Download II. Model for LED Optical Behaviour

Modelling the Optical Behaviour of LED's
and PD's for PSpice Simulation Readiness
Marian Vladescu, Norocel Dragos Codreanu, Andreea Bonea and Paul Svasta
Center for Technological Electronics and Interconnection Techniques
“Politehnica” University of Bucharest
Bucharest, Romania
[email protected]
Abstract—The paper presents a method of modelling the optical
behaviour of the optoelectronic devices, such as Light Emitting
Diodes and Photo Diodes, in order to handle the optical signals in
the PSpice environment.
Keywords-optoelectronic devices; modelling and simulation;
optical signals.
I.
Name
PSpice
Library
Current controlled voltage generator
EVALUE
abm.slb
Voltage controlled current generator
GVALUE
abm.slb
Table look-up
FTABLE
abm.slb
ABM2
abm.slb
Type of Component
Expression function
INTRODUCTION
TABLE I.
Including into simulation the optic flux emitted by a Light
Emitting Diode (LED), and received by a Photo Diode (PD),
by introducing optical pins, this leads to a complex PSpice
simulation, which can take into account the changes occurred
to the optic flux due to the coupling factor between the optical
emitter and the optical receiver.
The method proposed for modelling the optical pins, and
for the interactions in the optic domain as well, is based on
Analog Behaviour Modeling blocks, which are available in the
ABM library of PSpice.
The PSpice models available from the manufacturers of the
optoelectronic devices reflect only the electrical characteristics
of these devices, and allow a simple PSpice simulation, well
known. As a result, the simulator handles the voltages and
currents in the traditional way, same as for the usual diodes.
II.
TABLE TYPE STYLES
MODEL FOR LED OPTICAL BEHAVIOUR
A. Proposed Model for LED’s
In the case of a LED, we modelled the emitted optic flux
(Pe), considering the quantic efficiency of the device (E), and
the driving current (Id). The optic flux emitted by the LED is
given by (1).

Pe
Id

In the circuit shown in Figure 1, we placed a current
controlled voltage generator (H1) driven by the current passing
through the LED (D1), followed by a block which implements
the mathematical expression (1).
Our goal was to model the optical pins of LED’s and PD’s
to perform a complex simulation, extended to the optic domain,
being capable to handle also the optical signals within an
optoelectronic circuit.
The challenges we have had to face were the followings:

modelling the emitted optic flux and the quantic
efficiency for LED;

modelling the photocurrent
responsivity for PD.
generated
and
the
The ABM blocks we used in the models we created are:
current controlled voltage generator, voltage controlled current
generator, and table look-up and expression function, as
presented in Table 1.
Figure 1. Model for the emitted optic flux and LED quantic efficiency

We obtained in this way at the output of the circuit the optic
flux (Pout), which will be handled by the PSpice simulator as a
voltage. The characteristics of the driving current I(D1) and the
optical flux V(ABM11:OUT) vs. the forward voltage V_V1 are
shown in Figure 2.
The circuit shown in Figure 3 is an optical emitter, which
includes the LED driver. The results of the AC simulations are
shown in Figure 4.
III.
MODEL FOR PD OPTICAL BEHAVIOUR
A. Proposed Model for PD’s
In the case of a PD, we modeled the generated photocurrent
(Ip), considering the device responsivity (R), and the received
optic flux (Pr). The photocurrent is given by (2).

I p = R * P r

Figure 2. LED driving current and optic flux vs. forward voltage
B. Circuit Simulation for the Optical Emitter
The cut-off frequency for a LED, can be introduced in the
above model using a FTABLE block, which describes in a
table the frequency characteristic of the device, in order to use
the information about the analog bandwidth in simulations.
Figure 5. Model for the generated photocurrent and PD sensitivity
In the circuit shown in Figure 5, we placed a current
generator driven by the voltage V2, which is actually the optic
flux received by the PD. The characteristics of the forward
current I(D1) and the photocurrent I(ABMI I2) vs. forward
voltage V1 are shown in Figure 6.
Figure 3. Optical emmiter circuit
Figure 6.
Figure 4. Frequency characteristics of the optical emitter and LED
PD forward current and photocurrent vs. forward voltage
B. Circuit Simulation for the Optical Receiver
The cut-off frequency for the PD, can be introduced in the
above model using also a FTABLE block, in the same way we
have done for the LED. The circuit shown in Figure 7 is an
optical receiver, which includes the PD amplifier. The results
of the AC simulations are shown in Figure 4.

A basic model for the interaction in the optical domain,
using an ABM2 block, is presented in Figure 10.
Figure 7. Optical receiver circuit
Figure 10. Model for the interaction in the optical domain
In this case, the optical source is assimilated to the voltage
generator V1, so the voltage V(V1(+)) is representing the optic
flux modulated by the voltage V(V2(+)), from the voltage
generator V2, which is assimilated to the measured quantity.
The result of the modulation process V(out) obtained at the
output of the ABM block can be seen in Figure 11.
Figure 8. Frequency characteristics of the optical receiver and PD
IV.
MODELS FOR INTERACTIONS IN THE OPTICAL DOMAIN
This modelling method is creating a start up to more
complex electrical and optical simulations. For example, in the
case of optoelectronic sensors, we can analyze the changes of
the optical flux as a result of various interactions, providing
that we are able to create the appropriate models according to
the respective phenomena, and make a complete simulation of
an optoelectronic sensor.
A. Optical Sensor with Intensity Modulation
We will apply now the proposed modelling method to an
optical sensor based on modulation of the intensity of the optic
flux. The block diagram of such an optoelectronic sensor sown
in Figure 9 consists of three main blocks: the optical emitter,
the interaction with the measurement parameter (measured
quantity) and the optical receiver.
Measurement parameter
Optical
Emmiter
Optic
Interaction
Optical
Receiver
Figure 11. Simulation results for the intensity modulation
B.
Chemical Sensor based on Absorbtion
A more complex process that takes place in the case of the
absorption of the optic flux across a liquid substance with a
certain concentration will require a more complicated model,
starting from the equation that describes the absorption
phenomenon.
The intensity of the light measured at the distance z in an
absorptive medium for a focused beam can be expressed by
(3):
(3)
I( z)  I(0)  exp( z)
The absorption coefficient  is given by (4):

Figure 9. Block diagram of the optoelectronic sensor
where:
cS  c m
N
(4)
cS - absorptive molecule cross-section;
cm - concentration;
N - Avogadro’s number.
The circuit presented in Figure 12 describes the absorption
phenomenon using ABM blocks for the above expressions.
2


r2
I( z)  I(0)  
  exp( z)
 r1  z  tan( ) 
(5)
where  is the divergence of the beam at the output of the
emitting fiber optic.
The circuit presented in Figure 12 describes the absorption
phenomenon taking into accounts the divergence of the optical
beam. The output characteristics are shown in Figure 15.
Figure 12. Model for the chemical sensor based on absorbtion
The voltage V(V1(+)) is representing the optic flux
modulated by combining the voltage V(V2(+)), which is
assimilated to the absorption coefficient and the voltage
V(V3(+)), which is assimilated to the distance z.
The result of the modulation process V(out) obtained at the
output of the ABM2 block is shown in Figure 13.
Figure 14. Model for the chemical sensor with optical fibers
This model is valid for small values of the divergence.
Figure 15. Output characteristics for different distances
Figure 13. Output characteristics vs. absorption coefficient
V.
The output characteristics vs. the absorption coefficient, at
different distances and are shown in Figure 13.
This model is valid for a uniform illumination and does not
take into account the divergence of the optical beam.
C. Chemical Sensor with Optical Fibers
Optical fibers can be used to guide the optic flux toward,
and from the measurement place. If we consider the
divergence of the optical beam, we need to make a correction
with the distance. Assuming that the emitting optical fiber has
the radius r1 and the receiving optical fiber has the radius r2
(where r2 < r1), the intensity of the light at the distance z in an
absorptive medium can be expressed by (5).
CONCLUSIONS
The basic models we succeeded to create in this way are
discrete models, and have advantages, but also disadvantages,
compared with an embedded model. The advantages are related
to the fact that changes can be done into the basic model,
according to the needs for a specific device. An embedded
model does not allow such model adaptations, but it would be
easier and faster to handle within the PSpice simulator.
REFERENCES
[1]
[2]
***, “Analog Behavioral Modeling”, Cadence Design Systems, Inc.,
December 2009.
***, “PSpice User Guide”, Cadence Design Systems, Inc., December
2009.