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ENGS2613 Intro Electrical Science
Week 8
Dr. George Scheets




Read 5.5 – 5.7
Problems 5.8, 9, 12, 14, 19, 23, 28, 30, & 31
Next Quiz Friday 24 March
 Chapter 5 OpAmps
 Will not have +Vcc & -Vcc defined
So don't worry about hitting a power supply rail
Quiz 4 Results
Hi = 10, Low = 2, Ave = 5.71, Deviation = 1.95
No adjustments to scores required.
Quiz #5 Friday, 24 March
Closed Book & Neighbor
 Up to 3 unattached sheets of notes OK
Keep on your desk
Have them on hand before you start
 Calculator OK
 Smart Phones NOT OK
 Reaching down for something in backpack?

 Get

permission first
All we're doing Friday
OpAmps

High Gain Devices
 Typically,
Voltage Gain = Vout/Vin > 10,000
 Vout(t) = [Vp(t) – Vn(t)]*Voltage Gain

High Input Resistance
 Rin
typically > 1 MΩ
 Ignore current into or exiting OpAmp input
 So
long as external resistors < Rin/10
Op Amp Characteristics
vp(t)
Rin
vn(t)
+Vcc
+
vout(t) =
Av(vp(t)-vn(t))
Av
-
-Vcc

Rin?
 In

M ohms
Voltage gain Av?
 On
order of 104 - 106
OpAmps

High Gain Devices
 Typically,
Voltage Gain > 10,000
 Vout(t) = [Vp(t) – Vn(t)]*Voltage Gain

High Input Resistance
 Rin
typically > 1 MΩ
 Ignore current entering OpAmp input
 So

long as external resistors < Rin/10
Negative Feedback?
 Assume
 a.k.a.
Vp(t) = Vn(t)
Virtual Short
OpAmps

On quizzes & tests, assume Ideal OpAmp…
 Voltage
Gain = ∞
 Input impedance = ∞
Absolutely no current enters/exits OpAmp input side

 Current
will generally enter or exit OpAmp output
Output can source or sink any value

 Vp
= Vn if negative feedback
 Output doesn't hit Power Supply rails

…
If +Vcc & -Vcc not shown
unless specifically stated otherwise
OpAmps (Analysis Assumptions)

Is there negative feedback?
Generally, must be "Yes" to be Linear
 Yes?
Set Vp = Vn
 No? Output likely to hit power supply rail
Assume no current thru OpAmp input
 Analyze

 Ohm's
Law
Kirchoff's Current Law
Kirchoff's Voltage Law
Op Amps: No Feedback
+Vcc
+
vin(t)
vout(t) =
Av(vp(t)-vn(t))
Av
-
-Vcc

Output likely to hit rails
 Unless

tiny voltage
Use: Comparator
 Compares
two voltages
 Yields binary output
Op Amps: Positive Feedback
& No Negative Feedback
0v
0v5v
+
Av
vin(t)
-

vout(t) =
Av[vp(t) - 0]
0v
Output likely to hit rails
 May
get stuck there
Use: None
 Suppose |Vcc| = 15 v

Op Amps: Positive Feedback
10 v if feedback & input resistors =
5v
+
Av
vin(t)
-

15 v
Output likely to hit rails
 May

vout(t) =
Av[vp(t) - 0]
get stuck there
Suppose |Vcc| = 15 v
Op Amps: Positive Feedback
7.5 v if feedback & input resistors =
0v
+
Av
vin(t)
-

15 v
Output likely to hit rails
 May

vout(t) =
Av[vp(t) - 0]
get stuck there
Suppose |Vcc| = 15 v
Op Amps: Positive Feedback
≈ 0 v if feedback & input resistors =
-15 v
vin(t)
+
Av
-
vout(t) =
Av[vp(t) - 0]
15 v
Suppose |Vcc| = 15 v



Vp slightly > 0?
 Vout can be stuck at 15 V
Vp exactly = 0?
 Unstable. Vout will end up at -15 V
Vp slightly < 0
 Vout rockets to -15 V
Op Amps: Negative Feedback
0v
-
Av
vin(t)
vout(t) =
Av[vp(t)-vn(t)]
+
0v
Safe to assume vp(t) = vn(t)
 Assume no current enters Op Amp

 If
low R outside paths exist
Op Amps: Negative Feedback
0v
0v5v
vin(t)
-
Av
+
vout(t) =
Av[v+(t) – v-(t)]
0v
Stable System
 Linear so long as don't hit Power
Supply Limits & get Clipped Output
 Suppose |Vcc| = 15 v

Op Amps: Negative Feedback
(Ideal)
0.0+ v
5v
vin(t)
-
Av
+

vout(t)
-5.0 v
Suppose…
OpAmp Voltage Gain = ∞
External elements are Resistors of R Ω
V+ = V-
Op Amps: Negative Feedback
(Actual)
0.0004999 v
5v
vin(t)
-
Av
+

vout(t) =
10,000[v+(t) – v-(t)]
-4.999 v
Suppose…
OpAmp Voltage Gain = 10,000
OpAmp Input Impedance = ∞
External elements are Resistors of R Ω
OpAmps (Analysis Assumptions)

No Current enters or exits inputs
 Effectively,
the OpAmp input isn't there
 But Negative Feedback make Vp = Vn
|Vcc| = 25v
Av = 10,000
vin
5Ω
1Ω
|Vcc| = 25v
Av = 10,000
1Ω
-
vin
vout
+
10 Ω
5Ω
1Ω
1Ω
-
vout
+
10 Ω
OpAmps (Analysis Assumptions)

Look for Negative Feedback
 If
yes, set Vp(t) = Vn(t)
 If no, Vp(t) ≠ Vn(t)
= [Vp(t) – Vn(t)]*Voltage Gain
 Output will probably hit a power supply rail
 Vout(t)
|Vcc| = 25v
Av = 10,000
I
vin
5Ω
1Ω
Have Negative Feedback Here
→ V- = V+ = Vout(1/11)
1Ω
vout
+
10 Ω
[Vin – V-]/5 = I = [V- – Vout]/1
[Vin – Vout/11]/5 = [Vout/11 – Vout]
→ Vout/Vin = -11/49
5v in?
I2R = 1.040 W
1.020a
-.1020v
1.020a
|Vcc| = 25v
Av = 10,000
1Ω
-
5v
5Ω
+
-11/49*5v = -1.122v
-.1020v
1Ω
.1020a
10 Ω
.1020a
Opamp Output
must sink
1.122 amps
LM741 can't do it.
Max output current =
35 – 40 ma
OpAmps: External Resistors
1.020a
-.1020v
1.020a
1Ω
|Vcc| = 25v
Av = 10,000
Rin = 1 MΩ
-
5v
5Ω
+
-11/49*5v = -1.122v
-.1020v
1Ω
.1020a
10 Ω
.1020a
Generally not too
small: X or XX
Ohms.
Current flows too
large.
5v in?
I2R = 10.4 mW
1.020 ma
-.1020v
1.020 ma
10K Ω
|Vcc| = 25v
Av = 10,000
Rin = 1 MΩ
-
5v
5K Ω
+
-11/49*5v = -1.122v
-.1020v
1K Ω
102.0 μa
10K Ω
102.0 μa
Opamp Output
must sink
1.122 m amps
LM741 can do it.
Max output current =
35 – 40 ma
OpAmps? External Resistors
1.020 ma
-.1020v
1.020 ma
10K Ω
|Vcc| = 25v
Av = 10,000
Rin = 1 MΩ
-
5v
5K Ω
+
-11/49*5v = -1.122v
-.1020v
1K Ω
102.0 μa
10K Ω
102.0 μa
Just Right if in
X or XX
K Ohm range
OpAmps: External Resistors
< 10 μa
10 μa
1 MΩ
|Vcc| = 25v
Av = 10,000
Rin = 1 MΩ
5 MΩ
Generally too
large: X or XX
M Ohms.
+
1 MΩ
10 MΩ
Current flows
in/out OpAmp
inputs cannot be
ignored.
Op Amps: Output Load
-
vin(t)
Av
+
vout(t)
Rload
Ideally, load does not effect characteristics
 Practically, load may effect characteristics

 If
Op Amp output can't source or sink
enough current
25v in?
|Vcc| = 25v
Av = 10,000
5.102 ma
-.5102 v
5.102 ma
10K Ω
-
25v
LM741 can sink
35 – 40 ma
-11/49*25v = -5.612 v
5K Ω
+
RL
-.5102 v
1K Ω
510.2 μa
10K Ω
102.0 μa
LM741 can sink
additional
29.80 – 34.80 ma
Voltage gain is
independent of load if
load > 5.612/.0298 =
188.3 Ω
5v in & 10 Ω Load?
|Vcc| = 25v
Av = 10,000
1.020 ma
-.1020v
1.020 ma
10K Ω
-
5v
LM741 can sink
35 – 40 ma
-11/49*5v = -1.122v
5K Ω
I_load
+
10 Ω
-.1020v
1K Ω
102.0 μa
10K Ω
102.0 μa
I_load =
1.122/10 = 112 mA
LM741 can't sink
this!!
Current & Voltage
Values are Incorrect
5v in?
3.651 V
269.8 μA
269.8 μA
10K Ω
-
5v
Operating outside OpAmp's
Comfort Zone?
Voltages & Currents may not be as
expected.
Here sunk current maxes out at
40 mA.
-0.3960 V
5K Ω
0.03960 A
+
10 Ω
-.03600 V
1K Ω
36.00 μA
5Ω
1Ω
5v
40 mA
vout
10K Ω
36.00 μA
1Ω
10 Ω
OpAmp with
Positive & Negative Feedback

Do see Real World Use
 In
Reality: May have some instability issues
 Ideally: Tend to be stable

On Quiz or Test
 Analyze
as if stable
vin
Vp = Vn
 Circuit gain Vout/Vin
super high?
 Indication
unstable
system is possibly
1Ω
5Ω
1Ω
|Vcc| = 25v
Av = 10,000
vout
+
10 Ω