Avionics News September 2019 - 47

Figure 2: The relationship of applied voltage, current flow and counter EMF
in a purely inductive circuit.

lines move through the coil, inducing
voltage. As shown in Figure 2, the voltage
induced is the opposite phase of the voltage
applied. We call this counter electromotive
force, or counter EMF. This means the
coil is actively impeding the current flow
by producing voltage of opposite polarity
in relation to the applied voltage. We call
this inductive reactance (XL). Inductive
reactance impedes AC current flow in a
similar way to resistance in a DC circuit.
When all factors are accounted for (inductive reactance,
capacitive reactance (XC) and resistance), we have
impedance (Z). We will save capacitive reactance for
another month.
XL is similar to resistance in that the rules for series
and parallel circuits apply. For example, the inductive
reactance of a series circuit will be the sum of the
individual reactances. XL differs from resistance in
that the reactance changes with frequency. Reactance
is proportional to frequency. Put simply, as frequency
increases, so does reactance. Reactance can be
calculated by using the formula: XL=2πFL. F is the
frequency, and L is the inductance in henries. The
answer will be in ohms. For an example, let's use a 2
mH coil in a circuit using 1 kHz (2 x 3.14 = 6.28). For
the next step, we have 1,000 Hz, times 0.002 H (1,000 x
0.002 = 2). To finish, 6.28 x 2 = 12.56 Ω.
Let's increase the frequency to 4 kHz (2 x 3.14
x 4,000 x 0.002 = 50.24 Ω). When we quadruple
the frequency, we quadruple the impedance. This
relationship makes inductors useful for filters, which is a
subject for another story.
Things get more complicated when we factor in
resistance. Even the best conductors at any temperature
above absolute zero have some resistance, and inductors
are made of conductors. A perfect, zero resistance
inductor is only possible in theory. In reality, there will
be some resistance, and perhaps a lot of resistance.
Engineers will design circuits with both resistors and
inductors, raising the resistance even more. Resistance
will have an effect on the phase relationships within the
circuit.
To calculate the phase relationships in a resistive and
inductive (RL) circuit, we use phasor diagrams. To calculate
these phase angles, we use trigonometry. To visualize the
phase relationships, we can use a diagram. To keep this
short, we will focus on the diagram, with a minimum
amount of trigonometry. Detail on the trigonometric analysis
can be found in any electronics textbook.

Figure 3 shows a phasor diagram along with a
math example to solve for Z. Reactance is vectored
upward, and resistance is vectored to the right. With
the red lines added, we have a box. The Z vector is
drawn from corner to corner, thus forming two right
triangles. In this case, XL is equal to R. We can see
(or, you can use Pythagorean's theorem) that the phase
angle (Ф) between current and voltage is 45 degrees.
More resistance will reduce the phase angle, and less
resistance will increase the phase angle.
The total impedance of the circuit is represented by
the Z vector and can be calculated using Pythagorean's
theorem. Visually, we can see that Z is a greater value
than the individual R or XL, but less than the sum of R
or XL. For an easy example, we can use 10 Ω for both
R and XL as shown in Figure 3. The answer of 14.14 Ω
fits the rule where the Z is greater than the individual
reactance or resistance but is less than the sum of both.
Unless resistance is built into an inductor, it will
not dissipate any power; however, thanks to counter
EMF, there is a voltage drop. If one were to use I x E
to calculate power dissipation, then this person would
Continued on following page

XL

Z= R 2 +X L2

Z

R

Z=

10 2 +10 2

Z=

100+100

Z=

200

Z= 14.14 Ohms
o
= 45

Figure 3: Inductive reactance, resistance, and impedance shown
on a phasor type diagram.
avionics news

*

september

2019

47



Avionics News September 2019

Table of Contents for the Digital Edition of Avionics News September 2019

No label
Avionics News September 2019 - No label
Avionics News September 2019 - Cover1
Avionics News September 2019 - Cover2
Avionics News September 2019 - 1
Avionics News September 2019 - 2
Avionics News September 2019 - 3
Avionics News September 2019 - 4
Avionics News September 2019 - 5
Avionics News September 2019 - 6
Avionics News September 2019 - 7
Avionics News September 2019 - 8
Avionics News September 2019 - 9
Avionics News September 2019 - 10
Avionics News September 2019 - 11
Avionics News September 2019 - 12
Avionics News September 2019 - 13
Avionics News September 2019 - 14
Avionics News September 2019 - 15
Avionics News September 2019 - 16
Avionics News September 2019 - 17
Avionics News September 2019 - 18
Avionics News September 2019 - 19
Avionics News September 2019 - 20
Avionics News September 2019 - 21
Avionics News September 2019 - 22
Avionics News September 2019 - 23
Avionics News September 2019 - 24
Avionics News September 2019 - 25
Avionics News September 2019 - 26
Avionics News September 2019 - 27
Avionics News September 2019 - 28
Avionics News September 2019 - 29
Avionics News September 2019 - 30
Avionics News September 2019 - 31
Avionics News September 2019 - 32
Avionics News September 2019 - 33
Avionics News September 2019 - 34
Avionics News September 2019 - 35
Avionics News September 2019 - 36
Avionics News September 2019 - 37
Avionics News September 2019 - 38
Avionics News September 2019 - 39
Avionics News September 2019 - 40
Avionics News September 2019 - 41
Avionics News September 2019 - 42
Avionics News September 2019 - 43
Avionics News September 2019 - 44
Avionics News September 2019 - 45
Avionics News September 2019 - 46
Avionics News September 2019 - 47
Avionics News September 2019 - 48
Avionics News September 2019 - 49
Avionics News September 2019 - 50
Avionics News September 2019 - 51
Avionics News September 2019 - 52
Avionics News September 2019 - 53
Avionics News September 2019 - 54
Avionics News September 2019 - 55
Avionics News September 2019 - 56
Avionics News September 2019 - 57
Avionics News September 2019 - 58
Avionics News September 2019 - 59
Avionics News September 2019 - 60
Avionics News September 2019 - 61
Avionics News September 2019 - 62
Avionics News September 2019 - 63
Avionics News September 2019 - 64
Avionics News September 2019 - 65
Avionics News September 2019 - 66
Avionics News September 2019 - 67
Avionics News September 2019 - 68
Avionics News September 2019 - 69
Avionics News September 2019 - 70
Avionics News September 2019 - 71
Avionics News September 2019 - 72
Avionics News September 2019 - Cover3
Avionics News September 2019 - Cover4
http://www.brightcopy.net/allen/avne/57-11
http://www.brightcopy.net/allen/avne/57-10
http://www.brightcopy.net/allen/avne/57-9
http://www.brightcopy.net/allen/avne/57-8
http://www.brightcopy.net/allen/avne/57-7
http://www.brightcopy.net/allen/avne/57-6
http://www.brightcopy.net/allen/avne/57-5
http://www.brightcopy.net/allen/avne/57-4
http://www.brightcopy.net/allen/avne/57-3
http://www.brightcopy.net/allen/avne/57-2
http://www.brightcopy.net/allen/avne/57-1
http://www.brightcopy.net/allen/avne/56-12
http://www.brightcopy.net/allen/avne/56-11
http://www.brightcopy.net/allen/avne/56-10
http://www.brightcopy.net/allen/avne/56-9
http://www.brightcopy.net/allen/avne/56-8
http://www.brightcopy.net/allen/avne/56-7
http://www.brightcopy.net/allen/avne/56-6
http://www.brightcopy.net/allen/avne/56-5
http://www.brightcopy.net/allen/avne/56-4
http://www.brightcopy.net/allen/avne/56-3
http://www.brightcopy.net/allen/avne/56-2
http://www.brightcopy.net/allen/avne/56-1
http://www.brightcopy.net/allen/avne/55-12
http://www.brightcopy.net/allen/avne/55-11
http://www.brightcopy.net/allen/avne/55-10
http://www.brightcopy.net/allen/avne/55-9
http://www.brightcopy.net/allen/avne/55-8
http://www.brightcopy.net/allen/avne/55-7
http://www.brightcopy.net/allen/avne/55-6
http://www.brightcopy.net/allen/avne/55-5
http://www.brightcopy.net/allen/avne/55-4
http://www.brightcopy.net/allen/avne/55-3
http://www.brightcopy.net/allen/avne/55-02
http://www.brightcopy.net/allen/avne/55-01
http://www.brightcopy.net/allen/avne/54-12
http://www.brightcopy.net/allen/avne/54-11
http://www.brightcopy.net/allen/avne/54-10
http://www.brightcopy.net/allen/avne/54-9
http://www.brightcopy.net/allen/avne/54-8
http://www.brightcopy.net/allen/avne/54-7
http://www.brightcopy.net/allen/avne/54-6
http://www.brightcopy.net/allen/avne/54-5
http://www.brightcopy.net/allen/avne/54-4
http://www.brightcopy.net/allen/avne/54-3
http://www.brightcopy.net/allen/avne/54-2
http://www.brightcopy.net/allen/avne/54-1
http://www.brightcopy.net/allen/avne/53-12
http://www.brightcopy.net/allen/avne/53-11
http://www.brightcopy.net/allen/avne/53-10
http://www.brightcopy.net/allen/avne/53-9
http://www.brightcopy.net/allen/avne/53-8
http://www.brightcopy.net/allen/avne/53-7
http://www.brightcopy.net/allen/avne/53-6
http://www.brightcopy.net/allen/avne/53-5
http://www.brightcopy.net/allen/avne/53-4
http://www.brightcopy.net/allen/avne/53-3
http://www.brightcopy.net/allen/avne/53-2
http://www.brightcopy.net/allen/avne/53-1
http://www.brightcopy.net/allen/avne/52-12
http://www.brightcopy.net/allen/avne/52-11
http://www.brightcopy.net/allen/avne/52-10
http://www.brightcopy.net/allen/avne/52-9
http://www.brightcopy.net/allen/avne/52-8
https://www.nxtbook.com/allen/avne/52-7
https://www.nxtbook.com/allen/avne/52-6
https://www.nxtbook.com/allen/avne/52-5
https://www.nxtbook.com/allen/avne/52-4
https://www.nxtbook.com/allen/avne/52-3
https://www.nxtbook.com/allen/avne/52-2
https://www.nxtbook.com/allen/avne/52-1
https://www.nxtbook.com/allen/avne/51-12
https://www.nxtbook.com/allen/avne/51-11
https://www.nxtbook.com/allen/avne/51-10
https://www.nxtbook.com/allen/avne/51-9
https://www.nxtbook.com/allen/avne/51-8
https://www.nxtbook.com/allen/avne/51-7
https://www.nxtbook.com/allen/avne/51-6
https://www.nxtbook.com/allen/avne/51-5
https://www.nxtbook.com/allen/avne/51-4
https://www.nxtbook.com/allen/avne/51-3
https://www.nxtbook.com/allen/avne/51-2
https://www.nxtbook.com/allen/avne/51-1
https://www.nxtbook.com/allen/avne/50-12
https://www.nxtbook.com/allen/avne/50-11
https://www.nxtbook.com/allen/avne/50-10
https://www.nxtbook.com/allen/avne/50-9
https://www.nxtbook.com/allen/avne/50-8
https://www.nxtbook.com/allen/avne/50-7
https://www.nxtbook.com/allen/avne/50-6
https://www.nxtbook.com/allen/avne/50-5
https://www.nxtbook.com/allen/avne/50-4
https://www.nxtbook.com/allen/avne/50-3
https://www.nxtbook.com/allen/avne/50-2
https://www.nxtbook.com/allen/avne/50-1
https://www.nxtbook.com/allen/avne/49-12
https://www.nxtbook.com/allen/avne/49-11
https://www.nxtbook.com/allen/avne/49-10
https://www.nxtbook.com/allen/avne/49-9
https://www.nxtbook.com/allen/avne/49-8
https://www.nxtbook.com/allen/avne/49-7
https://www.nxtbook.com/allen/avne/49-6
https://www.nxtbook.com/allen/avne/49-5
https://www.nxtbook.com/allen/avne/49-4
https://www.nxtbook.com/allen/avne/49-3
https://www.nxtbook.com/allen/avne/49-2
https://www.nxtbook.com/allen/avne/49-1
https://www.nxtbook.com/allen/avne/48-12
https://www.nxtbook.com/allen/avne/48-11
https://www.nxtbookmedia.com