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BSEE - KB3UON
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July 1953 QST
Authors Cohen and Hessinger warn about the need to consider the capacitive loading effects of shielded and closely-space test leads when measuring other than direct current or very low audio or line frequencies. Lead capacitance is especially likely to affect measured values when the frequency is high and/or the source and load impedances are high. As was common in the day, capacitance units of μμfd (micro-micro farads = 10-6 x 10-6 = 10-12 F) are cited, which is equivalent to units of pF (10-12 F).
By George S. Cohen,* W8HTI, and Richard W. Hessinger*
Every audio enthusiast, amateur radio operator, and electronic technician finds it necessary at one time or another to make some sort of electrical measurement. Many of these measurements involve d.c. Bully for the man who has only this type of measurement to make. But there are those of us who are not quite so fortunate, for we must make many measurements on a.c. equipment. (This "a.c. equipment" means anything other than d.c., and so involves a.f. and r.f. as well as commercial power frequencies.)
All of these measurements require some type of connecting leads from the energy source to the measuring instrument. In the course of making many measurements it was found that a source of difficulty, in one instance, was in finding satisfactory leads for the particular job at hand. Although the measurements of current and voltage present similar, if not identical problems, we will consider voltage only.
Let us consider the generator of Fig. 1 with an internal impedance Zi. This source is feeding a load with an impedance equal to ZL. This circuit is very general and, as an aid in visualizing the problem, the generator may be thought of as a voltage-amplifier stage in an audio amplifier where Zi is the plate resistance of the tube and ZL is the impedance the tube is working into.
If we assume that the generator is a pentode voltage amplifier and that Zi is, therefore, of the order of 0.5 megohm and that ZL is in the vicinity of 0.3 megohm, we will have a specific value of voltage, V, across the load.
If Zs is all capacitive reactance, as in this case, it will combine with a resistive ZL of 0.3 megohm to give a resultant 0.21 megohm and not the 0.15 megohm shown in Fig. 4.
Now, as is often required, let us measure the voltage across the load impedance ZL. This circuit is-shown in Fig. 2. M is the meter or measuring instrument and ZS is the combined impedance of the instrument and its attached leads.
The voltage V that is measured in Fig. 2 will be approximately equal to V of Fig. 1 only if the impedance ZS is ten or more times greater than ZL. This happens because the shunting effect of the impedance, ZS, combines in parallel with ZL to give a lower resultant value.
As an example, let us suppose that ZS is equal to ZL - 0.3 megohm in this case. The parallel combination of ZS and ZL would then be equal to 0.15 megohm. Fig. 3 shows that under the original conditions V would be 0.375 times the generated voltage, EG. With the effect of ZS the voltage across the combination would drop to 0.23 times EG, as in Fig. 4. The difference in voltage is made up by additional drop across the plate resistance of the tube.
Further, if this amplifier were operating at 2 kc. (a reasonable frequency within the range of most audio amplifiers) then the shunt capacity necessary to give ZS a value of 0.3 megohm would be 265 μμfd.1
A value of 265 μμfd. may seem very large and unlikely to be found in an ordinary pair of test leads. Recently, in testing a circuit, we found that our calculations and actual results didn't agree very closely and that started the usual search.
The culprit was soon found. A shielded multi-conductor cable exhibited a capacity of 225 μμfd. from leads to shield and 128 μμfd. between leads. After this discovery, many leads in the laboratory were measured. One of these was a 4 1/2-foot shielded test lead supplied with an oscilloscope made by a well-known manufacturer. The lead measured 220 μμfd. between shield and the center conductor. A compilation of the capacities measured between other types of leads is recorded in Table I. An examination of Table I shows that the experimenter must use good judgment in choosing an instrument lead for voltage measurement.
There is a second consideration in choosing a lead and that is noise pick-up of the cable. But we will not enlarge on this subject here.
There are, obviously, many more types of leads than are listed in Table 1. The manufacturers of these usually list the capacity per foot of each of the different types and other characteristics that should be considered in using these cables.
We can do no more than point out one of the pitfalls and hope that it has, or will at some later date, save you from excessive blood pressure and loss of a few precious hairs.
* Commonwealth Engineering Co. of Ohio, 1771 Springfield St., Dayton, Ohio.
Posted May 9, 2016