Lecture 04
EE 2303/001-Electronics
2303/001 Electronics I
February
y 2,, 2009
Professor Ronald L. Carter
ronc@uta.edu
@
d
p
http://www.uta.edu/ronc/
K Web
Key
W b Sites
Si
• Instructor web site
http://www.uta.edu/ronc/
• Course web site
http://www.uta.edu/ronc/2303/syllabus.htm
• The hyperlink for viewing lectures is
http://tinyurl com/ee2303echo
http://tinyurl.com/ee2303echo
• Quiz results will be posted at
http://www uta edu/ronc/2303/Q1soln pdf
http://www.uta.edu/ronc/2303/Q1soln.pdf
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Id l Operational
Ideal
O
i
lA
Amplifier
lifi
• Infinite input impedance
open loop gain for the
• Infinite open-loop
differential input signal
• Zero gain for the common-mode signal
• Zero output impedance
• Infinite
I fi it b
bandwidth
d idth
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O
Operational
i
l Summing
S
i P
Point
i
• The gain and common-mode
assumptions
p
with sufficient feedback
present result in the operational
summing
g point
p
vdifferential = v+ - v- = 0
v+ = v • Thus the input operationally simulates
a virtual short-circuit
short circuit
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Figure
g
2.1 Circuit symbol
y
for the op
p amp.
p
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Figure
g
2.2 Equivalent
q
circuit for the ideal op
p amp.
p AOL is very
y large
g
(approaching infinity).
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Figure
g
2.3 Op-amp
p
p symbol
y
showing
g power
p
supplies.
pp
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http://www.national.com/ds/LM/LM741.pdf
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http://www.national.com/ds/LM/LM741.pdf
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http://www.national.com/ds/LM/LM741.pdf
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Schematic
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Neglecting input - offset, and due to high gain, we have v+ = v− .
This has the effect of creating a virtual short - circuit at the input.
v−
v+
High input impedance gives an nearly
open circuit for the input, i− = 0 = i+
Figure 2.5 We make use of the summing-point constraint in the analysis of the inverting amplifier.
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R2
R2
vo = − vin . Thus an inverting amplifier, Av = −
R1
R1
Zin = ?
v−
v+
Figure 2.5 We make use of the summing-point constraint in the analysis of the inverting amplifier.
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⎛ R2 R4 R4 R2 ⎞
⎟⎟
+
vo = −vin ⎜⎜ +
⎝ R1 R1 R1 R3 ⎠
Note that i1 = i2
i4 = i2 + i3
Figure 2.6 An inverting amplifier that achieves high gain with a smaller range of resistor values
than required for the basic inverter.
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vo = −va
Rf
Ra
− vb
Rf
Rb
Rin ,a = Ra
Rin ,b = Rb
Ro = 0
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Figure 2.7 Summing amplifier. See Exercise 2.1.
16
For the condition V−supply < AOL vi < V+supply
V−supply
V+supply
vo
v
= − i , requiring
< vi <
≈ 5μV
AOL
R
R
AOL
Either noise, or offset
So for
current will violate this So,
highly specific condition.
Thus the internal OA
f db k is b
feedback
broken
k and
d th
the
Summing Point (or Virtual
Ground) rule no longer holds.
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vi > vo,max , vo = vo,max ~ V+supply
vi < vo,min , vo = vo,min ~ V−supply
Figure 2.10a Schmitt trigger circuit and waveforms.
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t = t1+ε
t=0
t = t1-ε
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Figure 2.10b Schmitt trigger circuit and waveforms.
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In order for vi to be = 0, we must have
R1
vo = vs
R1 + R2
vo R1 + R2
=
vs
R1
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Figure 2.11 Noninverting amplifier.
19
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Figure 2.12 Voltage follower.
20
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Figure 2.14 Differential amplifier. See Exercise 2.5.
21
Figure
g
2.13 Inverting
g or noninverting
g amplifier.
p
See Exercise 2.4.
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R i
Resistors
• Integrated Circuit Resistors
• Discrete Resistors
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Figure 2.16 IC resistors are fabricated from a layer of conductive material.
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Figure 2.17 The resistance of the larger square is the same as the
resistance of each of the smaller squares.
L/W = 3, R = 3R
Figure 2.18 A resistor having L/W = 3.
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Figure 2.19 IC resistors are often folded to keep the distance between the contacts smaller.
R = Nstraight…•R… + Ncorner…•Rcorner… + 2•Rcontact
10 < R… < 1000, approximately
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From Vishay Resistor Manual
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L04, 02 Feb http://www.uoguelph.ca/~antoon/gadgets/resistors/resistor.htm
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10%
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20%
http://www.uoguelph.ca/~antoon/gadgets/resistors/resistor.htm
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From Ohmcraft Manual
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Figure 2.20 If low-value resistors are used, an impractically large current is required.
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Figure 2
2.21
21 If very high value resistors are used
used, stray capacitance can couple
unwanted signals into the circuit.
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Figure 2.22 To attain large input resistance with moderate resistances for an inverting amplifier,
we cascade a voltage follower with an inverter.
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R = Nstraight…•R… + Ncorner…•Rcorner… + 2•Rcontact
Nstraight… = 19, Ncorner… = 2, Ncontact = 2
R… = 100 Ω, Rcorner… = 56 Ω, Rcontact… = 65 Ω
Rtotal = 1,642 Ω
Figure 2.24 Resistor for Exercises 2.8.
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vo =
R2 R f
R1 RA
v1 −
Rf
RB
v2
Figure 2.23 Amplifier designed in Example 2.4.
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Effect of Finite Gain
AOL ( f ) =
A0OL
1 + j ( f f BOL )
f t = A0OL f BOL = unity gain frequency
A0OL = low frequency gain
f BOL = frequency
f
off gain
i break
b k - point
i
Figure 2.25 Bode plot of open-loop gain for a typical op amp.
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ACL =
β=
AOL
, the closed - loop gain
1 + β AOL
R1
R1 + R2
ACL ( f ) =
A0CL
, where f BCL = f BOL (1 + β A0OL )
1 + j ( f f BCL )
Figure 2.26 Noninverting amplifier.
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Figure 2.27 Bode plots for Example 2.5.
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References and Endnotes
• Where not otherwise noted, Figures
are taken from:
– Electronics, 2nd edition, by Allan R.
Hambley,
y Prentice Hall, Upper
pp Saddle
River, NJ, © 2000.
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