RF Cascade Workbook

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1996 -
2016

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Kirt
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BSEE - KB3UON

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October 1958 Radio-Electronics Article

## October 1958 Radio-Electronics[Table of Contents]These articles are scanned and OCRed from old editions of the Radio & Television News magazine. Here is a list of the Radio-Electronics articles I have already posted. All copyrights are hereby acknowledged. |

If you have ever placed a fixed resistor in parallel with a potentiometer to reduce the total resistance, then you
are familiar with how you also convert a linear relationship of the wiper movement with resistance to one that is
nonlinear. That is because the equation changes from R_{total} = xR_{potentiometer}
(where x is the potentiometer position) to R_{total} = (xR_{potentiometer} • R_{parallel}) / (xR_{potentiometer} +
R_{parallel}). The graph of it looks like one of the curves in this chart. Since the total parallel resistance
is always smaller than the lowest value of the two resistances, the greater the ratio of the two is, the more dominant
the smaller resistance value becomes. That means as the potentiometer wiper approaches the minimum resistance end
of its travel, the parallel resistor attached across it has virtually no effect.

Since parallel-connected inductors and series-connected capacitors scale in the same manner as parallel-connected resistors, this chart is useful for those circuits as well. Series-connected resistors and inductors, and parallel-connected capacitors are simply the sums of their individual values. Consequently, if you connect a fixed resistor in series with a potentiometer, the total resistance at any position of the potentiometer wiper will be the linear sum of the fixed resistor and the potentiometer resistance. Got that?

* Theoretically, x is a value from 0 to 1 that represents the relative position of the potentiometer wiper contact.

By Rudolph Wellsand

To
use the chart locate R_{1} along the top scale and R_{2} on the left-hand scale. Find the point
where they meet on a curve. Trace the curve to the R_{T} scale and read the answer. For total values of
parallel inductance and series capacitance use the scales at the bottom and right hand edges. To extend the ranges
of the scales, either multiply or divide each value in every scale by 1,000.

Posted January 4, 2015