Estimating the Pulse Performance of Wirewound Power Resistors

Inhalt:
Concerning wirewound resistors a method to estimate the electrical pulse performance based on energy input, not only for adiabatic boundary conditions, but also for non-adiabatic boundary conditions is presented. This involves solving the governing partial differential equation numerically. The numerical results can be extrapolated to any set of model parameters incl. customer specifications. This procedure is helpful in estimating the electrical pulse load capability of wirewound resistors for various specifications without the need of doing numerical simulations each time. The limit curve found by this combination of theoretical and numerical methods is in very good agreement with measured data and figures given in datasheets. We present a method, based on numerical solutions of the time dependent one-dimensional thermal diffusion equation with internal heating, derived from simplified resistor models, which allows for estimating the maximum permissible pulse load that can be put on the resistor. This method works quite well from very short pulses, almost adiabatic boundary conditions from the viewpoint of the wire, to almost continuous load. A comparison with results from Newton cooling law shows that that simpler approach typically underestimates the pulse handling capability of resistors. Mathematically we describe our resistor model by the time dependent patial differential equation (PDE) describing thermal diffusion with internal heating. We consider the thermal model to be one dimensional (1D) for the sake of simplicity. The PDE is solved with a finite element software in 1D polar coordinates. A 1st simulation calculates the model temperature for a given heat pulse in the wire. A 2nd simulation calculates the potential wire temperature of a thermally insulated wire. Then we scale the model temperature rise for non-adiabatic boundary conditions by the potential temperature rise for adiabatic boundary conditions and label the ratio F. Because of the applied scaling, we do not have to care about the absolute temperature rise. Instead we calculate a relative scaling factor F. This procedure can be repeated for different wire diameters and pulse durations in order to obtain an F-map. That F-map allows calculating the maximum permissible pulse energy for long pulses based on the maximum permissible pulse energy for adiabatic boundary conditions, which can be calculated from material properties. Because the basic physical mechanism simulated is thermal diffusion, the results for different pulse durations follow a p t-rule and hence can be scaled to each other. Therefore, only few simulations are needed to obtain such an F-map.