I've
always had a problem with book and article titles containing the word
'Modern' because it is utterly ambiguous. What was modern in 1932 is
usually obsolete merely a decade later, especially in high technology
(not so much in buggy whip state-of-the-art methods, though). Sometimes,
as with this article on insulation breakdown voltages, bringing the
information up to date requires only the substitution of a few words.
For instance, replace 'condenser' with 'capacitor' and units of 'mfd'
with 'μF' and 'mmfd' with 'pF,' then you'll be on your way to gaining
useful information. There is a nice nomograph for use in designing capacitors
for specific voltage handling and a table of dielectric puncturing voltages
as well.
Orion Instruments has a very extensive table of
dielectric constant values.
See all available
vintage Radio News
articles.
Modern Radio Practice in Using Graphs and Charts
By John M. Borst
Part Seven
Calculations in radio design
work usually can be reduced to formulas represented as charts which
permit the solution of mathematical problems without mental effort.
This series of articles presents a number of useful charts and explains
how others can be made
The capacity of a homemade condenser
is often more or less of a mystery. The amateur or experimenter who
does not possess a bridge or capacity standard must calculate the capacity.
Conversely, if a condenser of a given capacity is desired, only a calculation
will eliminate guesswork.
The standard formula has been transformed
into an alignment chart in Figure 1. The capacity of a condenser
can be found when the area of the plates, their number, distance and
the kind of dielectric are known.
The relation between centimeters
and inches or mils as well as the relation between square centimeters
and square inches, centimeters and microfarads is also shown in Figure
1. The "dielectric constant," also called "inductivity" or "specific
inductive capacity," is incorporated on the chart, which makes the consultation
of any sources superfluous.
The formula for the capacity of
a condenser consisting of parallel plates is
in micro-microfarads
where A = the area of one plate in square
centimeters
d = the distance between two plates in centimeters
n = the number of plates
K = the specific inductive capacity
Dielectric Strength
Figure 2 - Table
of break-down voltages for various types of sheet insulation. |
This expression refers to a condenser with alternate plates in parallel.
The formula does not take into consideration the spreading of the lines
of force at the edges of the plates. This effect is negligible so long
as the thickness of the dielectric is small compared to the area of
the plates.
In designing this chart the prime idea has been
to cover all possible cases which occur in practice. Therefore, the
capacity scale ranges from 1 micro-microfarad to over 10 micro-farads,
and the other quantities also cover a wide range.
Examples
Two metal plates have an area of 1 square inch and
are placed parallel, 1/4 inch apart, in air. What is the capacity?
Referring to the chart, draw a line from the 1-square-inch mark
on the "Area" scale to 1 on the K scale. The specific inductive capacity
of air is one (unity). This gives you an intersection on the turning
scale No. 1. From this newly found point draw another line through the
point 2 on the N scale and find a second point on the turning scale
No.2. The final line is drawn through the latter point and the 250-mils
mark on the d scale. This line intersects the capacity scale at 0.9 mmfd.
When exactly 1 mmfd. is required, the last line should
be turned around its point on the turning scale No. 2 until it intersects
the capacity scale at the 1 mmfd. mark and the intersection on
the d scale shows the required distance between the plates (225 mils).
The distance, however, can be left the same and the problem worked backwards,
in which case an area of 1.1 square inch is found necessary. These lines
have not been added in Figure 1 because they are so close together
that it might confuse the reader.
When using these charts. needless
to say, one should not actually draw the lines but use a transparent
ruler, a regular ruler or a tight thread.
The second example
shows how to work the problem backward. Suppose a paper condenser of
1 mfd. is wanted and the dielectric available has a thickness of 2 mils.
This is manilla paper, treated with paraffin. Its specific inductive
capacity is 3.65 and the break-down voltage may run as high as 250 volts
per mil. There is one more quantity which can be chosen and then the
other one is determined. This can be either the number of plates or
the size of the plates. The number of plates is the best to assume,
because this has to be a whole number. Let us assume there shall be
30 plates.
For the solution of this problem, start at the 1
mfd. mark on the capacity scale. A line from this point to the 2 mil.
mark on the d scale intersects the turning scale No. 2. Draw a line
through the latter point and through the point representing the number
of plates (30). Now note the intersection on the turning scale No. 1.
Finally draw the last line from the point representing the dielectric
constant. 3.65, through the point on the turning scale No.2, which shows
the necessary area of the plates as 84 square inches. As a check-up,
an actual calculation gave the area as 83.7 square inches.
The
experience of this second example teaches us that in certain cases the
last line would intersect the area scale beyond the limits of the paper.
This means that the area of the plates needed is going to be larger
than 100 square inches. If the area is to be smaller than 100 square
inches, either the number of plates have to be increased, the thickness
of the dielectric decreased or the material exchanged for one with a
greater inductivity. Then try again.
If one wishes the problem
solved for values of variables outside the range of the chart, then
some multiplying stunt has to be employed. For instance, suppose the
paper in the above example had been dry paper with a dielectric constant
of 1.8, then the last line does not intersect the area scale within
the limits of the page. Therefore, multiplying 1.8 with any convenient
number - say, 5 - the last line is drawn from 9 through the intersection
on the turning scale number one and the area scale is intersected at
34.
This result must now be multiplied by five in order to find
the correct answer, which is 170 square inches.
While determining
the specifications for a condenser it is important to be sure that the
dielectric will stand the applied voltage. Therefore a list of the break-down
voltages for different materials is found in Figure 2.
Capacity of a Condenser (aka Capacitor)
A Chart (Nomograph) That Works For You
Figure 1 - The size of condenser plates their distance apart, the
number of plates, kind of dielectric or capacity can be found from this
chart if the other four quantities are known. The five quantities are
on three straight lines as shown in the example above.
Temperature
influences the ability of a dielectric to withstand electric pressure.
When the condenser heats up under a continuous load, the breakdown voltage
is lowered. Therefore the tests of such condensers must be made over
a considerable time at working voltage or at a much higher voltage for
a short time.
Commercial paper condensers usually consist of
long strips of prepared paper, with tinfoil interleaved, which is then
rolled. In the case of rolling a condenser with an even number of plates,
the top plate and the bottom plate form an additional section of the
condenser so that in this case the rolling has the effect of adding
one more plate. The reader should see whether the dielectric for this
additional section has the same thickness as the other sections and
make allowances for any possible difference.
When the number
of plates is odd or when the paper is not rolled, the actual number
of plates is used for the calculation.
The accuracy of a calculation
by means of this chart will be sufficient only if the correct values
for the dielectric constant and the thickness of the dielectric have
been determined. This is sometimes difficult to accomplish, especially
with paper as a dielectric. If the reader guesses at the constant and
the actual separation of the plates, he must expect the result to be
off accordingly.
Posted
September 10, 2013