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Operational Amplifiers

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

Topics

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

Op-Amp

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

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

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

History (cont.)

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

Implementation of Op-Amps

- Non-Inverting
- Inverting

Implementation of Op-Amps

- Integrator
- Differentiator

Implementation of Op-Amps

- Summing

Op-Amp Data Sheets

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

The Ideal Op-Amp

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.

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.

Output Swing vs. Frequency

- This graph reflects a combination of both the DC

output swing and the slew rate.

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.

GBP Closed-Loop

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

GBP Closed-Loop

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

Error Multiplier

What Does This Mean?

- With a slight approximation of ADM, the error

term reduces to the equation for a pole - Where

High-Frequency Response

- Constant gain.
- What happens at higher frequencies?

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.

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

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.

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

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

Beta Circuit

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

Beta Circuit

Beta Circuit

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

Beta Circuit

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

the output. - Short the input.

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

Beta Circuit

- Now there is a zero.

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.

Beta Circuit

Beta Circuit

Beta Circuit

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

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

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.

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.

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

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)

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.

Questions?

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