EE 230 Lecture 25 Spring 2010

EE 230 Lecture 25 Spring 2010 - EE 230 Lecture 25 Waveform...

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EE 230 Lecture 25 Waveform Generators - Sinusoidal Oscillators The Wein-Bridge Structure
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Quiz 19 The circuit shown has been proposed as a sinusoidal oscillator. Determine the oscillation criteria and the frequency of oscillation. Assume the op amps are ideal. C R C R R X R 1A R 1A R
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And the number is ? 1 3 8 4 6 7 5 2 9 ?
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Quiz 19 The circuit shown has been proposed as a sinusoidal oscillator. Determine the oscillation criteria and the frequency of oscillation. Assume the op amps are ideal. C R C R R X R 1A R 1A R X X X V sRC XX G V sC+G - G + = 0 sRC ⎛⎞ ⎜⎟ ⎝⎠ () ( ) () 22 2 X Ds=sC+sCG - G +G 2 2 X G - G 1 Ds=s+s + C RC Oscillation criteria: G=G X OSC 1 ω = RC Solution:
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Sinusoidal Oscillation A circuit with a single complex conjugate pair of poles on the imaginary axis at +/- j β will have a sinusoidal output given by ( ) ˆ ) OUT k Xt = 2 a s i n ( t + β θ The frequency of oscillation will be β rad/sec but the amplitude and phase are indeterminate Review from Last Time:
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Sinusoidal Oscillation Criteria A network that has a single complex conjugate pair on the imaginary axis at and no RHP poles will have a sinusoidal output of the form X 0 (t)=Asin( ω t+ θ ) j ω ± A and θ can not be determined by properties of the linear network Review from Last Time:
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Characteristic Equation Requirements for Sinusoidal Oscillation If the characteristic equation D(s) has exactly one pair of roots on the imaginary axis and no roots in the RHP, the network will have a sinusoidal signal on every nongrounded node. OUT Characteristic Equation Oscillation Criteria: Review from Last Time:
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Characteristic Equation Oscillation Criteria (CEOC) If the characteristic equation D(s) has exactly one pair of roots on the imaginary axis and no roots in the RHP, the network will have a sinusoidal signal on every nongrounded node Barkhausen Oscillation Criteria A feedback amplifier will have sustained oscillation if A β = -1 Differences: 1.Barkhausen requires a specific feedback amplifier architecture 2.Sustained oscillation says nothing about wave shape Challenge: It is impossible to place the poles of any network exactly on the imaginary axis Sinusoidal Oscillator Design Approach: Place on pair of cc poles slightly in RHP and have no other RHP poles With this approach, will observe minor distortion of output waveforms Review from Last Time: Relationship between Barkhausen Criteria and Characteristic Equation Criteria for Sinusoidal Oscillation
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EE 230 Lecture 25 Spring 2010 - EE 230 Lecture 25 Waveform...

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