IEEE Power & Energy Magazine - January/February 2020 - 78

ω
A
θ
O

figure 2. A rotating phasor, the projection of which on the horizontal axis
is x(t) = A cos (~t+i).

Angular Velocity
ω Radian/s

sit
Tim ion a
et t

cos pt, can be represented by the
projection, on a fixed line, of a
vector of constant length A supposed to revolve uniformly so as
to complete one revolution in a
time T given by the relationship
pT = 2r. The angle between the
revolving vector and the fixed line
is pt at any instant t. In the first edition of Thomson and Tait's 'Natural Philosophy' (vol. 1, p. 38, § 58)
it is shown any two simple harmonic functions of one period can
be compounded to a single simple
harmonic function of the same period, and that the vector, representing the compounded function, is
obtained from those representing
the component functions by the ordinary process of vector addition.
This device has proved valuable for many purposes, but it has
proved especially useful for ac
problems. Its application to such
cases was first clearly pointed out
by T.H. Blakesley more than 12
years earlier.
Thus, we see that, before 1900, methods of combining vectors were known
and used in electrical engineering. The
Blakesley work referred to is most likely
his book Alternating Currents of Electricity, published in 1885.
The word vector was used by power
engineers by 1897, meaning the line

last passed through its middle position in the positive direction.
Although the word vector is not used
directly in association with this figure,
the expression radius-vector is used to
describe the line from the center of the
circle in other versions of the figure. In
Figure 1, that line is OQ.
At the time of this very early work, no
thought was given to using the diagram
or the idea of simple harmonic motion for
electrical applications: the book considers mechanical things. However, it did
not take long for electricians (as electrical
engineers were then called) to appreciate
the method. Electrical use was apparently "well known" in 1897 when W.E.
Sumpner, in a paper at the Royal Society,
referred back to T and T:
It has been well known for many
years that the variations of a simple harmonic function, such as A

ωt

i
ad

at
ion = 0
t
i
s
Po me t
Ti
s

dian

θ Ra

O
Acos(ωt + θ)

figure 3. A phasor diagram corresponding to Figure 2, as typically taught. In
some books, this is known as an Argand diagram.
78

ieee power & energy magazine

from the center of the circle of rotation to the point moving uniformly in a
circle the projection of which gives the
equation of simple harmonic motion. It
is a double abstraction. First, we have
to assume that the physical signal can
be represented as a mathematical sine
wave; then, we have to see that a vector
(a rotating line) can be used to generate
the sine wave. This use of the word to
signify a line persisted unchanged until
well after the suggestion to instead use
the word phasor in 1944.

Post-1944 Use
Adopting the Word
After 1944, the word phasor was adopted somewhat gradually. Its use was
described in 1960 in a general-purpose
electrical engineering textbook (Electrical Engineering Science, by Clement
and Johnson) with the following words:
For convenience in the mathematical treatment to be given in
Chap. 11, we shall choose to project the arrow onto the horizontal
axis. The arrow is termed a phasor.
Somewhere along the way, the rotating
line has gained an arrowhead, and the
direction of projection changed, but it
is still a line. There is a footnote that
introduces the word sinor, apparently
another term for the same thing. Sinor
was used in some works published between 1945 and approximately 1955,
but it was falling out of favor by then.
In the 1952 book Analysis of Alternating Currents, W.R. LePage writes,
"The term 'sinor' is to be interpreted
as an abbreviation for the phrase 'symbolic representation for a sinusoid'," A
footnote in the original adds the following, highlighting the idea of a line:
A sinor does not represent a sinusoid in the sense that an ordinary
variable represents a quantity. The
directed line is quite different from
a sinusoid. Therefore the word
"symbolic" is important.
LePage acknowledges the double abstraction. He continues with an explanation suggesting that the sinor includes
only the magnitude and the angle in its
symbolic representation. Perhaps because
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