Transcript ELEN136_OpampIntro_Ideal_NonInv_Inv

Operational Amplifiers
What is an Op Amp?
High voltage gain IC with
differential inputs
– Designed to have
characteristics near ideal
Inexpensive, widely used IC
Available in wide range of
packages
Typically require a positive
and a negative power supply
Uses: amplifier, buffer, summer, differentiator,
integrator, comparator, instrumentation amp,
Schmitt trigger, negative impedance, super
diode, logarithmic/exponential output, simulated
inductor
History of Op Amps
Originally designed for analog computers using vacuum
tubes
– Output voltage is a function of input voltage (addition, subtraction,
integration, differentiation, exponential, logarithm…)
K2-W: first mass produced op amp (1952)
– Invented by George Philbrick
– $22. Gain ≈ 20,000. Gain-bandwidth ≈ 1MHz.
Input impedance ≈ 50kΩ
– See picture (K2-W with and without shell)
History of Op Amps
First transistor op amp (μA702) used 12 BJTs
– Invented in 1964 by Bob Widlar
– Sold for $300
– Prone to short circuits
μA709 improved on μA702 (used 14 transistors)
– Invented in 1965 also by Bob Widlar
– Higher gain, more bandwidth, cheaper, more robust
– Sold for $70 to start, then $2 within a few years
741 Op Amp
Introduced in 1968, and versions still
available and in use today
μA741 Op Amp
Op Amp Flavours
High output power
High speed
large bandwidth
Low noise
Low power
Low voltage
Precision
Rail-to-Rail
Small package
>1 Op Amp per package
Ideal Op Amp
• Input resistance is infinite
RIN  
• Output resistance is zero
ROUT  0
• Bandwidth is infinite
• Input current is zero
• Open loop gain is infinite
• Output voltage is zero
when input voltages are
zero
I  0
A
I  0
VOUT
V
 OUT  
V  V
VIN
Ideal Op Amp Gain
If open loop gain of ideal op amp → ∞, what’s
the use?
– Any input will result in + or – saturation
Even non-ideal op amps not useful with open
loop
– Only small input voltages before + or - saturation
Op amps almost never use open loop.
– Use feedback to control the actual gain
Feedback!
Feedback
Positive Feedback
– Output feeds back to input, and increase
output leading to out of control system
– E.g., microphone picks up speaker output,
driving speaker output higher which is picked
up by microphone…
Negative Feedback
– Output feeds back to input to allow system to
adjust and keep output within a certain range
– E.g., body controlling blood glucose levels
Feedback in Op Amps
If output is fed back to non-inverting input –
positive feedback occurs
– Not useful
If output is fed back to inverting input – negative
feedback occurs
– Widely used configuration
Golden Rules for Op-Amps
1. With negative feedback:
The op amp drives the output so that
the two inputs are at equal voltage
2. Assume that the input current is zero.
Buffer or Voltage Follower
No voltage difference between the output and
the input
Buffer draws no current, so it puts no load on the
source. Output current supplied by VCC.
Used to isolate sources from loads
Non-Inverting Amplifier
Non-Inverting Amplifier
V2
AV = Vo/VI
VI = V2 (i.e., Vin+ = Vin- ) … from “Golden Rules”
No current flows into Vin+ (Golden Rule) therefore:
VI = V2 = Vo * R1/(R1 + R2) … voltage divider
AV = Vo/VI = (R1 + R2)/R1 = 1 + (R2 / R1)
Non-Inverting Amplifier
Other Considerations
R2 can’t be too low since the Op Amp has
limited current capability
R1 should be much smaller than the input
impedance
Circuit voltage gain should be much less
than the open loop gain of the Op Amp
The output voltage swing has to be less
than the supply voltages
Non-Inverting Amplifier
Examples
(from course package)
Inverting Amplifier
Inverting Amplifier
Current through R1 equals the current
through Rf
No current into the inputs
The voltage at both op amp inputs is zero
Inverting Amplifier
• Current through R1
• Current through Rf
V1  0 V1
I1 

R1
R1
VO  0
VO
I2  

Rf
Rf
Inverting Amplifier
Why the minus sign for the current through
Rf?
– The convention for Ohm’s Law is that the
current flows from the high voltage to the low
voltage for a resistor
– Here the current flows from the low voltage
(ground) to the high voltage (VO)
Inverting Amplifier
• The current through R1
must equal the current
through R2 since there is
no current in the inputs.
• Combining the two
Rf
VOUT  VIN
equations for the
R1
currents
Inverting Amplifier Examples
(from course package)
Op Amp Applications
Arithmetic
– Summing, differencing
Calculus
– Integration, differentiation
Level detectors
– Comparators, Schmitt Triggers