KickStart
b y M ike Tooley
Part 3: Making sense of inductors
Our occasional KickStart series aims to
show readers how to use readily available
low-cost components and devices to
solve a wide range of common problems
in the shortest possible time. Each of the
examples and projects can be completed
in no more than a couple of hours using
off-the-shelf parts. As well as briefly
explaining the underlying principles and
technology used, the series will provide
you with a variety of representative
solutions and examples, along with just
enough information to enable you to
adapt and extend them for your own use.
This third instalment shows you how to
design and realise inductive components
in a wide range of electronic applications
and, in keeping with the KickStart
philosophy, we’ve provided ideas for you
to start making use of inductors in your
own projects.
frequency-selective circuits. Inductors are also used in noise
and interference suppression applications across a wide range
of frequencies, from mains (50/60Hz) to RF.
The most basic form of air-cored inductor is nothing more
than a coil of insulated wire wound on a non-conductive
former. Larger values of inductor can benefit from the enhanced
magnetic properties offered by a core made from a ferromagnetic
material such as steel (often laminated) or ferrite (a ceramiclike material with magnetic properties).
Inductors are widely available in a range of off-the-shelf
values and ratings, but they can also be made at home relatively
easily, though this can sometimes be a hit and miss process.
Before we explain this, take a look a typical selection of the
small inductors that you might encounter in electronics, as
shown in Fig.3.1 and Table 3.1.
Fig.3.1. A typical selection of small inductors.
W
hat are inductors? They are components that
store energy in the form of an electromagnetic field,
and like resistors and capacitors, they are classified
as passive devices. When a changing or alternating current is
applied to an inductor it will respond by temporarily storing
energy in an electromagnetic field, releasing it back at some
later time. This temporary storage of energy has the effect of
slowing the change in current that causes it.
When is an inductor not an inductor?
Unfortunately, compared with resistors or even capacitors,
inductors rarely behave perfectly, and this can be an important
factor in their design and application. Fig.3.2 shows an
‘ideal’ inductor together with its real-world equivalent which
incorporates the losses and stray reactance found in ‘real’
components. The essential features shown in Fig.3.2(b) include:
L
The inductance value, determined by the number of turns
and magnetic properties of the core material.
Cp The distributed capacitance (ie, the lumped-together
capacitance between adjacent turns, connecting wires
and/or terminals). This capacitance can be problematic
at high frequencies where the capacitive reactance may
fall to a relatively low value.
When an alternating current (eg, a sinewave) is applied to an
inductor the effect of the inductor (in terms of opposition to
current flow) is referred to as ‘inductive reactance’. The faster
the current changes, the greater will be the
Table 3.1 Brief details of the inductors shown in Fig. 3.1
reactance, and vice versa. Hence inductive
reactance is directly proportional to the
Ref.
Inductance
Notes
frequency of the applied current. Like
resistance (which strictly applies to steady
A
3.5mH
Adjustable ferrite inductor for PCB mounting
direct current) reactance is measured in
B
2.8mH
Choke for use in low-frequency radio applications
ohms ( ) and is defined simply as the ratio
of applied alternating voltage to the current
C
1mH
Small ferrite pot-cored inductor for general-purpose applications
flowing. A 100mH inductor will exhibit a
D
100µ H
Large ferrite pot-cored inductor for high-current applications
reactance of approximately 63 at 100Hz,
E
100µ H
Fixed toroidal inductor for use in filters
630 at 10kHz, and 6.3k at 100kHz.
Inductors are used in power supplies
F
33µ H
Wire-ended axial-lead choke for RF applications
to filter alternating current from direct
G
3.9µ H
Small axial-lead inductor for general-purpose applications
current, in which case they are sometimes
referred to as ‘chokes’ or ‘reactors’. In audio
H
2µ H
Adjustable ferrite-cored inductor for use in RF tuned circuits
and communication systems inductors
I
300nH
Air-cored inductor for use in VHF and UHF radio applications
are often employed in filters and other
36
Practical Electronics | June | 2021
effective permeability (µe) of the core
material, its physical dimensions and
construction. Specific inductance is
usually quoted in nH and can be found
from the core manufacturers’ published
data. The value of inductance can be
calculated using the relationship:
Fig.3.2. ‘Ideal’ and ‘real’ inductors.
Rloss The total loss resistance of the
inductor. This is the sum of its
copper winding loss resistance (Rs)
and the core loss resistance (Rc).
Rs The copper winding loss resistance
which can be measured between
the terminals of an inductor using
an ohmmeter
Rc The core resistance is attributable
to the continuous process of
magnetising and demagnetising the
core during each cycle of the applied
alternating current. Note that, in the
case of large inductors Rc can be
significantly greater than Rs.
Quality factor
The quality factor (Q) of an inductor
is simply the ratio of its effective
reactance to its loss resistance; it can
thus be taken as an indicator of how
Part 3: Making sense of inductors
‘good’ a component it is. Q-factor can
be calculated from:
X
2p fL
Q= L =
Rloss Rs + Rc
We have chosen an off-the-shelf toroidal
core manufactured by TDK using N30
Part 3: Making sense of inductors
SIFFERIT material. Referring to the
manufacturer’s data, the core has a quoted
permeability
(µ)
of 4300 and a resulting
XL
2p fL
= Making
= sense (A
Q3:
specific
inductance
) of 5460 (in nH).
Part
of Linductors
Rloss Rs + Rc
Rearranging
the formula that we met
earlier allows us to calculate the number
Part 3: Making sense of inductors
X required,
2p fL as follows:
L = n2AL
of turns
Q= L =
Rloss Rs + Rc
L
Where AL is the specific inductance
n=
X
2p fL -9
AL
quoted in in nanohenries
= 10 H).
=
Q = L (1nH
Rloss to good
Rs + Rcuse in
We will put this formula
Where
the next section.
L L is the required value of
ninductance
=
(in henry) and AL is the value
AL
(5460
Manufacturing toroidal inductors of specific
1.1inductance
´ 10-3
1100 in the case
= N30 core). -Hence
= the number
= 201.5of
» 14 turns
L with values
of nthe
Fortunately, inductors
9
n=
5460 ´ 10
5.46
turns required is given by:
ranging from about 10µH
A L to 100mH,
can be very easily manufactured using
1.1 ´ 10-3
1100
stock ferrite toroidal cores. However,
n=
=
= 201.5 » 14 turns
when purchasing a suitable core, you
5460 ´ 10-9
5.46
may need to consider several
1.1 ´properties,
10-3
1100
n=
=
= 201.5 » 14 turns
including the following:
5460 ´ 10-9
5.46
Core material and its magnetic
characteristics
The core measures 35.5 × 13.6mm and
Physical dimensions of the core
will easily accommodate the number
(notably external and internal
of turns required. To safely carry the
diameter and thickness)
required current and minimise copper
Required current handling capacity
winding losses, the wire will need to
and maximum allowable winding
resistance (these will in turn
determine the required wire gauge)
Number of turns required for a
specified value of inductance (note
that the physical dimensions will
limit the maximum number of turns
that can be used).
The design process is best illustrated by
taking a simple example. Let’s suppose
that we need an inductor with the
following specifications for use in a highcurrent switched-mode power supply:
Q-factor is important in many applications
and it might be worth illustrating this
Inductance
1.1mH
with an example. Let’s assume that we
L
Current-handling capacity
5A
have
n =two inductors with the properties
Operating frequency
300kHz
shown A
inL Table 3.2. The Q-factor for
Maximum winding resistance 0.2
each component has been calculated
for a working frequency of 10kHz – note
the large reduction in quality factor due
-3
to the relatively
core material
1.1 ´ 10imperfect
1100
n =in the manufacture
= of component
= 201.5B.
» 14 turns
used
5460 ´ 10-9
5.46
Fig.3.3. Author’s 1.1mH toroidal inductor.
Inductance
1
The value of inductance (L) is determined
by the specific inductance of the core,
AL. This, in turn, is determined by the
1
Table 3.2 Comparison of two inductors
Inductor A
Inductor B
L = 100mH
L = 100mH
Cp = 11pF
Cp = 18pF
Rs = 1Ω
Rs = 5Ω
Rc = 29Ω
Rc = 95Ω
Q = 209
Q = 63
Practical Electronics | June | 2021
1
Fig.3.4. Checking the 1.1mH inductor using a low-cost component tester.
37
be of appropriate gauge and diameter. The chosen
diameter (1.5mm) of enamelled copper wire has a
quoted resistance of less than 0.01 /m and thus the
voltage drop resulting from a continuous direct current
of 5A and a total winding length of 500mm should be
less than 25mV. See the Going further section for further
information on selecting suitable wire.
The value of inductance can be checked using a test
meter with an inductance range or by using a network
analyser or an AC bridge. Alternatively, a low-cost
component tester like the one in Fig.3.4 can be used
to provide an indication sufficient to confirm that
the required value of inductance has been achieved.
A tolerance of up to about ±10% is usually quite
acceptable for most applications, but it is always wise to
check the calibration of a test instrument using a known Fig.3.5. A gyrator-based equivalent inductor – note that in both circuits
component before attempting to make a measurement. R1 >> R2, and R1 is grounded. Thanks to the high gain and negative
At this point, a few notes of caution would feedback of the op amp, the effective impedance looking into the R2/C
not go amiss. First, the permeability of ferrite terminal is: R2 + L, where L = R1 × R2 × C.
and other ferromagnetic
alloy materials tends to
fall very sharply at high
temperatures (ie, above
about 125°C). Beyond this
point a material’s magnetic
properties can collapse
very quickly. Second, it
is not unusual for cores to
heat up during operation,
particularly when high
flux densities are present,
along with high-frequency
current. This can further
exacerbate the reduction
in permeability, and it
can severely limit the
performance of a core. In Fig.3.6. Circuit of the gyrator-based bandpass audio filter.
Fig.3.9. Pin connections for the gyrator-based bandpass audio filter.
all cases it is worth referring to manufacturers’ data, checking both
the permeability characteristics and recommended frequency range.
Fig.3.7. PCB track layout for the gyrator-based
bandpass audio filter.
KS3-2021
Simulating inductors
Unfortunately, it can sometimes be difficult to manufacture the relatively
large-value inductors needed for use in audio and low-frequency
applications. However, there’s a potential solution in the form of a
circuit that can simulate an inductor using just capacitors and resistors,
together with an active device such as a transistor or operational
amplifier. This arrangement is called a ‘gyrator’, and it works by acting
like a mirror which effectively reflects an equal but opposite reactance
to that present at its input. The circuit of a gyrator-based equivalent
inductor is shown in Fig.3.5. Note that, in common with most gyrator
circuits, this arrangement expects to be fed from a ground-referenced
(0V) low-impedance source.
A bandpass audio filter based on a gyrator
Fig.3.8. Component overlay for the gyrator-based
bandpass audio filter.
38
To put this into context let’s take a look at a practical application for a
gyrator in the form of a tuneable bandpass audio filter where the gyrator
Practical Electronics | June | 2021
Parts list – gyrator-based audio filter
Table 3.3 Recommended values of C1, C2 and C5 for
different audio frequency ranges
Integrated circuit
1 TL082 8-pin dual operational amplifier
Nominal frequency
Capacitance
Adjustment range
200Hz
680nF
180Hz to 400Hz
300Hz
470nF
220Hz to 480Hz
400Hz
220nF
350Hz to 700Hz
600Hz
100nF
500Hz to 1kHz
800Hz
68nF
600Hz to 1.2kHz
1kHz
47nF
700Hz to 1.5kHz
1.2kHz
33nF
900Hz to 1.8kHz
1.4kHz
22nF
1kHz to 2kHz
1.8kHz
10nF
1.5kHz to 3kHz
Resistors (all fixed resistors are 0.2W 5%)
1 100kΩ (R1)
1 47Ω (R2)
1 47kΩ (R3)
1 10kΩ (R4)
1 2.2kΩ (R5)
2 1kΩ (R6 and R7)
1 200kΩ miniature skeleton pre-set (RV1)
Capacitors
3 100nF 100V miniature polyester (see Table 3.3)
2 220uF 16V radial electrolytic
Miscellaneous
1 single-sided PCB, 74 × 50mm code KS3-2021, available from
the PE PCB Service
1 8-way header (P1)
1 3-way header (P2)
1 2-way jumper shunt for use with P2
1 8-pin low-profile DIL socket for use with IC1
1 9V PP3 battery (B1)
1 Battery connector for use with B1
replaces a variable inductor of several hundred millihenries
(mH). Fig.3.6 shows the complete circuit of the filter in which
IC1a acts as a unity-gain inverting amplifier for the gyrator,
while IC1b is a non-inverting output buffer configured for a
modest voltage gain.
With the quoted component values, the filter covers a
nominal frequency range of 500Hz to 1.5kHz and is adjustable
by means of RV1 (which effectively alters the value of
inductance simulated by the gyrator). For normal operation,
the link at P2 is normally placed in position A, but the direct
output from IC1b can be used by placing the link in position B.
The input impedance of the filter (100k ) is set by R1, while
C1 acts as a coupling capacitor which will remove any DC
Topic
Coils and
inductors
level present at the input. The filter tuned circuit comprises
C5 together with the simulated gyrator inductance obtained
from IC1b, C2, R2 and the series combination of RV1 and
R3. A symmetrical voltage supply for IC1 is obtained from a
standard 9V battery (PP3) and potential divider arrangement
comprising R6 and R7 together with decoupling capacitors,
C4 and C3 respectively. The measured performance of the
filter is as follows:
Approximate voltage gain 6dB
Nominal centre frequency 600Hz
Adjustment range
450Hz (min.) to 1.09kHz (max.)
Centre frequency
567Hz (at mid-position of RV1)
Bandwidth
60 Hz at –3dB (at 600Hz)
Input impedance
100k
Output impedance
less than 100
Supply
9V DC at less than 9mA
The PCB track layout and component overlay for the gyratorbased audio filter are shown in Fig.3.7 and Fig.3.8 respectively.
Pin connections for IC1 and P1 are shown in Fig.3.9 and the
finished board appears in Fig.3.10. Note that several sets
Source
Notes
TDK’s Product Centre details a comprehensive range of inductive
components: http://bit.ly/pe-jun21-tdk
TDK’s publication TDK Inductor’s World provides an
entertaining and accessible introduction to inductors. See
http://bit.ly/pe-jun21-tdk2 or download from the June 2021
page of the PE website.
Coilcraft’s website provides a useful introduction to inductors
and chokes: http://bit.ly/pe-jun21-cc
Coilcraft’s website also provides useful application notes on
L-C filter design.
Inductance
and Q-factor
The author’s own book, Electronic Circuits: Fundamentals
and Applications (5th Ed, 2020 published by Routledge
9780367421984)
General introduction to alternating voltage and current,
together with sections on inductance, Q-factor and
resonant circuits
Tina-TI
The Tina-TI SPICE-based analogue simulation software can be
freely downloaded from the Texas Instruments website at:
www.ti.com/tool/TINA-TI
The full version 11 of Tina can be purchased and downloaded
from the Practical Electronics website. Budget versions of the
software are available for students and hobbyists
Filters
Part 8 of Electronics Teach-in 4 (available from PE Magazine)
Provides a general introduction to analogue circuit
applications including passive and active filters
TL082
Texas Instruments TL082 datasheet: http://bit.ly/pe-jun21-082
Details of the TL082 op amp
Going Further with inductors
This section details a variety of sources
that will help you locate the component
Practical Electronics | June | 2021
parts and further information that will allow
you to make and use inductors in your own
applications. It also provides links to some
useful websites that will help you get up to
speed with underpinning knowledge for the
key topics discussed.
39
Fig.3.10. The completed gyrator-based
bandpass audio filter.
of pads are provided for C1 and C2 so
that components of different size can
be accommodated.
Table 3.3 lists recommended values
of C1, C2 and C5 for different audio
frequency ranges.
If the circuit shows a tendency to
oscillate with no input connected, this
can be resolved by connecting a 1N4148
diode in parallel with C5. The diode can
be easily added to the underside of the
board and soldered directly to the pads
used for C5.
Finally, Fig.3.11 shows a SPICE
simulation of the gyrator-based audio filter
shown in Frig.3.5. This simulation was
created using a free version of the popular
Tina-TI SPICE package (see Going Further)
and readers can download the application
from: www.ti.com/tool/TINA-TI
Fig.3.11. Tina-TI SPICE simulation of the gyrator-based bandpass audio filter.
Note how Tina’s Virtual Signal Analyser
has plotted the filter response and that
this shows a sharp peak at 600Hz, together
with rapid roll-off on either side.
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Practical Electronics | June | 2021
