edition, McGraw-Hill, 1993.
Diode, Optocoupler, Photodiode
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