τP = 2.08 ps, τN = 2.5 ns, g = 23. 10-12 m3 /s, n0 = 1024 m-3 , ε = 1.2 10-23 m3 , β = 10-4 , Γ= 0.05, V = 1.2 10-16 m3 , η = 0.24 W/V
N .P 2 2 2 N TOT i2 + β. TOT O N =q . F N (f) = 2.q . τN τN
2
giving
the
transmission
Vopt 2 = A.H(f).E(f).Vopt1
I
V
VN
2
Figure 2. Noise sources and parasitic elements The following values give an example of the different elements for a InGaAsP BRS laser working at 1.55 µm.
2 2 2 v2 N = q . FP (f) = 2.q .
Fibre model Figure 3 shows the diagram of the fibre model.
β.NTOT .PO τN
VO P T 1
VO P T 2
Where NTOT is the total number of electrons in the active layer and PO is the total number of photons. Figure 2 shows the introduction of these noise sources and parasitic elements. Figure 3. Fibre model The expressions coefficients are: IN
Where: A is the attenuation = 10α(λ)/10 Η is the chromatic dispersion term E is the vanishing coefficient in case of two image wavelengths D is the chromatic dispersion coefficient L is the fibre length f is the modulation frequency
Abstract First of all, this paper presents a tool being able to simulate optical links working in microwaves. Then, at the level of the optical receiver, the PIN diode is replaced by a phototransistor. As this component is a threeport, the value of microwave impedance which should be put on the base and on the collector to maximise the gain has to be studied. Finally, the Spurious Free Dynamic Range of a link including a phototransistor is presented. Introduction For numerical communication systems in which a part of the link is done with an optical carrier and another part is done with a microwave carrier, many different configurations are feasible [3]. For some of them, the modulated microwave signal is carried optically in the fibre, for others, the microwave carrier is generated by a local oscillator following the optical detection. At the level of the optical receiver, it is possible also to use a phototransistor instead of the usual PIN photodiode. This component is a three-port and in this case, the type of microwave load that should be presented to the base and the collector to maximise the gain is studied. To realise the simulation of the link, a good solution is to use a non linear frequency domain simulator (like ADS) in which the various components are introduced w ith their different models. These models should include a non linear response and noise sources. The models of lasers, optical fibre and PIN photodiodes with non-linearities and noise sources have already been discussed. They only have to be adapted to the circuit simulator (ADS). A model was already presented for the phototransistor . But it is a three-port and the maximum current and power gains must be studied as a function of the impedances presented on base and collector ports [1]. New results concerning the current gains are presented. Finally, the simulation of the Spurious Free Dynamic Range of an optical link including a phototransistor is shown. An optical link with a PIN photodiode The different models used for the components of the link are recalled. Laser model The basic equations of a laser [2] are given on figure 1. This figure also shows how these equations can be solved in circuit simulator with an equivalent circuit representation. In these relations, S: photon density in the mode n: electron density in the active layer n0 : electron density at transparency Γ: confinement factor in the active layer β: proportion of spontaneously emitted photons in the particular mode τp : photons life time τn : electrons life time ε : gain compression coefficient q: electron charge d: height of active layer V: volume of the active layer g: differential gain of the active layer Because of numerical stability, S is normalised with a coefficient SN , giving a new variable:
S' =
S Γ SN V Eg τP
Then the optical power is given by:
POPT = η
Squantum efficiency of the laser Eg is the band gap energy
I = q.V.
n dn + q.V. + q.V.g.(n − no).(1 − ε.S).S τN dt
Simulation of optical links including a phototransistor in microwaves L. Paszkiewicz, J.-L. Polleux, A.-L. Germond, C. Rumelhard, J. Salset Communication Systems Laboratory CNAM-ESIEE-UMLV Marne la Vallée, France rumelhard@cnam.fr
λ 2 .D( λ).L.f 2 = A.exp( − j.π.DISP.f 2 ).cos2 .Vopt 1 4.π.c