# Inductors and Magnetic fields

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```					    Inductors
and Magnetic fields
BITX20 bidirectional SSB transceiver
BITX20 bidirectional SSB transceiver

RF Filter                       IF Filter
Mixer

Antenna
Mixer
LO                    BFO

Transmit direction shown
Mic
The Colpitts oscillator
+12 V
L1              See the BITX20 circuit
R1

LO: Local Oscillator

C1
BFO: Beat frequency Oscillator
R2
C3          R3

C2
0V
Discharge of an Inductor

Switch             I
+10 A

R              L

0V
Graph of inductor discharge from 10A
R=1 Ohm, L=1 Henry
Amps
10

8

6

4

2

Seconds
0.5     1      1.5     2
The same discharge from 27.18A

Amps

25
10*2.718              e=2.718
20

15

10                                 10

5
10/2.718
Seconds
0.5     1    1.5     2
Exponential decay
The decay time constant = L / R

If R is in Ohms and L in Henries the time is in seconds

Every time constant the voltage decays by the ratio of 2.718

This keeps on happening (till its lost in the noise)

This ratio 2.718 is called “e”.
Exponential decay
It’s a smooth curve. We can work out the current at any
moment.

The current at any time t is: I   = I0 / e (t*R/L)
I0 is the current at time zero.

t*R/L is the fractional number of decay time constants

For e( ) you can use the ex key on your calculator
Fields

•   Electric fields
–   Capacitors
•   Magnetic Fields
–   Inductors
•   Electromagnetic (EM) fields
–   Antennas
–   Cables
Construction of inductors

www.germes-online.com
Key to diagrams
Red rectangle = Outline of a Coil
Blue Rectangle = Outline of a Core
Stronger shading is more positive / negative
An air cored coil
Magnetic potential in air
Magnetic potential is measured in
Amps!

One often talks about Ampere turns but what
counts is the total amps round a closed
circuit.

The magnetic potential between 2 points on
an iron bar is equal to the current in a loop
round the bar between those points
A coil on an iron bar
Magnetic potential with an iron bar
A coil on a closed iron core
Magnetic potential for the closed core
Field strength H

=>
X component =>     Y component
Flux density B

=>
X component =>     Y component
Magnetic field strength H is
measured in Amps per metre

Since magnetic potential is in amps the field
strength H must be in amps per metre.
Magnetic flux density B is
measured in Webers per square
metre

(Or Tesla)
Permeability
• Magnetic field strength H (Amps/Metre)
• Magnetic flux density B (Webers/m2)
• B= μ * H (like Ohms law but for
magnetics )
• Permeability μ = μ0 * μr
• μ0 is 4 Pi*10-7 Henries per Metre (by
definition of the Amp)
Induced Voltages
A moving magnet near a coil of wire will induce a voltage in
the coil. This is due to the varying magnetic flux through the
coil not the motion itself.
The voltage will be:
• Voltage = Magnetic flux change per second times number of
turns in the coil.
• We can calculate the magnetic flux (in Webers) from the
flux density B and the area.
Inductance
When a current flows round a coil it produces a magnetic field.
The magnetic field H produces a magnetic flux density B.
Some or all of the flux (in Webbers) passes through the coil.
If the current is varying then the magnetic flux varies.
The varying magnetic flux causes a back EMF in the coil.
We can calculate the inductance from the geometry and the
permeability before making the coil.
Inductance of a toroid
Toroids are the easiest to calculate since one can assume that
their magnetic flux is uniform and only passes round the core.
Magnetic field strength H = Amps * turns / circumference
Magnetic flux density B = H * permeability
Magnetic flux = B*cross section of toroid.
Induced voltage = turns * Magnetic flux /second

So induced voltage = (Amps /second)*turns*cross section*
permeability* turns/circumference
Inductance of a toroid
So for a Toroid (from previous slide):
Induced voltage = (Amps /second)*turns*cross section*
permeability* turns/circumference
But for any Inductor:
Induced voltage = (Amps/second)*Inductance

So for any Toroid:
Inductance = turns*turns*cross section* permeability
/circumference
A real toroid example
For a T37-2 toroid (all dimensions must be in metres)
Mean circumference = 22.87*10-3 metres
Cross section = 6.4*10-6 square metres
Relative permeability = 10
So the permeability is = 12.57 * 10-6

So inductance = Turns squared * 3.51*10-9 Henries
Or Turns squared * 3.51 nano Henries
The manufacturers quote a value of: Turns squared * 4.3nH
What approximations did we
make?
A T37 toroid has an inner diameter of 5.21 mm and an outer of
9.35 mm Almost a 2:1 ratio.
We assumed the flux was uniform across the cross section. In
fact it will be almost double on the inner surface due to the
higher magnetic field strength on the shorter path.
We assumed the flux in the air was negligible. However this
core has a relative permeability of only 10 so the flux in the air
could be significant. (However by symmetry it should be small
if the coil is wound evenly)
Questions

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 views: 7 posted: 2/10/2012 language: pages: 31