TELECOMMUNICATIONS

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TELECOMMUNICATIONS

• Dr. Hugh Blanton
• ENTC 4307/ENTC 5307

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RADIO FREQUENCY OSCILLATORS

• In the most general sense, an oscillator is a non
  linear circuit that converts DC power to an AC
  waveform.
• Most oscillators used in wireless systems provide
  sinusoidal outputs, thereby minimizing undesired
  harmonics and noise sidebands.

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• The basic conceptual operation of a sinusoidal
  oscillator can be described with the linear
  feedback circuit.

Vo(w)
Vi (w)
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• An amplifier with voltage gain A has an output
  voltage Vo.
• This voltage passes through a feedback network
  with a frequency dependent transfer function H(w)
  and is added to the input Vi of the circuit.
• Thus the output voltage can be expressed as

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• If the denominator of the previous equation
  becomes zero at a particular frequency, it is
  possible to achieve a nonzero output voltage for
  a zero input voltage, thus forming an oscillator.
  
• This is known as the Barkhausen criterion.
• In contrast to the design of an amplifier, where
  we design to achieve maximum stability,
  oscillator design depends on an unstable circuit.

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General Analysis

• There are a large number of possible RF
  oscillator circuits using bipolar or field-effect
  transistors in either common emitter/source,
  base/gate, or collector/drain configurations.
• Various types of feedback networks lead to the
  well-known oscillator circuits
• Hartley,
• Colpitts,
• Clapp, and
• Pierce

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• All of these variations can be represented by a
  general oscillator circuit.

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• The equivalent circuit on the right-hand side of
  the figure is used to model either a bipolar or a
  field-effect transistor.
• We can simplify the analysis by assuming real
  input and output admittances of the transistor,
  defined as Gi and Go, respectively, with a
  transistor transconductance gm.
• The feedback network on the left side of the
  circuit is formed from three admittances in a
  bridged-T configuration.
• These components are usually reactive elements
  (capacitors or inductors) in order to provide a
  frequency selective transfer function with high
  Q.

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• A common emitter/source configuration can be
  obtained by setting V2 0, while common
  base/gate or common collector/drain
  configurations can be modeled by setting either
  V1 0 or V4 0, respectively.

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• The feedback path is achieved by connecting node
  V3 to node V4.
• Writing Kirchoffs current law for the four
  voltage nodes of the circuit gives the following
  matrix equation

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• Recall from circuit analysis that if the ith node
  of the circuit is grounded, so that V 0, the
  matrix will be modified by eliminating the ith
  row and column, reducing the order of the matrix
  by one.
• Additionally, if two nodes are connected
  together, the matrix is modified by adding the
  corresponding rows and columns.

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Oscillators Using a Common Emitter BJT

• Consider an oscillator using a bipolar junction
  transistor in a common emitter configuration.
• V2 0, with feedback provided from the
  collector, so that V3 V4.
• In addition, the output admittance of the
  transistor is negligible, so we set Go 0.

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• These conditions serve to reduce the matrix to
  the following
• where V V3 V4

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• If the circuit is to operate as an oscillator,
  then the new determinant must be satisfied for
  nonzero values of V1 and V, so the determinant of
  the matrix must be zero.
• If the feedback network consists only of lossless
  capacitors and inductors, then Y1,Y2, and Y3 must
  be imaginary, so we let Y1 jB1, Y2 jB2. and
  Y3 jB3.
• Also, recall that the transconductance, gm , and
  transistor input conductance are Gi, are real.

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• Then the determinant simplifies to

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• Since gm and Gi are positive, X1 and X2 must have
  the same sign, and therefore are either both
  capacitors or both inductors.
• Since X1 and X2 have the same sign, X3 must be
  opposite in sign from X1 and X2, and therefore
  the opposite type of component.
• This conclusion leads to two of the most commonly
  used oscillator circuits.

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Colpitts Oscillator

• If X1 and X2 are capacitors and X3 is an
  inductor, we have a Colpitts oscillator.

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Hartley Oscillator

• If we choose X1 and X2 to be inductors, and X3 to
  be a capacitor, we have a Hartley oscillator.

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Lab 5

• Implement the following Colpitts oscillator using
  PSpice.

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• Determine the frequency of the tank circuitwhich
  sets the oscillation frequency.
• When we display the output waveform (from 0 to 10
  ms), there is no signal!
• The problem is one of insufficient spark.
• One solution is to pre-charge one of the tank
  capacitors.
• Using either CT1 or CT2, initialize either
  capacitor with a small voltage (such as .1 v).

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• Again, display the output waveform from 0 to 10
  ms.
• This time the signal existsbut clearly, it has
  not reached steady-state conditions by 10 ms.
• Using the No-Print Delay option, display the
  waveform from 200 to 210 ms.
• Measure the resonant frequency and compare it to
  the calculated value.
• Are they similar?

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• Add a plot of Vf (the feedback signal shown in
  the figure).
• Is Vf 180? out of phase with Vout?
• Generate a frequency spectrum for the Colpitts
  oscillator.
• Is there a DC component?
• Does the fundamental frequency approximately
  equal measured the time-domain frequency?