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input impedance close to 50⍀ at both frequencies (1.57 and 5.25 GHz). The LC resonant-load at the output terminal was added to boost the gain. In addition, the capacitance divider was added in order to achieve output matching. Therefore, the frequency response could be shaped to achieve the required gain and matching at the dual bands of interest. MEASURED RESULTS AND DISCUSSIONAn InGaP/GaAs HBT IC process with f T ϭ 40 GHz was used to fabricate the LNA. The die photograph of the finished monolithic 1.57/5.25-GHz dual-band LNA is shown in Figure 1 (b). This circuit occupies an area of 700 ϫ 700 m, excluding the test pads. This LNA drains 3-mA current at supply voltage 5 V, that is, it only consumes 15-mW power.The noise and scattering parameters were measured on wafer using an automated NP5 measurement system from ATN Microwave Inc. This LNA achieved transducer gains (S 21 ) of 25.3 dB and 14.3 dB, and input return losses (S 11 ) of 6.8 dB and 11.5 dB at the 1.57-and 5.25-GHz frequency bands, respectively, as shown in Figure 2(a). As can be seen in Figure 2(b), the measured reverse isolation (S 12 ) for the LNA was quite good, that is, Ϫ30.8 dB and Ϫ32.2 dB, at the 1.57-and 5.25-GHz frequency bands, respectively, and with more than 30 dB of isolation for frequencies lower than 8 GHz. This is due to the use of the cascode configuration. The measured noise figure (NF) was 2.55 and 4.5 dB at the 1.57-and 5.25-GHz frequency bands, respectively, as shown in Figure 3.The performances of our 1.57/5.25-GHz concurrent dual-band InGaP/GaAs LNA (NF of 4.5 dB, and S 21 of 14.3 dB) at 5.25 GHz are comparable with those of the 2.45/5.25-GHz concurrent dualband CMOS LNA (NF of 4.5 dB, and S 21 of 15.5 dB) with a bonding wire as the gate inductor using 0.35-m CMOS technology [1]. This means the performance of our InGaP/GaAs dualband LNA can be better than that of its CMOS version without the use of bonding wire. CONCLUSIONThe first monolithic concurrent 1.57/5.25-GHz dual-band LNA using InGaP/GaAs HBT technology has been reported. This LNA only consumes 15-mW power. S 21 of 25.3 and 14.3 dB, S 11 of 6.8 and 11.5 dB, S 12 of Ϫ30.8 and Ϫ32.2 dB, and NF of 2.55 and 4.5 dB are achieved at the 1.57/5.25-GHz bands, respectively. The performance at 5.25 GHz is comparable with the 2.45/5.25-GHz concurrent dual-band CMOS LNA with a bonding wire as the gate inductor using 0.35-m CMOS technology [1], which means the performance of our InGaP/GaAs dual-band LNA can be better than that of its CMOS version without the use of bonding wire. ACKNOWLEDGMENTSThis work was supported by the National Science Council of the R.O.C. under contract no. NSC91-2219-E-002-021. The authors are also grateful for measurement support from the High-Frequency Measurement Center of the NDL.

Abstract.The wave equation describing the vector propagation of a femtosecond laser pulse of a few optical cycles in a uniaxial crystal is solved numerically by the method of unidirectional waves. Propagation of the pulse in the direction normal to the optical axis is studied, taking into account both second-and third-order nonlinearities of the crystal. Conversion efficiency as a function of crystal length, pump intensity and pulse duration is studied. As an example, the propagation of femtosecond laser pulse of ¼ 10 fs duration at l ¼ 810 nm in a LiNbO 3 crystal 12 mm thick is studied numerically. IntroductionRecent progress in the generation of extremely short optical pulses has stimulated the development of propagation theory of optical pulses of a few cycles in crystals. It is known that during the propagation of such extremely short pulses in a nonlinear crystal the radiation generation takes place both at difference and at sum frequencies. At the same time the generation of difference frequencies in a medium with second-order nonlinearity is usually used for the generation of a coherent short radiation pulse in the infrared spectrum range [1].It is clear that the approximation of slowly varying amplitude is not applicable to the description of such processes [2]. Therefore, for the description of the propagation process of a femtosecond laser pulse of a few optical cycles in an anisotropic optical crystal it is necessary to use either numerical methods or some special analytical methods.In particular, in [3] the results of numerical simulation of propagation process of a femtosecond laser pulse with 10 fs duration in a nonlinear potassium dihydrogen phosphate crystal with 100 mm thickness obtained by the numerical integration of the Maxwell vector equation are given. There a comparison of those results with similar data obtained by the slowly varying amplitude (SVA) method is given, and it is shown that the description of the second-harmonic generation process by such short pulses by the SVA method is not correct.So, the correct analytic description of the propagation of femtosecond laser pulse of a few optical cycles in an anisotropic nonlinear optical crystal is a very topical problem.In [4] the analytic description of the propagation of a femtosecond laser pulse of a few optical cycles in a medium with second-order nonlinearity was given on the basis of the method of unidirectional waves (MUW). It has been shown there

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Tel: (3 74 I ) 442 158, Fax: (3 74 I ) 442 I55, e-mail: David. Hovhannisyan@epygilab. am ABSTRACTIn the presented paper we show the new approach in analysis of femtosecond soliton pulse propagation withduration of GlOOfs in nonlinear dispersive medium. Investigations are carried out by using of method of, unidirectional waves (MUW) and solving nonlinear wave equation that is different from nonlinear Schrodinger equation. Newly obtained results are presented.