Small-signal Frequency Response Research Articles

High-frequency modulation characteristics of hybriddielectric/AlGaAs mirrorsinglemode VCSELs

The authors have measured the small-signal frequency response characteristics of a GaAs VCSEL (λ = 835 nm) implementing a novel MOVPE-grown AlOaAs/AlAs-TiO2/SiO2 hybrid distributed Bragg reflector used to control emission to a single mode. A small-signal 3 dB bandwidth of 12.1 GHz was recorded at a bias level of only 2.8 mA. A very high modulation efficiency of 9.5 GHz/√(mA) was measured which is the highest reported for VCSELs or any semiconductor laser of any variety. In addition, large signal measurements were conducted which showed open eye patterns with pre-bias currents of ~0 mA demonstrating the possibility of direct logic-level drive.

Dynamic properties of partly gain-coupled 1.55-μm DFB lasers

The lasing characteristics and dynamic properties of partly gain-coupled 1.55-/spl mu/m DFB lasers with a gain corrugation in the strained-layer MQW active region are presented. Narrow spectral linewidth, which is associated with the low linewidth enhancement factor, was experimentally measured. By analyzing data from RIN measurements, the damping rate, the damping factor, the intrinsic bandwidth and the effective differential gain were obtained. From the small-signal frequency response, a measured 3 dB bandwidth of 22 GHz at 10 mW output power was achieved. The high bandwidth is believed to be related to the high differential gain, resulting from the combination of longitudinal gain and index-coupling mechanisms and the reduction of the carrier transport time, which is due to an efficient lateral carrier injection along the longitudinal interface. Experimental results show that under 10 Gbit/s pseudorandom NRZ modulation, the devices have small wavelength chirp and clear eye openings making them suitable for long haul and high bit-rate applications. >

Analysis of Immittance Spectroscopy Data: Model Comparisons, Universality?, and Estimation of Distributions of Activation Energies

ABSTRACTImmittance spectroscopy [IS] involves the measurement of the small-signal frequency response of dielectrics, semiconductors, electrolytes, biological cells, and polycrystalline, amorphous, and single-crystal electrically conducting materials. Analysis of such data to provide insight into the detailed, microscopic, physicochemical processes present in the full electrode and bulk material system is a crucial part of IS. Background information on IS and a discussion of its strengths and weaknesses are presented. The use of weighted, complex, nonlinear-least-squares for direct data fitting and for the solution of the ill-posed inversion problem of estimating continuous distributions of activation energies for important response models and for experimental data is illustrated. Replacements for the widely used, but incorrect, complexelectric- modulus data-analysis relations proposed long ago by C. T. Moynihan and associates for disordered ionic conductors, are presented and discussed. Recent proposals for various kinds of universal response behavior are examined and found to be unjustified. The present analysis methods are illustrated by applying them to 24°C data on a lithium aluminosilicate glass and to data over a wide temperature range on single-crystal CaTiO3:30%Al3+

Performance of 1.3 µm ridge waveguide distributed feedback lasers fabricated by one-step metalorganic chemical vapour deposition

Ridge waveguide distributed feedback (DFB) lasers emitting at 1.3 µm wavelength have been fabricated by one-step metal-organic chemical deposition over a first order grating in an InP substrate. Threshold currents as low as 13-18 mA were obtained for devices with as-cleaved facets and 15-20 mA for devices with one AR-coated facet. A slope efficiency as high as 0.32 mW/mA, single mode performance up to 20 mW, and a side mode suppression ratio of 45 dB have been achieved. For lasers with a coupling*length product, kappa L, of 2.5-3.5 and the single longitudinal-mode detuned 10-20 nm to the shorter wavelength side of the material gain peak, a high resonance frequency and a small wavelength chirp have been observed. Small signal frequency responses were measured with a -3 dB bandwidth of 11 GHz at 12 mW output power. The devices showed good open eye patterns under direct modulation up to 10 Gbit/s.

Beyond 20 GHz bandwidth of partly gain-coupled 1.55 μm strained multiquantum well DFB lasers

The small signal frequency responses of partly gain-coupled 1.55 mu m strained MQW DFB lasers were measured with a record -3 dB bandwidth of 22 GHz at 10 mW optical output power. Experimental results show that under 10 Gbit/s pseudorandom NRZ modulation, the devices have small wavelength chirps and clear eye openings making them suitable as light sources for direct modulation in 10 Gbit/s and higher bit rate optical communication systems.

A small-signal frequency response model with electron and hole transports in multiquantum-well lasers

The authors propose a small-signal frequency response model for high-speed multi-quantum-well (MQW) lasers. Electrons and holes are treated independently to deal with the high-frequency range faster than the carrier thermionic emission from the well, where the ambipolar approximation is unsuitable. The electron current modulates the stimulated emission even in the high-frequency range beyond the hole transport limit. Therefore, the present model predicts a larger response than the conventional ambipolar model in the high-frequency range, and it gives a better explanation of the experimental results for high-speed MQW lasers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The response of systems with exponential distributions of activation energies for two classes of material temperature behavior

Methods for calculating the small-signal ac frequency and temperature responses of thermally activated materials arising from the presence of a distribution of transition rates are discussed. The specific case of a double-exponential distribution of activation energies (DEDAE), of great importance as a data-analysis model, is discussed in detail for distributed dielectric and intrinsically conducting materials, and important differences in the proper analyses of these systems are particularly emphasized. For both dielectric and conducting distributed systems, two different and important types of temperature response are described and related to earlier work. Model calculations are presented to illustrate frequency and temperature response possibilities for such thermally activated, distributed systems. Various errors in earlier work are corrected, particularly the near-universal identification of theoretical slope parameters appearing in the analysis of exponentially distributed systems with actual measured slopes and power-law exponents. The quite different experimental temperature dependences of the power-law exponents of many dielectric and conductive materials agree qualitatively and often quantitatively with the predictions of the DEDAE response model. Finally, the behavior is briefly discussed of systems which can exhibit wide-range dispersive results simultaneously in both their conductive and dielectric responses.

Cavity length dependence of K -limited bandwidth in 1.6 μm compressive-strained quantum well lasers

The intrinsic small signal frequency response of 1.6 μm compressive-strained quantum well lasers is measured at various cavity lengths. The highest 3 dB bandwidth reached is approximately 18 GHz. Cavity length dependence on the K factor is investigated. It was found that the optimal condition for obtaining the highest possible K-limited bandwidth is the same as that for obtaining the highest relaxation oscillation frequency for a given optical power

Gain modulation response of erbium-doped fiber amplifiers

The small-signal low frequency response characteristics of erbium-doped fiber amplifiers (EDFAs) are examined theoretically and experimentally. Modulating the pump laser results in a low-pass transfer of modulation from the pump to signals amplified in the EDFA. A signal modulated at low frequencies and amplified by an EDFA experiences a transfer function that is similar to that of a lead compensator, which has one zero followed in frequency by one pole. Experimental results verify both the magnitude and phase response of the theoretical transfer functions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Computer Assisted Learning in An Electronics Course

Computer assisted learning in an electronics course The CAD software package Electronic Workbench has been used for computer assisted learning for analogue electronics in the second year of a degree course. After a description of the package, the approach used to generate text files to describe the subject matter for transistor biasing, small signal analysis and frequency response is described. The student response is considered, as are the problems encountered in using the package for CAL.

Normal-mode small-signal analysis of traveling-wave directional couplers

The small-signal frequency responses of the 1*2 and 2*2 directional coupler traveling-wave modulators are analyzed in closed forms including the effect of both the optical/microwave velocity mismatch and microwave loss. When the microwave loss is negligible, the small-signal bandwidths of 1*2 and 2*2 directional coupler traveling-wave modulators are 20 and 28%, respectively, larger than that of an interferometric modulator with the same electrode length. However, when the microwave loss is large, the 1*2 coupler has a larger bandwidth. >

The phototransistor revisited: all-bipolar monolithic photoreceiver at 2 Gb/s with high sensitivity

The authors revisit the three-terminal phototransistor and demonstrate the application of the HPT (heterojunction phototransistor) at 2 Gb/s in an all-bipolar monolithic photoreceiver. They also show a performance comparable to the best p-i-n photoreceiver. The phototransistors were fabricated from epitaxial layers grown by metal-organic molecular beam epitaxy on a Fe-doped semi-insulating InP substrate. The phototransistor had a small-signal electrical current gain between 150 and 200. The quantum efficiency of the base-collector photodiode was 40%. Microwave on-wafer measurements yielded a unity current gain cutoff frequency of 30 GHz and a maximum oscillation frequency of 20 GHz at a collector current of 5.0 mA. The small-signal frequency response of the packaged monolithic photoreceiver indicated a 3-dB bandwidth of 1.1 GHz, at a wavelength of 1.53 mu m, with no peaking in the response.

High speed and low loss, bulk electroabsorption waveguide modulators at 1.3 mu m

Bulk InGaAsP electroabsorption waveguide modulators based on a novel multiquaternary layer design which have a tapered-fiber-modulator-tapered-fiber insertion loss as low as 4.5 dB and a small-signal frequency response in excess of 11 GHz at lambda =1.33 mu m are described. This design allows one to decouple somewhat the electrical and optical properties of the device. By choosing the appropriate quaternary composition of the core and the cladding layers, the coupling to a tapered fiber can be optimized, while the position and thickness of the p-i-n junction can be varied independently to meet operating voltage and speed requirements without affecting the waveguide mode. A -3 dB small-signal modulation bandwidth in excess of 11 GHz was measured. >

Demonstration of enhanced performance of an InP/InGaAs heterojunction phototransistor with a base terminal

The optical gain and the small-signal frequency response of an InP/InGaAs heterojunction phototransistor (HPT) with a base terminal are investigated in detail for the first time. When operated under an optimally chosen external base current, the optical gain is enhanced more than five times over that of the same device operated as a two-terminal device, over a 17-dB range of input optical power. The small-signal 3-dB bandwidth of the three-terminal device is enhanced 15 times over that of the two-terminal device over the same range of input optical power. For a pseudorandom NRZ bit stream at 100 Mb/s, a clear eye opening is observed at an incident optical power of -33 dBm (500 nW).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An efficient small signal frequency analysis method of nonlinear circuits with two frequency excitations

One of the excitations, 'carrier', is a large signal and an arbitrary T-periodic function of time. The other excitation, 'signal', is considered as a small perturbation to the periodic steady-state response driven by the carrier. To find a small signal frequency response for the 'signal', the method uses variational equations around the periodic steady-state response. These linearized time-varying differential equations are solved in the frequency domain using a time discretization method. The method can be used to compute the small signal frequency responses of nonideal switched capacitor filters, mixers, and other nonlinear circuits, if the circuit has a stable periodic response. The formulation of the problem, computational complexity of the method, error analysis, sensitivity analysis, implementation of the method, and some applications are covered. >

Frequency response of bipolar junction transistors after electron-beam irradiations

The small-signal frequency response of silicon bipolar junction transistors was measured after the devices were irradiated with electrons below the displacement threshold. The measurements indicated that the high-frequency response of transistors is unchanged by electron irradiation, even though the low-frequency gain is degraded. Whereas process variations intended to change either the gain or cutoff frequency of transistors inevitably affect both, the electron-beam irradiation changes only the gain, giving a clear demonstration of the fact that the cutoff frequency is determined by the physical base transit time. As a practical consequence, the result implies that electron-beam irradiation has relatively little effect on circuit performance. >

Some small-signal relaxation response models and their limiting responses

This paper is concerned with the small-signal time and frequency response of anomalous dispersion and distributed circuit elements in either conductive or dielectric systems. In the course of responding to recently published comments and criticisms of Dissado and Hill, a detailed discussion is presented of high and low frequency limiting response possibilities, with a special consideration of such response for a single broad dispersion region. For such a region the Dissado-Hill criticisms are shown to be either incorrect, inappropriate or irrelevant. The usefulness of distribution of relaxation and distribution of activation energy approaches is demonstrated and the response of a general exponential-distribution-of-activation-energies model is compared with that of a relaxation response function which was derived by Dissado and Hill in two different ways, with the two approaches based on different physical assumptions. It is concluded that the Dissado-Hill response function does not lead to the necessary low and high frequency limiting response for a single broad dispersion region, is essentially limited to dielectric materials and cannot describe intrinsically conductive ones which can pass DC, and is severely limited in its temperature dependence possibilities. By comparison, these limitations and restrictions do not apply to the distribution of activation energy model, one which has been shown capable of fitting a great variety of conductive and dielectric system experimental data for thermally activated situations.

Planar-embedded InGaAsP/InP heterostructure laser with a semi-insulating InP current-blocking layer grown by metalorganic chemical vapor deposition

We used metalorganic chemical vapor deposition to fabricate a planar-embedded InGaAsP/InP heterostructure laser with a semi-insulating InP current-blocking layer. The laser exhibits cw operation with a low, 20 mA threshold current and a high external differential quantum efficiency of 40% at room temperature. Measurements have also shown a small-signal frequency response of 10 GHz due to an extremely small parasitic capacitance of 3.5 pF.

A flexible procedure for analyzing impedance spectroscopy results: Description and illustrations

General considerations in nonlinear least squares fitting of small-signal ac frequency response data (conductive or dielectric systems) are first discussed. A very general and flexible complex nonlinear least squares fitting (CNLS) program (LOMFP) is described which runs on microcomputers of the PC and AT type. Advantages and disadvantages of LOMFP are discussed and compared to those of a recent CNLS program developed by Boukamp. LOMFP incorporates many thousands of equivalent circuits fitting possibilities and ten different distributed circuit elements which can be used in these circuits. Its fitting is both speedy and accurate, and it provides considerable insurance against confusing local minima fits with true least squares fits. It is optimized for fitting real, imaginary, or complex data of either partly conducting or purely dielectric character, and it incorporates great flexibility in handling and fitting data in different forms (different immittance levels and rectangular or polar representation). Seven different data weighting choices are provided. Exact synthetic data were generated from a typical Impedance Spectroscopy equivalent circuit, and the effects on CNLS fitting were investigated of rounding the exact data to 4, 3, and 2 decimal places. We present the results of an extensive study of the effects of transforming exact data to different immittance levels and representations and then rounding to two places or of transforming rounded 2-place data directly. We conclude that real data should not be transformed from its original measured form before carrying out CNLS fitting. Finally, the effects were investigated of various kinds of weightings on CNLS fitting of 2-place data, leading to the conclusion that in spite of its advocacy and use by Zoltowski and Boukamp, modulus weighting generally yields misleading and appreciably worse CNLS fitting results than does proportional weighting. The LOMFP program (source and executable files) is available from the first author.

Impedance spectroscopy and its use in analyzing the steady-state AC response of solid and liquid electrolytes

Impedance spectroscopy is defined and some of its applications illustrated for both liquid and solid electrolyte situations. Particular emphasis is placed on complex least squares fitting of small-signal frequency response data at various immittance levels. Most such response data must be fit to an equivalent electrical circuit since a detailed microscopic model of the response is usually lacking. It is found for most ionic response data, as well as that from purely dielectric systems, that one usually must include in the equivalent circuit one or more distributed circuit elements in addition to the usual ideal elements, such as resistors and capacitors. Important distributed circuit elements useful in equivalent circuits are described. A number of actual equivalent circuits used in the past for both liquid and solid electrolytes are presented and compared. Equivalent circuits following from detailed continuum models of the electrical response of blocking and partly conducting systems are compared, and it is shown that some of the same circuits may be used even in the presence of dc bias which usually makes the charge distribution in the system very inhomogeneous. Because frequency response data have often been inadequately analyzed, the author's general and powerful complex nonlinear least squares fitting program is now available for use by others.