MathCAD functions perform log interpolation
Edited by Bill Travis
James Bach, Delphi Delco Electronics Systems, Kokomo, IN -- EDN, October 30, 2003
MathCAD provides a number of interpolation and curve-fitting functions, so that, given a set of X-Y data points, you can estimate the Y value for any given X coordinate. Unfortunately, these functions work poorly with data that is to be displayed in a nonlinear (logarithmic) manner. Examples of these functions are:
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Log-Lin: phase/magnitude-versus-frequency (Bode plots);
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Log-Log: impedance-versus-frequency (reactance plots); and
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Lin-Log: impedance-versus-temperature (thermistor data).
Using the built-in "linterp" function, MathCAD estimates and plots the data (Figure 1). As you can see, at X coordinates between the original data points, the "linterp" function creates a "bulging" effect. The following trio of simple interpolation functions allows the correct interpolation of nonlinear data on its appropriate scale. These routines function by prewarping the incoming-data matrices before feeding them into the existing "linterp" function; for logarithmic Y-axis functions, you raise 10 to the result of the "linterp" function to restore the values to the proper decade:
Using the newly created LogLogInterp function, the straight-line data is displayed (Figure 2).
