Microwave design engineers find themselves dealing with an increasing number of optical components, as communications systems become hybrid combinations of wired, wireless, and optical components. In order to perform simulation and analysis of these high-frequency "hybrid" circuits, it can be useful to learn how to apply a commercial circuit-simulation program such as the APLAC RF Design Tool simulator from APLAC Solutions Corp. (Espoo, Finland, www.aplac.com) for this modeling assignment.

The optical transmitter is designed for communications over optical fibers at a rate of 1.1 Gb/s. The transmitter is based on a model MAX3930 laser driver integrated circuit (IC) from Maxim Integrated Products (Sunnyvale, CA, www.maxim-ic.com) and a model ULM850-10-TT-A0112B vertical cavity surface emitting laser (VCSEL) by Ulm Photonics GmbH (Ulm, Germany, www.ulm-photonics.de). The laser model is based on work performed in ref. 1. The driver model is based on an earlier SPICE model developed by Maxim Integrated Products. The laser model relies on simple rate equations with no carrier-density-dependent effects included. In addition, any phenomena related to the multimode operation of the laser diode have been omitted. In spite of these simplifications, good agreement was achieved between the simulation results and measurements made on the actual circuit.

The design goal for the 1.1-Gb/s laser diode and driver circuit is to achieve good output signal integrity, which can be determined by examining an optical eye diagram depicting the output performance. In developing the optical model, design entry was performed with the APLAC editor, using the schematic diagrams shown in Fig. 1. The electrical portion of the circuit consists of a differential pair model of the driver, which includes parasitic circuit elements for the interconnections. Coupling capacitors with their parasitic reactances and the transmission line between the driver and the laser are also included in the schematic model.

The electrical model of the laser is a standard diode model with its parameters matched to the voltage/current characteristics of the ULM850-10-TT-A0112B laser diode. The current through the diode is available at branch b11 and is used as an input (injection current) for the equivalent circuit of the laser carrier and photon dynamics. Since the APLAC software can be used to model a variety of physical systems by using circuit analogs to represent mechanical, electrical, and optical systems, it was possible to use differential equations to describe the circuit behavior that is analogous with the laser rate equations.

The output voltage of the equivalent circuit at Output_1 is proportional to the emitted light power of the laser diode. The voltage at Output_2 represents the number of free charge carriers in the active region of the laser diode. The parameters related to the laser's dynamics, such as the carrier and photon lifetimes, gain, and other characteristics, are in part based on typical values for published laser diodes and in part calculated from the published data for the ULM850-10-TT-A0112B device.

Based on the thermal modeling capabilities of the APLAC software, a thermal circuit was used to model the temperature dependence of the lasing threshold and the offset currents. The current entering node nJ is proportional to the thermal flow and is calculated from the total dissipated electrical power of the diode. Since some fraction of this power is emitted as light, a current corresponding to the emitted light power is subtracted from the current representing the dissipated power. A polynomial function fitted on the measured data is used to control the current source representing the change in threshold and offset currents by effectively adjusting the injection current with the device temperature. All of these functions are implemented within the LaserDynamicsSub subcircuit shown in Fig. 1.

In order to validate the accuracy of the models developed for the optical diode and driver circuit, a prototype of the optical transmitter was fabricated on low-temperature-cofired-ceramic (LTCC) substrate (Fig. 2). The substrate was constructed with two identical transmitters.

Figure 3 shows a simulated optical eye diagram for the transmitter with a 1.1 Gb/s pseudorandom-bit-sequence (PRBS) modulated signal. The flexible sweep capabilities of the APLAC software allows the results of this type of transient simulation to be presented in a familiar eye-diagram format.

For performing measurements on the LTCC prototype laser transmitter, a model DG2040 data generator from Sony/Tektronix (Beaverton, OR) was used to generate test signals at the 1.1-Gb/s bit rate and with the PRBS modulation. The optical output from the transmitter was coupled to the optical input port of a model HP83480 digital communications analyzer from Agilent Technologies (Palo Alto, CA). The results of those measurements are shown as the eye diagram of Fig. 4b.

As can be seen, the simulation portrays the actual measured characteristics of the optical transmitter quite closely. The only real deviation is the absence of an off-state bounce in the simulation. This is a consequence of charge-distribution-related effects that are not covered by the simple VCSEL model. Relaxation oscillation due to charge- and photon number interaction can be clearly seen in both the simulation and the measured results.

A second simulation on the laser transmitter was performed with a lower modulation level set beneath the lasing threshold in order to study the effect of charge buildup in the case of bad biasing. The simulation results are shown in Fig. 5. Operation below the lasing threshold causes varying delays in the startup of the laser's emission, evidenced as rising-edge jitter. During the delay, there is an excessive charge buildup in the active region of the laser, which causes the overshoot at the beginning of the emission. Figure 6 shows the measured results for this case in the form of the eye diagram.

In short, the simple laser diode model was able to effectively model an actual optical transmitter circuit. By including thermal effects, the software was able to include the laser's physical effects (i.e., laser output power dependence on temperature and power dissipation). In spite of the simplicity of the model, the simulated results were in good agreement with actual measurements on the LTCC prototype of the laser transmitter. Good agreement between the simulation and measurements was also found for situations resulting from inefficient biasing of the laser diode.

REFERENCE

1. P. Mena et al., "A Simple Rate-Equation Based Thermal VCSEL Model," Journal of Lightwave Technology, Vol. 17, No. 5, May 1999