Oscillators

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					                  Lecture 3 Oscillator
• Introduction of Oscillator
• Linear Oscillator
    – Wien Bridge Oscillator
    – RC Phase-Shift Oscillator
    – LC Oscillator
• Stability


Ref:06103104HKN          EE3110 Oscillator   1
                  Oscillators
Oscillation: an effect that repeatedly and
 regularly fluctuates about the mean value

Oscillator: circuit that produces oscillation

Characteristics: wave-shape, frequency,
 amplitude, distortion, stability
Ref:06103104HKN     EE3110 Oscillator           2
         Application of Oscillators
• Oscillators are used to generate signals, e.g.
    – Used as a local oscillator to transform the RF
      signals to IF signals in a receiver;
    – Used to generate RF carrier in a transmitter
    – Used to generate clocks in digital systems;
    – Used as sweep circuits in TV sets and CRO.



Ref:06103104HKN        EE3110 Oscillator               3
                  Linear Oscillators
1.    Wien Bridge Oscillators
2.    RC Phase-Shift Oscillators
3.    LC Oscillators
4.    Stability




Ref:06103104HKN         EE3110 Oscillator   4
    Integrant of Linear Oscillators
            +              V
   Vs                           Amplifier (A)            Vo
              +
Positive              Vf        Frequency-Selective
                                Feedback Network ()
Feedback

For sinusoidal input is connected
“Linear” because the output is approximately sinusoidal

A linear oscillator contains:
- a frequency selection feedback network
- an amplifier to maintain the loop gain at unity

Ref:06103104HKN                 EE3110 Oscillator              5
            Basic Linear Oscillator
              +            V
       Vs                             A(f)                     Vo
                  +

                            Vf    SelectiveNetwork
                                  (f)

      Vo  AV  A(Vs  V f )         and          V f   Vo
                      Vo    A
                        
                      Vs 1  A
      If Vs = 0, the only way that Vo can be nonzero
      is that loop gain A=1 which implies that
             | A | 1       (Barkhausen Criterion)
              A  0
Ref:06103104HKN                   EE3110 Oscillator                  6
               Wien Bridge Oscillator
              1             1                Frequency Selection Network
Let X C1        and XC2 
             C1           C2                          Z1
Z1  R1  jX C1                                        R1   C1             Z2
                      1
     1      1         jR2 X C 2
Z2                                     Vi                   C2   R2        Vo
      R2  jX C 2    R2  jX C 2

Therefore, the feedback factor,

  Vo   Z2             ( jR 2 X C 2 / R2  jX C 2 )
          
  Vi Z1  Z 2 ( R1  jX C1 )  ( jR 2 X C 2 / R2  jX C 2 )

                   jR 2 X C 2

   ( R1  jX C1 )( R2  jX C 2 )  jR 2 X C 2

  Ref:06103104HKN                  EE3110 Oscillator                            7
 can be rewritten as:
                             R2 X C 2
    
       R1 X C 2  R2 X C1  R2 X C 2  j ( R1 R2  X C1 X C 2 )
For Barkhausen Criterion, imaginary part = 0, i.e.,
                                                               0.34
        R1 R2  X C1 X C 2  0                                 0.32




                                           Feedback factor 
                                                               0.3
                      1 1                                             =1/3
        or   R1 R2                                            0.28

                     C1 C2                                   0.26
                                                               0.24
           1 / R1 R2C1C2                                    0.22
                                                               0.2
                                                                      f(R=Xc)
  Supposing,                                                     1

  R1=R2=R and XC1= XC2=XC,                           Phase      0.5    Phase=0


             RX C                                                0
   
      3RX C  j ( R 2  X C )
                          2
                                                               -0.5


                                                                -1
  Ref:06103104HKN                 EE3110 Oscillator                             Frequency   8
                   1
                              Example
By setting   RC , we get
                           1                                    Rf
Imaginary part = 0 and  
                           3                    R1
Due to Barkhausen Criterion,                               

Loop gain Av=1                                            +
where                                                           C     R
                                                                               Vo
Av : Gain of the amplifier
                             Rf                        R             Z1
Av   1  Av  3  1                           C         Z2
                             R1
                   Rf
Therefore,              2                            Wien Bridge Oscillator
                   R1

 Ref:06103104HKN                  EE3110 Oscillator                            9
         RC Phase-Shift Oscillator
                             Rf

                  R1
                                         C      C   C

                        +
                                                 R   R   R




       Using an inverting amplifier
       The additional 180o phase shift is provided by an RC
        phase-shift network

Ref:06103104HKN              EE3110 Oscillator                 10
Applying KVL to the phase-shift network, we have
V1  I1 ( R  jX C )  I 2 R                                                       C    C        C
0   I1 R              I 2 (2 R  jX C )  I 3 R                      V1                                     Vo
0                      I2R                     I 3 (2 R  jX C )
                                                                                        R        R        R
                                                                                   I1       I2       I3
Solve for I3, we get

                 R  jX C      R        V1
                   R       2 R  jX C   0
                               R
         I3        0                    0
                                              R  jX C      R             0
                                                R       2 R  jX C      R
                                                 0          R        2 R  jX C


                                           V1R 2
    Or          I3 
                     ( R  jX C )[(2R  jX C ) 2  R 2 ]  R 2 (2R  jX C )

    Ref:06103104HKN                              EE3110 Oscillator                                            11
The output voltage,
                                      V1R3
   Vo  I 3 R 
                ( R  jX C )[(2R  jX C ) 2  R 2 ]  R 2 (2R  jX C )
Hence the transfer function of the phase-shift network is given by,
             Vo               R3
             3
             V1 ( R  5RXC )  j ( X C  6 R 2 X C )
                         2           3


For 180o phase shift, the imaginary part = 0, i.e.,
           X C  6 R 2 X C  0 or X C  0 (Rejected)
             3


                     XC  6R 2
                       2


                          1
                      
                         6 RC                Note: The –ve sign mean the
   and,                                      phase inversion from the
                            1
                                          voltage
                            29
  Ref:06103104HKN                   EE3110 Oscillator                      12
                      LC Oscillators
     The frequency selection
      network (Z1, Z2 and Z3)                     
      provides a phase shift of                   Av Ro
      180o                                            ~
     The amplifier provides an                   +
      addition shift of 180o
                                     2       Z1           Z2   1
Two well-known Oscillators:
• Colpitts Oscillator                                     Z3
                                                                        Zp
• Harley Oscillator



    Ref:06103104HKN          EE3110 Oscillator                     13
                               Av Ro                                          Z1
                                   ~                      V f   Vo                Vo
                                                                            Z1  Z 3
                               +
          Vf        Z1                 Z2      Vo         Z p  Z 2 //(Z1  Z 3 )
                                                                    Z 2 ( Z1  Z 3 )
                                       Z3                       
                                                    Zp              Z1  Z 2  Z 3
      For the equivalent circuit from the output
               Ro         Io
                                +            AvVi    Vo    Vo  Av Z p
                                                        or   
      +                    Zp Vo            Ro  Z p Z p    Vi Ro  Z p
       AvVi
                              

      Therefore, the amplifier gain is obtained,
                            Vo           Av Z 2 ( Z1  Z 3 )
                         A    
                            Vi Ro ( Z1  Z 2  Z 3 )  Z 2 ( Z1  Z 3 )
Ref:06103104HKN                             EE3110 Oscillator                             14
The loop gain,
                           Av Z1Z 2
      A 
             Ro ( Z1  Z 2  Z 3 )  Z 2 ( Z1  Z 3 )
If the impedance are all pure reactances, i.e.,
       Z1  jX 1 , Z 2  jX 2 and Z 3  jX 3
                                             Av X 1 X 2
The loop gain becomes, A 
                            jR o ( X 1  X 2  X 3 )  X 2 ( X 1  X 3 )
The imaginary part = 0 only when X1+ X2+ X3=0
    It indicates that at least one reactance must be –ve (capacitor)
    X1 and X2 must be of same type and X3 must be of opposite type
                                                Av X 1  AX
With imaginary part = 0, A                             v 1
                                               X1  X 3   X2
                                                                        X2
For Unit Gain &        180o     Phase-shift,            A  1    Av 
                                                                        X1
Ref:06103104HKN                       EE3110 Oscillator                      15
Hartley Oscillator                       Colpitts Oscillator

                                                  C1
            R     L1                          R
                          C                               L
                                                  C2
                  L2


                1                           1
     o                              o          CT 
                                                         C1C2
           ( L1  L2 )C                     LCT         C1  C2
           L1                              C
     gm                               gm  2
          RL2                              RC1
Ref:06103104HKN           EE3110 Oscillator                   16
                   Colpitts Oscillator
                                         Equivalent circuit
              C1                                L
        R
                      L              +
              C2             C2     V                    R   C1
                                             gmV


   In the equivalent circuit, it is assumed that:
    Linear small signal model of transistor is used
    The transistor capacitances are neglected
    Input resistance of the transistor is large enough

Ref:06103104HKN           EE3110 Oscillator                   17
At node 1,                                           L        I1
   V1  V  i1 ( jL)                                             node 1
                                                     I2                     V
where,                                     +                   I3
    i1  jC2V                    C2     V              R                  C1
                                                  gmV             I4
  V1  V (1   LC 2 )
                    2



Apply KCL at node 1, we have
                      V1
     jC2V  g mV   jC1V1  0
                      R
                                        1       
     jC2V  g mV  V (1   2 LC 2 )  jC1   0
                                        R       
For Oscillator V must not be zero, therefore it enforces,
         1  2 LC2 
     gm  
               R 
                           
                      j  (C1  C2 )   3 LC1C2  0
         R         
 Ref:06103104HKN               EE3110 Oscillator                            18
      1  2 LC2 
  gm  
            R 
                                                
                   j  (C1  C2 )   3 LC1C2  0
      R         

 Imaginary part = 0, we have
           1             C1C2
 o               CT 
           LCT          C1  C2

 Real part = 0, yields
         C2
  gm 
         RC1


Ref:06103104HKN              EE3110 Oscillator        19
                  Frequency Stability
• The frequency stability of an oscillator is
  defined as
           1  d 
                              ppm/ o C
           o  dT    o

• Use high stability capacitors, e.g. silver
  mica, polystyrene, or teflon capacitors and
  low temperature coefficient inductors for
  high stable oscillators.

Ref:06103104HKN               EE3110 Oscillator   20
                  Amplitude Stability
• In order to start the oscillation, the loop gain
  is usually slightly greater than unity.
• LC oscillators in general do not require
  amplitude stabilization circuits because of
  the selectivity of the LC circuits.
• In RC oscillators, some non-linear devices,
  e.g. NTC/PTC resistors, FET or zener
  diodes can be used to stabilized the
  amplitude
Ref:06103104HKN         EE3110 Oscillator       21
Wien-bridge oscillator with bulb stabilization

                  R                   C

                      +

  R        C                                      irms
                          R2

                               Blub                       Operating
                                                            point



                                                                      Vrms

Ref:06103104HKN                EE3110 Oscillator                             22
Wien-bridge oscillator with diode stabilization

                       Rf

                  R1
                            
                                                Vo
                            +
                                C        R

                       R
                  C


Ref:06103104HKN             EE3110 Oscillator        23
                    Twin-T Oscillator
 low pass filter
                                              Filter output

                      
                                                low pass region        high pass region


                      +

 high pass filter



                                                                  fr                           f




Ref:06103104HKN           EE3110 Oscillator                                               24
                          Bistable Circuit
                                                                    vo
                                                                               +Vcc
       v+      +
                                                                         Vth
                                        vo                                            v1
  v1           
                                                             -Vcc

                   vo                                               vo
                   +Vcc                                                        +Vcc

        -Vth                                          -Vth               Vth
                                v1                                                    v1

    -Vcc                                           -Vcc

Ref:06103104HKN                EE3110 Oscillator                                       25
           A Square-wave Oscillator

 vc
            

                       vo
      vf    +
                                         v
                                        + f

                            vc           v
                                        ¡Ð f

                                        +vmax
                            vo
                                          v
                                        ¡ Ð max




Ref:06103104HKN     EE3110 Oscillator    26

				
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