Introduction to OpAmps and the Frequency Domain

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Introduction toOp-Ampsand theFrequency Domain
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What This Course is All AboutFour Central Ideas
of Engineering

• The Dual Variables of Effort and Flow
• how power flows between interacting objects,
  regardless of their domain (e.g. Electrical,
  Mechanical, Thermal, Biological, etc).
• State
• how systems remember the past, and which results
  from the time integration and storage of energy.
• Transduction
• the bidirectional transformation of effort and
  flow from one domain to another.
• Feedback
• used in almost all engineered devices to bring
  about desired behavior despite undesired
  disturbances.

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Who is this guy?
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The OPA551 Op-Amp
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A Zero-Order Model of Op-Amps
Forklift
Left Eye Negative Input Right Eye Positive
Input Actuates Biceps if Right Eye gt Left
Eye Actuates Triceps if Left Eye gt Right
Eye Rate of Arm Motion Proportional
to Difference eyes see Proportionality Constant
is very High Eyes Dont Disturb what they look
at Due to buff build, arms cant extend or
contract all the way
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Our first Model of an Op-Amp
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Output Saturation
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Our second Model of an Op-Amp
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Finite Slew Rate
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Our third Model of an Op-Amp
Next Time Flattening out at Low
Frequencies Feedback
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Bode Plot of OPA551Open Loop Response
Looks Like an Integrator From about 10 Hz to 100
KHz
0dB is at 2 MHz ! Gain at 10Hz is over 100 dB!
100dB 20 log10(Vgain) 5 log10(Vgain)
Vgain 105 100,000 WOW!
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Who is this guy?
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Jean Baptiste Joseph Fourier

• Born 21 March 1768 in Auxerre, Bourgogne, France
• Died 16 May 1830 in Paris, France
• 1807 On the Propagation of Heat in Solid
  Bodies
• Won 1811 Paris Institute Mathematics Prize
• Much political mathematical wrangling with
• Lagrange
• Laplace
• Legendre
• Biot
• Poisson
• Carnot
• Napoleon (!)
• Mathematics compares the most diverse phenomena
  and discovers the secret analogies that unite
  them.

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Our link to Fourier

• Fourier Series
• Represent a time-domain signal as the sum of a
  number of sine waves of different frequencies,
  phases, and amplitudes
• Fourier Transform
• Convert a time-domain signal into a frequency
  domain waveform and visa-versa

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What Do these Do?
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How about This?
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Anybody Ever Seen These?
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Basic Idea
Measure response as we change w
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Important Class of SystemsLinear Systems
H
a(t)
H(a(t))
H
b(t)
H(b(t))
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Important Class of SystemsLinear Systems
H
a(t)b(t)
H(a(t)) H(b(t))
H
k a(t)
k H(a(t))
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Do you think This is Linear?
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If sine waves go in,and System is Linear,what
might come out?
Im Linear, Ha! Ha! Ha!
Amplitude
Phase
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Are Time-Integrators Linear?
i.e. Are the Following True?
YES!
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Back to IntegratorsIf sine goes in, what Comes
Out?
Input frequency goes up by 10x, output amplitude
goes down by 10x Output phase is always 90
degrees delayed from input.
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The Bode Plot
Developed 1930s Published 1945
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Essential Characteristicsof Bode Plots
Magnitude in dB
Phase in degrees (or radians)
Frequency in Hz or radians/sec LOG SCALE
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Whats a dB? Acoustically
Phenomena Our ears are sensitive to the log of
acoustic power. 10 times power 10 dB 100 times
power 20 dB 1000 times power 30 dB
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Rock Roll (120 dB) power compared to Rustling
Leaves (20 dB) power
120dB 20dB 100dB
100dB 1010 power ratio RR 10 Billion Times
more power than rustling leaves
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dB for Voltage and Current is a little different
dB for Power
dB for Voltage or Current
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Bode Plot of an Integrator
-90 degrees phase -20dB/decade 0dB at 1 rad/sec