2Y Electronics

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2Y Electronics
http//pburton.maps.susx.ac.uk/varcoe/electronics2
001/index.html

• Dr. Ben Varcoe
• Pevensey II Rm. 3A3
• Ph. 01273 87 7490
• Email B.Varcoe_at_sussex.ac.uk
• Office Hour 10-11 Friday

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Lecture 3

• Thévenins Theorem Review
• Nortons Theorem
• Capacitors
• Series and Parallel laws
• RC circuits
• Differential Equations for RC circuits
• Differentiation and integration using RC circuits
• Inductors
• Faradays Law
• Differential equations for LR and LC circuits

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Thévenins Theorem

• Insofar as a load is concerned, any one port
  network of resistance elements and energy sources
  can be replaced by a series combination of an
  ideal voltage source Vth and a resistance Rth
  where Vth is the open circuit voltage and Rth is
  the ratio of the open circuit voltage to the
  closed circuit resistance.

Rth
Vth
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Thévenins Theorem
Voc
Isc
Resistance and energy sources
Resistance and energy sources
Find the open circuit voltage Voc
Find the short circuit current Isc
RthVoc/Isc
Vth Voc
Thévenins Equivalent
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Nortons Theorem

• Insofar as a load is concerned any one port
  network of resistance can be replaced by a
  parallel combination of an ideal current source
  IN and a resistance RN. Where IN is the short
  circuit current (IN ISC). RN is the ratio of
  the current to the open Circuit voltage. RN
  VOC/ISC.

RN
IN
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Nortons Theorem
Voc
Resistance and energy sources
Resistance and energy sources
Isc( IN)
Find the open circuit voltage Voc
Find the short circuit current Isc
RNVOC/IN
IN
Nortons Equivalent
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Capacitance

• A capacitor is a device used to store charge in a
  circuit
• A capacitor with capacitance of C farads (mF, nF
  etc.) with V volts across its terminals has Q
  coulombs of charge on one plate and -Q on the
  other.
• Taking the derivative
• In a capacitor, the current is proportional to
  the rate of change of the voltage.

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Addition of Capacitance

• Series Law
• Parallel Law

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RC circuits

• Combining our two components, the resistor and
  capacitor
• This is a differential equation and its solution
  is
• The RC circuit has a transient response.
• The product RC is called the time constant of the
  circuit.

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Discharging a Capacitor

• A charged capacitor placed across a resistor will
  discharge exponentially.

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RC circuits

• When charging a capacitor
• This is a differential equation and its solution
  is
• The time constant of the circuit is still RC.

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Charging a capacitor

• For this slightly different circuit, a battery is
  connected at the time t 0. The capacitor
  charges with the charge approaching its final
  value exponentially.

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Response to a square wave

• When tgtgtRC the voltage V reaches Vf (the rule is
  5RC to 1 of the final value).
• When the voltage is changed to a new value the
  exponential starts again.

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RC circuits as differentiators

• In the figure right the voltage across C is Vin -
  V therefore
• If R and C are small then,
• which means that

• Rearranging gives
• In other words the output is the derivative of
  the input

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RC circuits as integrators

• In the figure right now the voltage across R is
  Vin - V therefore
• If the product RC is large then,
• which means that

• or
• In other words the output is the integral of the
  input ( but only in the limit
  )

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Example

• The capacitor in the top picture is initially
  uncharged. Find the current through the battery
  (a) immediately after the switch is closed, (b) a
  long time after the switch is closed.

a
b
c
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Inductors

• An inductor is a coil of wire (hence the symbol)
  thus a current in the coil will induce a magnetic
  field that acts against the incident field.
• Faradays Law

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Inductors

• Thus the defining equation for an inductor is
• Thus the voltage is proportional to the rate of
  change of the current (the opposite to a
  capacitor).
• An inductor is similar to a capacitor having the
  LR circuit differential equation of
• The circuit response is therefore very similar
  also.