Loop Analysis 3.2 Circuits with OpAmps 3.3

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Loop Analysis (3.2)Circuits with Op-Amps (3.3)

• Prof. Phillips
• February 19, 2003

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Op Amps

• Op Amp is short for operational amplifier.
• An operational amplifier is modeled as a voltage
  controlled voltage source.
• An operational amplifier has a very high input
  impedance and a very high gain.

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Use of Op Amps

• Op amps can be configured in many different ways
  using resistors and other components.
• Most configurations use feedback.

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Applications of Op Amps

• Amplifiers provide gains in voltage or current.
• Op amps can convert current to voltage.
• Op amps can provide a buffer between two
  circuits.
• Op amps can be used to implement integrators and
  differentiators.
• Lowpass and bandpass filters.

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The Op Amp Symbol
High Supply
Non-inverting input
Output
Inverting input
Ground
Low Supply
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The Op Amp Model
v
Non-inverting input

vo
Rin


Inverting input
A(v -v- )
v-
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Typical Op Amp

• The input resistance Rin is very large
  (practically infinite).
• The voltage gain A is very large (practically
  infinite).

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Ideal Op Amp

• The input resistance is infinite.
• The gain is infinite.
• The op amp is in a negative feedback
  configuration.

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The Basic Inverting Amplifier
R2
R1




Vin
Vout

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Consequences of the Ideal

• Infinite input resistance means the current into
  the inverting input is zero
• i- 0
• Infinite gain means the difference between v and
  v- is zero
• v - v- 0

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Solving the Amplifier Circuit

• Apply KCL at the inverting input
• i1 i2 i-0

R2
i2
R1

i1
i-
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KCL
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Solve for vout

• Amplifier gain

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Recap

• The ideal op-amp model leads to the following
  conditions
• i- 0 i
• v v-
• These conditions are used, along with KCL and
  other analysis techniques, to solve for the
  output voltage in terms of the input(s).

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Where is the Feedback?
R2
R1




Vin
Vout

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Review

• To solve an op-amp circuit, we usually apply KCL
  at one or both of the inputs.
• We then invoke the consequences of the ideal
  model.
• The op amp will provide whatever output voltage
  is necessary to make both input voltages equal.
• We solve for the op-amp output voltage.

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The Non-Inverting Amplifier




vin
vout
R2
R1

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KCL at the Inverting Input




i-
vin
vout
i1
i2
R2
R1

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KCL
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Solve for Vout
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A Mixer Circuit
Rf
R1
R2

v1




v2
vout

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KCL at the Inverting Input
Rf
R1
i1
if
R2

v1
i2

i-



v2
vout

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KCL
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KCL
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Solve for Vout
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Class Example