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ECSE-2010
Lecture 6.1
Amplifier circuit model
Ideal Operational Amplifiers (Op Amps)
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sv
+
−Ov
+
−
Voltage
Amplifier
O sWant v A v ; A Voltage Gain≈ [email protected] www.rpi.edu/~sawyes 3
+
−
1Av1R
OR
Ov
+
−
1v
+
−
1R Input Resistance=
OR Output Resistance=
O 1 O Ov Av i R= −
Oi
1i
O O 1For small R ; v Av≈[email protected] www.rpi.edu/~sawyes 4
Add source network at input:Model with Thevenin Equivalent circuit
vT in series with RT
Add load network at output:Model with Req
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Tv
TR
1R
OR
eqR1Av
+
−1v
+
−
11 T
1 T
Rv v
R R
= +
eqO 1
O eq
Rv Av
R R
= +
Ov
+
−
1i Oi1iOi
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1
ECSE-2010
Lecture 6.2
Op Amps Without negative feedback
With negative feedback (Circuits)
OP Amp CAD Interactive Learning Module (ILM)
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1v
No Negative Feedback
Ov
1 O CCIf v 0, v V> = + Saturation+
1 O CCIf v 0, v V< = − Saturation−
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1v
2v
Ov
No Negative Feeback
1 2 O CCIf v v v V> => = +
1 2 O CCIf v v v V< => = −
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For most Op Amp circuits, we add negative feedback:
Circuit connection between vO and vN
Helps to keep Op Amp in Linear Range
This will help keep vP = vN
Output, vO = A(vp - vN), will be finite, as long as its magnitude is less than VCC
Output can never be greater than +VCC
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Pv
Nv
Ov
P Nv v= Negative Feedback
O Sv v=
S PApply v to v
Sv
Sv=
SvSv
Draws No Current from SourceBuffer, or Isolation Amplifier
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2
1R
2R
Nv
PvSv
0 =
0
S1
1
v 0i
R
−=
Ov
O F 2v 0 i R= −
F 1i i=
S2
1
vR
R= −O 2
S 1
v R
v R= −
+ −
Sv
Pv
Nv
2R 1R
Ov
Sv
Sv=
S2
2
vi
R=
F 2i i=
O S F 1v v i R= +
SS 1
2
vv R
R= +
O 1
S 2
v R1
v R
= +
− +
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R1
R2
0
vp=vs=vn
vo
iF = i2
i2 = vs/R2
1R
2R
FR
Nv
Pv0 =
01v
2v
Ov1i
11
1
v 0i
R
−= 22
2
v 0i
R
−=
2i
F 1 2i i i= +
O F Fv 0 i R= −
F FO 1 2
1 2
R Rv v v
R R
= − +
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1R
2R
FR
Nv
Pv
1v
2v
Ov
F FO 1 2
1 2
R Rv v v
R R
= − +
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Pv
2R
2v
1v
1R
3R
4R
Ov
Let's Use Superposition
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3
Go to WebCT Site, Click on Modules
Click on Op Amp CAD Module
Move top slider to choose type of circuit
Inverting, Non-Inverting Amplifier
Differential Amplifier, Comparator
Integrator, D
•••••• ifferentiator (Later in Course)
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http://www.academy.rpi.edu/projects/ccli/module_display.php?ModulesID=11
F
F
Move slider to Inverting Amplifier
Change R from 1k to 4k
Observe Clipping
Change R from 4k to 10k
Observe Square Wave
Change f from 1 kHz to 5 kHz
••• =>•• => ≈•
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DC
Move slider to Non-Inverting Amplifier
Change V to 5, 5 V
Observe Clipping
Change f from 1 kHz to 5 kHz
Same effect as changing Gain
•• + −• =>••
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F 1 2
Move slider to Differential Amplifier
Change R , R , R , f
Observe what happens
Will Discuss Differential Amplifiers
More Next Class
••••
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2
Tv
TR
1R
OR
eqR1Av
+
−1v
+
−Ov
+
−
1 TIf: R R>>11 T
1 T
Rv v
R R
= +
1 Tv v≈
Want Input Resistance [email protected] www.rpi.edu/~sawyes 7
Tv
TR
1R
OR
eqR1Av
+
−1v
+
−Ov
+
−
eq OIf: R R>>eqO 1
O eq
Rv Av
R R
= +
O 1v Av≈Want Output Resistance Small
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8
Tv
TR
1R
OR
eqR1Av
+
−1v
+
−Ov
+
−
1 T
eq O
If: R R
R R
>>>>
O
T
v Voltage Gain A
v=> = ≈
Design Challenge
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An Operational Amplifier is a High Gain Voltage Amplifier that can be used to perform Mathematical Operations:
Addition and Subtraction
Differentiation and Integration
Other Functions as Well
Op Amps are the building blocks for many, many electronic circuits
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Op Amps have existed since 1947:
First made with vacuum tubes
Then with discrete transistors
Now with Integrated Circuits
Op Amps are complex arrays of transistors, diodes, resistors and capacitors – All on a chip:
But can be modeled quite simply
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TYPICAL 741 OP AMP CIRCUIT
From Sedra and Smith
3
U1A
LM324
1
3
2
411
OUT
+
-
V+
V-
Non-Inverting Input
Inverting Input
Output
Positive DC Voltage
Negative DC [email protected] www.rpi.edu/~sawyes 13
Pv
Nv
1R1v
+
−1 P Nv v v= −
+
−1Av
OR
Ov
+
−1
6 121
R "Large"
10 R 10 ≤ ≤ ΩO
O
R "Small"
10 R 100 ≤ ≤ Ω
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P Nv v−
Ov
CCV+
CCV−
Saturation+
Saturation−
Linear RangeO P Nv A(v v )= −
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Pv
Nv
1R1v
+
−1 P Nv v v= −
+
−1Av
OR
Ov
+
−6 12
1 10 R 10 ≤ ≤ Ω
O10 R 100 ≤ ≤ Ω 5 8
A is "Large"
10 A 10≤ ≤
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Model for Real Op Amp
Ideal Op Amp has:
1 Input Resistance R = → ∞ Ω
OOutput Resistance R 0 = → Ω
Gain A= → ∞
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O CCv Can Never be greater than V
Pv
Nv
Pi 0=
Ni 0=
Ov
1Since R , Ideal Op Amp Draws No Current!→ ∞
P NSince A , v v in Linear Range→ ∞ [email protected] www.rpi.edu/~sawyes 18
4
Pv
Nv
Pi 0=
Ni 0=
OvP Nv v=
In Linear Range:
Virtual Short
Ideal Op Amp has a Virtual Short at Input
P N P Nv v ; i i 0= = [email protected] www.rpi.edu/~sawyes 19
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