Lecture 13 Dependent Sources

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Lecture 13Dependent Sources

• ECE 205
• Prof. Ali Keyhani

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Active Devices

• Active Device Device that are dependent on an
  external power supply to operate
• Active Circuit Circuits that contain one or more
  active devices
• Linearly active devices input-output
  relationship of the active devices is governed by
  the equation yKx
• K is called the proportionality factor

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Dependent Sources

• Linear active devices are usually modeled using
  resistors and dependent sources
• Dependent sources a voltage or current source
  whose output is controlled by a voltage or
  current in another part of the circuit
• Depending on the type of the source and the
  control there are four types of dependent sources

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Dependent Sources

• Current Controlled Voltage Source (CCVS)
• Voltage Controlled Voltage Source
• (VCVS)
• Current Controlled Current Source
• (CCCS)
• Voltage Controlled Current Source
• (VCCS)

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Dependent Sources

• All the linearly dependent sources have an output
  proportional to the input current or voltage as
  yKx
• The proportionality factor is called gain in the
  dependent sources
• Voltage gain µ (dimensionless)
• Current gain ß (dimensionless)
• Transresistance (transfer resistance) r (ohm)
• Transconductance (transfer conductance)
  g(siemens)

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Circuit Analysis with Dependent Sources

• Turning on and off the dependent voltages sources
  requires turning on and off their independent
  sources
• Superposition, source transformation and circuit
  reduction also apply to active circuits

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Example 1

• What is the output voltage, current and power?

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• Current division to find ix
• Dependent voltage source
• Current division

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• Input-output relationship of the circuit
• Signal inversion K-6000 which means input
  and output have opposite signs
• Output power
• Input power

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• Power gain of the system is greater than one

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Example 2

• Find the output voltage vo in terms of input
  voltage vs.

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Example 2

• Solution

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Node Voltage Analysis with Dependent Sources

• To write the node voltage equations first the
  dependent sources are treated as independent
  sources
• After writing the symmetrical equations the
  dependent sources are expressed in terms of the
  node voltages
• The new sets of non-symmetrical equations are
  solved to find the unknown node voltage equations

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Example 3

• Formulate node-voltage equations
• Find vo and io in terms of is.

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• Solution
• a) Symmetrical node-voltage equations
• Since vxvA the equations can be simplified

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• vovB therefore by solving the equations the vB
  is found

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Mesh Current Analysis with Dependent Sources

• The same pattern as the node-voltage analysis is
  followed
• The mesh current equations are written as if the
  sources are all independent
• The dependent sources are then replaced by their
  equivalent expression in terms of unknown mesh
  currents

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Example 4

• Find current io with mesh analysis.