Saturday, September 18, 2010

5.1 V Zener Diode Conductance and Estimated Error in Voltages

We can refer to the ratio of small changes in current for small changes in voltage as a conductance*. It is the slope of the a line tangent to the V-I characteristics and in calculus is referred to as a derivative. The unit for conductance is the Siemens, S. If one plots this function for the 5.1 V Zener diode one sees that the conductance starts to increase rapidly at about 4.75 volts.

This conductance can be used to estimate the errors in the voltage measurements and compute corrections. The formula is ΔV = ΔI/G. The results for the steep part of the V-I characterists is shown below. This shows that even though the residuals are relatively large the corrections to the voltage needed to place the points on the curve are within about 1/2 the precision of the measurements and appear to be just round off errors.

The residuals for these points were more randomly distributed. The "corrections" for lower voltages were larger where the curve was flatter and where the fit appeared to deviate somewhat from the data. The conclusion is that relatively larger residuals are to be expected where the slope of the curve is relatively steep.

*edit: This is not the usual conductance which is defined in terms of Ohm's Law, G = I/V. My terminology is somewhat lax. A more appropriate expression might be "small signal conductance" or "differential conductance."

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