Operational Amplifiers

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Operational Amplifiers

• Team 05
• Emily Baker
• Rollin Garcia
• Andrew Herman
• Bryan Reemmer
• Tania Yusaf

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Topics

• History
• Ideal Op-Amps
• Limitations
• Fixes
• Op-Amp Applications

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Op-Amp

• High Gain Voltage amplifier
• Amplifies difference between 2 inputs
• Positive and negative effect

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History

• Vacuum Tube Era, 1950s
• 1st used in Analog Computers
• Addition
• Subtraction
• Integration
• Differentiation
• Heavy
• Prone to failure

Analog Computer
K2-W tubes general purpose Op-Amp. 1952
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History (cont.)

• Now in Integrated Circuits
• 1965- Bob Widlar
• 1st integrated Op Amp bipolar Fairchild µA709
• Lacked short circuit protection
• 2nd 741
• Better performance
• More stable
• Easier to use

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History (cont.)

• Major Differences
• Internal compensation capacitor
• Extra transistorsshort circuit protection
• New Designs based on
• FET (1970s)
• MOSFET (1980s)

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Implementation of Op-Amps

• Non-Inverting
• Inverting

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Implementation of Op-Amps

• Integrator
• Differentiator

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Implementation of Op-Amps

• Summing

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Op-Amp Data Sheets

• V Max rail voltage
• V- Min rail voltage
• OUTPUT Vin (resistor ratio 1)

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The Ideal Op-Amp
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Voltage Clipping

• Output is AT MOST the supply voltage.
• Output swing further limits the range.
• Parasitic values lead to less than 100
  efficiency.
• With a 15V supply, one gets a 28V output swing.

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Slew Rate

• Maximum rate of change of the output voltage for
  all possible input signals.
• More than 3 distortion if you exceed the slew
  rate.

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Output Swing vs. Frequency

• This graph reflects a combination of both the DC
  output swing and the slew rate.

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Gain-Bandwidth Product

• The GBW for an amplifier is the product of the
  open loop gain and its 3 dB bandwidth.
• This is about 1 MHz for the LM741.

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GBP Closed-Loop

• It can be shown that
• Where
• K ideal gain
• ADM open-loop gain

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GBP Closed-Loop

• It can be shown that
• Where
• K ideal gain
• ADM open-loop gain

Error Multiplier
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What Does This Mean?

• With a slight approximation of ADM, the error
  term reduces to the equation for a pole
• Where

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High-Frequency Response

• Constant gain.
• What happens at higher frequencies?

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High Frequency Response

• At a frequency fc the Bode plot of the Op-Amp and
  the gain of the amplifier meet.
• Past fc the gain of the non-inverting amplifier
  follows the ADM (open-loop gain) plot.

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Stability

• The distance from ADM to 1/? is ADM?.
• Intersection point is ADM?1.
• IF ADM?gtgt1 then the gain is K.
• IF ADM?ltlt1then the gain is ADM?K.
• IF ADM?1 then the gain is

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Stability

• The meaning of this equation is at fc measure the
  angle of ADM and place that angle into ADM?.
• This equation can cause the instability of the
  circuit.
• If ADM?180 then the gain is infinity.

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Stability

• A circuit will be stable if at the frequency
  where
• ANG(ADM?) 180 MAG(ADM?)lt1
• PHASE MARGIN(PM) 180-ANG(ADM?)
• ROC (SLOPE(1/?)-SLOPE(ADM)) at fc

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Stability

• For a circuit to be stable
• PMgt45
• 20Db/decltROClt40Db/dec
• For a circuit to be marginally stable
• 0ltPMlt45
• ROC40Db/dec
• For a circuit to be unstable
• PMlt0
• ROCgt40Db/dec

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Beta Circuit

• Unstable.
• Due to the feedback loop.
• Also due to the 1/? term.

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Beta Circuit
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Beta Circuit

• Let C10.1µF and R210K?
• Gain(-R2C2)S where Sj?
• 1/?(1C1 R2S)
• f11/(2?C1R2)159.15Hz
• fc12.616kHz

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Beta Circuit

• Will not give you 1/?, but ?.
• Take off the op-amp and apply a test voltage at
  the output.
• Short the input.

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Beta Circuit

• Gives ?
• Is a flip over the ? axis
• Need to add a zero instead of a pole
• V?? (Voltage divider)
• (1C1 R2S)-1
• Add R1 in series with C1

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Beta Circuit

• Now there is a zero.

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Beta Circuit

• Need the zero before fc
• fz1/(2?C1R1)
• Choose fz to be at 9kHz.
• R1177?
• Since R2gtgtR1, f1 stays approximately where it is.

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Beta Circuit
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Beta Circuit
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Beta Circuit

• Check the phase margin.
• Check the ROC.
• The data sheet gives the open loop gain.

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Op-Amp Applications

• Op-Amps are used in many different situations
  such as
• Digital-to-Analog Converters (DAC)
• Active Filters
• Precision Rectifiers
• Pre-Amplifiers
• Voltage Clamps

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Op-Amp Applications (cont.) Digital-to-Analog
Converter (DAC)

• DACs commonly used in MP3 and CD players.
• Op-Amp significance
• Serves as a summer of digital inputs.
• Outputs an analog signal based on gain.

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Op-Amp Applications (cont.) Active Filters

• Op-Amps frequently used in designs.
• Active Components
• Similar to transistors or vacuum tube
  applications.
• Op-Amp significance
• Used to shape filters response.
• Used to buffer the filter from other components.

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Op-Amp Applications (cont.) Precision Rectifiers

• a.k.a Super Diode
• Used in high precision signal processing.
• Converts AC to DC.
• Op-Amp significance
• Aids in controlling the diode
• operation.
• Input positive Diode on
• Input negative Diode off

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Op-Amp Applications (cont.) Pre-Amplifiers

• Precedes a larger amplifier.
• Used to prepare a signal for greater
  amplification.
• Used in many audio applications.
• Op-Amp significance
• Input Low-level signal (Microphone)
• Output Line-level signal (MP3, TV)

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Op-Amp Applications (cont.) Voltage Clamps

• Used to measure ion currents.
• Voltage held at set level.
• Consists of generator with two electrodes.
• Op-Amp significance
• Holds voltage at designated set level.
• Sends error signal.

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Questions?