Experiment 4

1
Experiment 4

• Operational Amplifiers
• Op-Amp Circuits
• Op-Amp Analysis

2
Operational Amplifiers

• Op-Amps are possibly the most versatile linear
  integrated circuits used in analog electronics.
• The Op-Amp is not strictly an element it
  contains elements, such as resistors and
  transistors.
• However, it is a basic building block, just like
  R, L, and C.
• We treat this complex circuit as a black box!
• Do we know all about the internal details? No!
• Do we know how to use it and interface it with
  other electronic components? Yes, we must!

3
Op-Amp Circuits perform Operations

• Op-Amps circuits can perform mathematical
  operations on input signals
• addition and subtraction
• multiplication and division
• differentiation and integration
• Other common uses include
• Impedance buffering
• Active filters
• Active controllers
• Analog-digital interfacing

4
The Op-Amp Chip

• The op-amp is a chip, a small black box with 8
  connectors or pins (only 5 are usually used).
• The pins in any chip are numbered from 1
  (starting at the upper left of the indent or dot)
  around in a U to the highest pin (in this case
  8).

741 Op Amp
5
Op-Amp Input and Output

• The op-amp has two inputs, an inverting input (-)
  and a non-inverting input (), and one output.
• The output goes positive when the non-inverting
  input () goes more positive than the inverting
  (-) input, and vice versa.
• The symbols and do not mean that that you
  have to keep one positive with respect to the
  other they tell you the relative phase of the
  output. (VinV1-V2)

A fraction of a millivolt between the input
terminals will swing the output over its full
range.
6
Powering the Op-Amp

• Since op-amps are used as amplifiers, they need
  an external source of power.
• The op-amp must be connected to an external
  constant DC source in order to function.
• Typically, this source will supply 15V at V and
  -15V at -V. The op-amp will output a voltage
  range of of somewhat less because of internal
  losses.

The power inputs determine the output range of
the op-amp. It can never output more than you
put in. Here the maximum range is about 28 volts.
7
Op-Amp Intrinsic Gain

• Amplifiers increase the magnitude of a signal by
  multiplier called a gain -- A.
• The internal gain of an op-amp is very high
  (105-106).
• The exact gain is often unpredictable.
• We call this gain the open-loop gain or intrinsic
  gain.

8
Op-Amp Saturation

• Note that in spite of the huge gain, the maximum
  or minimum output is still limited by the input
  power.
• When the op-amp is at the maximum or minimum
  extreme, it is said to be saturated.
• Ideally, the saturation points for an op-amp are
  equal to the power voltages, in reality they are
  1-2 volts less.

9
Internal Model of a Real Op-amp

• Zin is the input impedance (very large 2 MO)
• Zout is the output impedance (very small 75 O)
• Aol is the open-loop gain

10
Real Op-Amp Characteristics

• dc-coupled the op amp can be used with ac and dc
  input voltages
• differential voltage amplifier the op amp has
  two inputs (inverting and non-inverting)
• single-ended low-resistance output the op amp
  has one output whose voltage is measured with
  respect to ground. The output looks like a
  voltage source.
• very high input resistance the op-amp input
  looks like a load circuit to any circuit
  connected to its input (ideally 0 current
  actually lt 1nA)
• very high voltage gain the op-amp will saturate
  either positive or negative depending on the
  inputs

11
Problems using op-amps directly as amplifiers

• The op-amp intrinsic gain, Aol, can be relied
  upon to be very large (1 to 5 million V/V ) but
  cannot be relied upon to be an accurate stable
  value.
• Using op-amps, we can construct circuits whose
  performance depends mainly on passive components
  selected to have accurate and stable values.
• As long as Aol is large enough, the behavior of
  our circuits will depend upon the values of the
  stable components rather than Aol
• Feedback is the process of coupling the op-amp
  output back into one of the inputs.
  Understanding feedback is fundamental to
  understanding op-amp circuits.

12
Types of Feedback

• Negative Feedback
• As information is fed back, the output becomes
  more stable. Output tends to stay in the desired
  range.
• Examples cruise control, heating/cooling systems
  
• Positive Feedback
• As information is fed back, the output
  destabilizes. The op-amp will saturate.
• Examples Guitar feedback, stock market crash

13
Op-Amp Circuits use Negative Feedback

• Negative feedback couples the output back in such
  a way as to cancel some of the input.
• This lowers the amplifiers gain, but improves
• Freedom from distortion and nonlinearity
• Flatness of frequency response or conformity to
  some desired frequency response
• Stability and Predictability
• Insensitivity to variation in Aol
• Amplifiers with negative feedback depend less
  and less on the open-loop gain and finally depend
  only on the properties of the feedback network
  itself.

14
Op-Amp Circuits

• Op-Amp circuits we will do now
• inverting amplifier (multiply signal by negative
  gain)
• non-inverting amplifier (multiply signal by
  positive gain)
• differential amplifier (multiply difference
  between two signals by a positive gain)
• Op-Amp circuits we will do in experiment 8
• weighted adder
• integrator
• differentiator
• buffer (voltage follower)

15
Inverting Amplifier
16
Non-inverting Amplifier
17
Differential (or Difference) Amplifier
18
PSpice circuit you will use in exp 4
19
Op-Amp Analysis

• We assume we have an ideal op-amp
• infinite input impedance (no current at inputs)
• zero output impedance (no internal voltage
  losses)
• infinite intrinsic gain
• instantaneous time response

20
Golden Rules of Op-Amp Analysis

• Rule 1 VA VB
• The output attempts to do whatever is necessary
  to make the voltage difference between the inputs
  zero.
• The op-amp looks at its input terminals and
  swings its output terminal around so that the
  external feedback network brings the input
  differential to zero.
• Rule 2 IA IB 0
• The inputs draw no current
• The inputs are connected to what is essentially
  an open circuit

21
How to analyze a circuit with an op-amp

• 1) Remove the op-amp from the circuit and draw
  two circuits (one for the and input terminals
  of the op amp).
• 2) Write equations for the two circuits.
• 3) Simplify the equations using the rules for op
  amp analysis and solve for Vout/Vin

22
Analysis of Non-inverting Amplifier
Note that step 2 uses a voltage divider to find
the voltage at VB relative to the output voltage.
23
Analysis of Difference Amplifier(1)
24
Analysis of Difference Amplifier(2)
Note that step 2(-) here is very much like step
2(-) for the inverting amplifier and step 2()
uses a voltage divider.
What would happen to this analysis if the pairs
of resistors were not equal?
25
Op-Amp Cautions (1)

• In all op-amp circuits, the golden rules will
  be obeyed only if the op-amp is in the active
  region, i.e., inputs and outputs are not
  saturated at one of the supply voltages.
• Typically it can swing only to within 1-2V of the
  supplies.
• There must always be negative feedback in the
  op-amp circuit. Otherwise, the op-amp is
  guaranteed to go into saturation.
• Do not not mix the inverting and non-inverting
  inputs.

26
Op-Amp Cautions (2)

• Many op-amps have a relatively small maximum
  differential input voltage limit. The maximum
  voltage difference between the inverting and
  non-inverting inputs might be limited to as
  little as 5 volts in either polarity. Breaking
  this rule will cause large currents to flow, with
  degradation and destruction of the op-amp.
• Note that even though op-amps themselves have a
  high input impedance and a low output impedance,
  the input and output impedances of the op-amp
  circuits you will design are not the same as that
  of the op-amp.