Inductance

1
Inductance

• The property of inductance might be described as
• "when any piece of wire is wound into a coil form
  it forms an inductance which is the property of
  opposing any change in current".

2
Inductance

• Alternatively it could be said
• "inductance is the property of a circuit by
  which energy is stored in the form of an
  electromagnetic field".

3
Inductance

• We said a piece of wire wound into a coil form
  has the ability to produce a counter emf
  (opposing current flow) and therefore has a value
  of inductance.

4
Inductance

• The standard value of inductance is the Henry, a
  large value which like the Farad for capacitance
  is rarely encountered in electronics today
• Typical values of units encountered are
  milli-henries mH, one thousandth of a henry or
  the micro-henry uH, one millionth of a henry.

5
Inductance

• A small straight piece of wire exhibits
  inductance (probably a fraction of a uH) although
  not of any major significance until we reach UHF
  frequencies.
• The value of an inductance varies in proportion
  to the number of turns squared.

6
Inductance

• If a coil was of one turn its value might be one
  unit.
• Having two turns the value would be four units
  while three turns would produce nine units
  although the length of the coil also enters into
  the equation.

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Inductance formula

• The standard inductance formula for close
  approximation - imperial and metric is

8
Imperial measurements

• L r2 X N2 / ( 9r 10len ) where L
  inductance in uH r coil radius in inches N
  number of turns len length of the coil in
  inches

9
Metric measurements

• L 0.394r2 X N2 / ( 9r 10len ) where L
  inductance in uH r coil radius in centimetres
  N number of turns len length of the coil in
  centimetres

10
Reactance

• Reactance is the property of resisting or
  impeding the flow of ac current or ac voltage in
  inductors and capacitors.
• Note particularly we speak of alternating current
  only ac, which expression includes audio af and
  radio frequencies rf.

11
Reactance

• NOT direct current dc.
• This leads to inductive reactance and capacitive
  reactance.

12
Inductive Reactance

• When ac current flows through an inductance a
  back emf or voltage develops opposing any change
  in the initial current.
• This opposition or impedance to a change in
  current flow is measured in terms of inductive
  reactance.

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Inductive Reactance

• Inductive reactance is determined by the formula
  
• 2 pi f L
• where 2 pi 6.2832 f frequency in hertz
  and L inductance in Henries

14
Capacitive Reactance

• When ac voltage flows through a capacitance an
  opposing change in the initial voltage occurs,
• this opposition or impedance to a change in
  voltage is measured in terms of capacitive
  reactance.

15
Capacitive Reactance

• Capacitive reactance is determined by the
  formula
• 1 / (2 pi f C)
• where 2 pi 6.2832 f frequency in hertz
  and C capacitance in Farads

16
Some examples of Reactance

• What reactance does a 6.8 uH inductor present at
  7 Mhz? Using the formula above we get
• 2 pi f L
• where 2 pi 6.2832 f 7,000,000 Hz and L
  .0000068 Henries
• Answer 299 ohms

17
Some examples of Reactance

• What reactance does a 33 pF capacitor present at
  7 Mhz? Using the formula above we get
• 1 / (2 pi f C)
• where 2 pi 6.2832 f 7,000,000 Hz and C
  .0000000000033 Farads
• Answer 689 ohms

18
Resonance

• Resonance occurs when the reactance of an
  inductor balances the reactance of a capacitor at
  some given frequency.
• In such a resonant circuit where it is in series
  resonance, the current will be maximum and
  offering minimum impedance.

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Resonance

• In parallel resonant circuits the opposite is
  true.
• Resonance formula
• 2 pi f L 1 / (2 pi f C)
• where 2 pi 6.2832 f frequency in hertz L
  inductance in Henries and C capacitance in
  Farads

20
Resonance

• Which leads us on to
• f 1 / 2 pi (sqrt LC)
• where 2 pi 6.2832 f frequency in hertz L
  inductance in Henries and C capacitance in
  Farads

21
Resonance

• A particularly simpler formula for radio
  frequencies (make sure you learn it) is
• LC 25330.3 / f 2
• where f frequency in Megahertz (Mhz) L
  inductance in microhenries (uH) and C
  capacitance in picofarads (pF)

22
Resonance

• Following on from that by using simple algebra we
  can determine
• LC 25330.3 / f 2  and  L 25330.3 / f 2 C
   and  C 25330.3 / f 2 L

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Impedance at Resonance

• In a series resonant circuit the impedance is at
  its lowest for the resonant frequency
• whereas in a parallel resonant circuit the
  impedance is at its greatest for the resonant
  frequency.
• See figure.

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Resonance in series and parallel circuits
25
Impedance

• Electrical impedance describes a measure of
  opposition to alternating current (AC).
• Electrical impedance extends the concept of
  resistance to AC circuits,

26
Impedance

• describing not only the relative amplitudes of
  the voltage and current, but also the relative
  phases.
• When the circuit is driven with direct current
  (DC) there is no distinction between impedance
  and resistance
• the latter can be thought of as impedance with
  zero phase angle.

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Impedance

• The symbol for impedance is usually Z and it may
  be represented by writing its magnitude and phase
  in the form Zlt ?

28
Combining impedances

• The total impedance of many simple networks of
  components can be calculated using the rules for
  combining impedances in series and parallel.

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Combining impedances

• The rules are identical to those used for
  combining resistances,
• except that the numbers in general will be
  complex numbers.
• In the general case however, equivalent impedance
  transforms in addition to series and parallel
  will be required

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Series combination

• For components connected in series, the current
  through each circuit element is the same
• the total impedance is the sum of the component
  impedances

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Impedance
32
Parallel combination

• For components connected in parallel,
• the voltage across each circuit element is the
  same
• the ratio of currents through any two elements is
  the inverse ratio of their impedances

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Parallel combination
34
Parallel combination

• Hence the inverse total impedance is the sum of
  the inverses of the component impedances

35
Diodes

• Diodes are semiconductor devices which might be
  described as passing current in one direction
  only.
• The latter part of that statement applies equally
  to vacuum tube diodes.

36
Diodes

• Diodes can be used as voltage regulators,
• tuning devices in rf tuned circuits,
• frequency multiplying devices in rf circuits,
• mixing devices in rf circuits,
• switching applications or can be used to make
  logic decisions in digital circuits.

37
Diodes

• There are also diodes which emit "light", of
  course these are known as light-emitting-diodes
  or LED's.

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Schematic symbols for Diodes
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Types of Diodes

• The first diode in figure is a semiconductor
  diode
• Commonly used in switching applications
• You will notice the straight bar end has the
  letter "k", this denotes the "cathode" while the
  "a" denotes anode.

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Types of Diodes

• Current can only flow from anode to cathode and
  not in the reverse direction, hence the "arrow"
  appearance.
• This is one very important property of diodes

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Types of Diodes

• The second of the diodes is a zener diode which
  are fairly popular for the voltage regulation of
  low current power supplies.

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Types of Diodes

• The next is a varactor or tuning diode.
• Depicted here is actually two varactor diodes
  mounted back to back with the DC control voltage
  applied at the common junction of the cathodes.
• These cathodes have the double bar appearance of
  capacitors to indicate a varactor diode.

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Types of Diodes

• When a DC control voltage is applied to the
  common junction of the cathodes,
• the capacitance exhibited by the diodes (all
  diodes and transistors exhibit some degree of
  capacitance) will vary in accordance with the
  applied voltage.

44
Types of Diodes

• The next diode is the simplest form of vacuum
  tube or valve.
• It simply has the old cathode and anode.
• These terms were passed on to modern solid state
  devices.
• Vacuum tube diodes are mainly only of interest to
  restorers and tube enthusiasts

45
Types of Diodes

• The last diode depicted is a light emitting diode
  or LED.
• A led actually doesn't emit as much light as it
  first appears,
• a single LED has a plastic lens installed over it
  and this concentrates the amount of light.

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Types of Diodes

• Seven LED's can be arranged in a bar fashion
  called a seven segment LED display and when
  decoded properly can display the numbers 0 - 9 as
  well as the letters A to F.

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