Transcript Document 7341187

ECE 20B: Introduction to Electrical and
Computer Engineering
Winter 2003
Recitation 1: Operational Amplifiers
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Ideal Amplifier
 “Amplifies” weak (= low voltage) electrical signals. E.g.
Cassette/CD player, strain gauge, accelerometer.
 Ideal amplifier: Output Signal = Gain x Input Signal
 Ideal amplifier: has infinite input resistance, zero output
resistance.
- Infinite input resistance: Does not load input signal
- Zero Output resistance: Does not “eat up” output signal

Gain of ideal amplifier A = Voutput/Vinput
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Ideal Amplifier…contd.
 Schematic of amplifier
RS
+
-
Rout
+
vS
vin
Rin
+
-
+
Avin
vL
RL
-
-
 (Figure 12.3)
Rin = equivalent resistance seen at
input of amplifier; Rout = internal (output) resistance
of amplifier
 vin = (Rin / (RS + Rin)) vS
 vL = Avin (RL / (Rout + RL))
(Rin / (RS + Rin))] vS
= vin [A(RL / (Rout + RL))
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Operational Amplifiers
 Op-amp:
4 inputs, 1 output
+V positive power supply
Inverting input
Output goes positive when non-inverting
input (+) goes more positive than the
inverting input (-), and vice-versa.
_
+
Vout
Non-inverting input
-V negative power supply
(v+ - v-)
 Vout = AV(OL)
 Amplification factor, or gain, AV(OL) is called the open-loop
voltage gain; typically O(105 – 107)
 Open-loop assumption (Rizzoni Eq. 12.10):
iin = 0
(“Golden Rule #2: The inputs of an op-amp draw no current.” – cf.
Horowitz and Hill textbook)
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Operational Amplifier…contd.
 Consider some typical values:



Ri = 105 – 1012 Ohms
Ro = 1 – 50 Ohms
A = 105 – 107 V/V
 Suppose A = 105 , +V = 12V, -V = -12V




120uV achieves saturation (output voltage cannot exceed supply)
Current into input terminals is 120uV / 105 Ohms = 120 x 10–11 A
(open circuit)
Rout is low, approximated as 0
 Vout = A(v+ - v-)
 How does op-amp output vary with A when v- is sinusoidal?
• A continuous sinusoid generates a square wave as output
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Square wave output
 For a sinusoid, the output of Op-amp is a square wave
with only two distinct voltage levels –1V and +1V
 We can represent the voltage levels as ‘0’ (= -1V) and ‘1’
(= +1v).
 Op-amp is a primitive digital element
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Op-amp comparator
 In comparator configuration of Op-amp, the inverting
input is connected to ground and input is given in noninverting input.
 If the input signal is slightly positive, then the output
jumps to V+ ( = supply voltage)
 If the input- signal is slightly negative, then the output
jumps to V (= - supply voltage)
 The output jumps between two extremes V+ and V- since
the open-loop gain is very high.
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Op-amp – Digital output in open loop mode
 Output of comparator in open-loop mode
Source: http://www.tonmeister.ca/main/textbook/electronics/12.html
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Feedback
 Negative feedback:
process of coupling the output back
in such a way as to cancel some of the input



Lowers gain, but amplifier characteristics become less
dependent on characteristics of the open-loop (no-feedback)
amplifier; eventually depend only on properties of the feedback
network itself
A “self-balancing mechanism” that allows amplifier to preserve
zero potential difference between its input terminals
Feedback can also be positive (oscillators, etc.)
 Observe:
voltage gain is so high that a tiny voltage
between input terminals will swing the output over its
entire range

Ignore this small voltage  “Golden Rule #1: The output
attempts to do whatever is necessary to make the voltage
between the inputs zero.”
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Inverting (gain = negative) Amplifier
R2
R1
A
in
B
 Point B is at ground  Point A is also (G.R. #2)
  voltage across R2 is Vout , and voltage across R1 is Vin
 G.R. #1  across R2 is Vout / R2 = - Vin / R1
 Voltage gain = across R2 is Vout / Vin = - R2 / R1
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Non-Inverting (gain = positive) Amplifier
 VA comes from a voltage divider  VA = VoutR1 / (R1 + R2)
 G.R. #2  VA = Vin
 Gain = Vout / Vin = 1 + R2 / R1
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Voltage follower
 Output voltage follows input voltage.
 Gain = 1 since feedback resistance R2 = 0
 Is used as a buffer to isolate input signal from output
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Mixer amplifier
 A mixer amplifier mixes several input signals and
amplifies them at various levels
 Inputs from several sources are connected to the
inverting input of the Op-amp as shown
 The gain can be varied by modifying the series
resistances
 The total voltage at the output will be
Vout = -(v1 (Rf/R1) + v2 (Rf/R2))
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Op-amp oscillators
 An Op-amp with a
positive feedback
produces an oscillator
 An oscillator produces
output voltage without
any input signal
 Positive feedback refers
to the case where output
is fed back to the input
such that it augments the
input signal
 The Op-amp circuit with
a single R and C
produces a square wave
output with a frequency
of 1/(2RC)
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Op-amp oscillators…contd
 RC phase-shift oscillators are used to produce sinusoidal
outputs
 A RC network is used in the positive feedback loop to
shift phase by desired amount
 A simple sinusoidal oscillator shown below consists of
three CR ladders cascaded and given to inverting input
of Op-amp
C1
C2
+V
C3
R1
R2
R3
vout
+
-V
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Op-amp summary
Source: http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/Op-ampcon.html
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