An improved transmission line laser model for multimode laser diodes incorporating thermal effects

Madhan, M. Ganesh; Neelakandan, R.

doi:10.1007/s11082-008-9240-7

Cited by 9 publications

(1 citation statement)

References 18 publications

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“…Such a derivation leads to the telegraph equation with constant coefficients, which can be readily solved in the time domain using well-known analytical or numerical techniques. Maisano [15] derives an equivalent circuit with frequency-independent parameters, with two parameters more than the one derived in this paper, which is claimed to be quite accurate over a wide range of frequencies. However, Maisano's derivation, as usual, begins from the Navier-Stokes equation and shifts immediately into the frequency domain by taking Laplace transforms.…”

Section: Introductionmentioning

confidence: 96%

A didactically novel derivation of the telegraph equation to describe sound propagation in rigid tubes

Till¹,

Driessen²

2013

Eur. J. Phys.

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Starting from first principles, we derive the telegraph equation to describe the propagation of sound waves in rigid tubes by using a simple approach that yields a lossy transmission line model with frequency-independent parameters. The approach is novel in the sense that it has not been found in the literature or textbooks. To derive the lossy acoustic telegraph equation from the lossless wave equation, we need only to relax the assumption that the dynamical variables are constant over the entire cross-sectional area of the tube. In this paper, we do this by introducing a relatively narrow boundary layer at the wall of the tube, over which the dynamical variables decrease linearly from the constant value to zero. This allows us to make very simple corrections to the lossless case, and to express them in terms of two parameters, namely the viscous diffusion time constant and the thermal diffusion time constant. The coefficients of the resulting telegraph equation are frequency-independent. A comparison with the telegraph equation for the electrical transmission line establishes precise relationships between the electrical circuit elements and the physical properties of the fluid. These relationships are thus proven a posteriori rather than asserted a priori. In this way, we arrive at an instructive and useful derivation of the acoustic telegraph equation, which takes viscous damping and thermal dissipation into account, and is accessible to students at the undergraduate level. This derivation does not resort to the combined heavy machinery of fluid dynamics and thermodynamics, does not assume that the waveforms are sinusoidal, and does not assume any particular cross-sectional shape of the tube. Surprisingly, we have been unable to find a comparable treatment in the standard introductory physics and acoustics texts, or in the literature.

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Section: Introductionmentioning

confidence: 96%