1. 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.

2. 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

3. OpAmps High Gain Devices High Input Resistance
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

4. Op Amp Characteristics
+Vcc
vp(t) Av
Rin +
vout(t) =
Av(vp(t)-vn(t))
vn(t) -
-Vcc
Rin?
In M ohms
Voltage gain Av?
On order of

5. OpAmps High Gain Devices High Input Resistance Negative Feedback?
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 Vp(t) = Vn(t)
a.k.a. Virtual Short

6. 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

7. 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

8. Op Amps: No Feedback Av Output likely to hit rails Use: Comparator
+Vcc Av +
vout(t) =
Av(vp(t)-vn(t))
vin(t) -
-Vcc
Output likely to hit rails
Unless tiny voltage
Use: Comparator
Compares two voltages
Yields binary output

9. Op Amps: Positive Feedback & No Negative FeedbackAv
vout(t) = Av[vp(t) - 0] +
vin(t)
0 v -
Output likely to hit rails
May get stuck there
Use: None
Suppose |Vcc| = 15 v

10. Op Amps: Positive Feedback
10 v if feedback & input resistors =
5 v Av
vout(t) = Av[vp(t) - 0] +
vin(t)
15 v -
Output likely to hit rails
May get stuck there
Suppose |Vcc| = 15 v

11. Op Amps: Positive Feedback
7.5 v if feedback & input resistors =
0 v Av
vout(t) = Av[vp(t) - 0] +
vin(t)
15 v -
Output likely to hit rails
May get stuck there
Suppose |Vcc| = 15 v

12. Op Amps: Positive Feedback
≈ 0 v if feedback & input resistors =
-15 v Av
vout(t) = Av[vp(t) - 0] +
vin(t)
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

13. Op Amps: Negative FeedbackAv
vout(t) =
Av[vp(t)-vn(t)] -
vin(t) +
0 v
Safe to assume vp(t) = vn(t)
Assume no current enters Op Amp
If low R outside paths exist

14. Op Amps: Negative Feedback
vout(t) =
Av[v+(t) – v-(t)]
0 v
5 v Av -
vin(t)
0 v +
Stable System
Linear so long as don't hit Power Supply Limits & get Clipped Output
Suppose |Vcc| = 15 v

15. Op Amps: Negative Feedback (Ideal)Av
vout(t) -
vin(t)
-5.0 v +
Suppose… OpAmp Voltage Gain = ∞ External elements are Resistors of R Ω V+ = V-

16. Op Amps: Negative Feedback (Actual)
vout(t) =
10,000[v+(t) – v-(t)]
5 v Av -
vin(t) v +
Suppose… OpAmp Voltage Gain = 10,000 OpAmp Input Impedance = ∞ External elements are Resistors of R Ω

17. OpAmps (Analysis Assumptions)
No Current enters or exits inputs
Effectively, the OpAmp input isn't there
But Negative Feedback make Vp = Vn - +
vout
1 Ω
5 Ω
10 Ω
vin
|Vcc| = 25v
Av = 10,000 - +
vout
1 Ω
5 Ω
10 Ω
vin
|Vcc| = 25v
Av = 10,000

18. OpAmps (Analysis Assumptions)
Look for Negative Feedback
If yes, set Vp(t) = Vn(t)
If no, Vp(t) ≠ Vn(t)
Vout(t) = [Vp(t) – Vn(t)]*Voltage Gain
Output will probably hit a power supply rail - +
vout
1 Ω
5 Ω
10 Ω
vin
|Vcc| = 25v
Av = 10,000 I
Have Negative Feedback Here
→ V- = V+ = Vout(1/11)
[Vin – V-]/5 = I = [V- – Vout]/1
[Vin – Vout/11]/5 = [Vout/11 – Vout]
→ Vout/Vin = -11/49

19. Max output current = 35 – 40 ma
5v in?
I2R = W
1.020a
|Vcc| = 25v
Av = 10,000
-.1020v
1 Ω
1.020a - 5v
5 Ω +
-11/49*5v = v
-.1020v
Opamp Output
must sink
1.122 amps
10 Ω
1 Ω
.1020a
.1020a
LM741 can't do it.
Max output current = 35 – 40 ma

20. OpAmps: External Resistors
|Vcc| = 25v
Av = 10,000
Rin = 1 MΩ
-.1020v
1 Ω
1.020a - 5v
5 Ω +
-11/49*5v = v
-.1020v
Generally not too small: X or XX Ohms.
Current flows too large.
10 Ω
1 Ω
.1020a
.1020a

21. Max output current = 35 – 40 ma
5v in?
I2R = 10.4 mW
1.020 ma
|Vcc| = 25v
Av = 10,000
Rin = 1 MΩ
-.1020v
10K Ω
1.020 ma - 5v
5K Ω +
-11/49*5v = v
-.1020v
Opamp Output
must sink
1.122 m amps
10K Ω
1K Ω
102.0 μa
102.0 μa
LM741 can do it.
Max output current = 35 – 40 ma

22. OpAmps? External Resistors
1.020 ma
|Vcc| = 25v
Av = 10,000
Rin = 1 MΩ
-.1020v
10K Ω
1.020 ma - 5v
5K Ω +
-11/49*5v = v
-.1020v
Just Right if in
X or XX
K Ohm range
10K Ω
1K Ω
102.0 μa
102.0 μa

23. OpAmps: External Resistors
|Vcc| = 25v
Av = 10,000
Rin = 1 MΩ
1 MΩ
10 μa -
5 MΩ +
Generally too large: X or XX
M Ohms.
Current flows in/out OpAmp inputs cannot be ignored.
10 MΩ
1 MΩ

24. Op Amps: Output Load Av Ideally, load does not effect characteristics-
vout(t)
vin(t) +
Rload
Ideally, load does not effect characteristics
Practically, load may effect characteristics
If Op Amp output can't source or sink enough current

25. Voltage gain is independent of load if
25v in?
|Vcc| = 25v
Av = 10,000
5.102 ma v
LM741 can sink
35 – 40 ma
10K Ω
5.102 ma -
25v
-11/49*25v = v
5K Ω +
LM741 can sink
additional
29.80 – ma v RL
10K Ω
1K Ω
102.0 μa
Voltage gain is independent of load if
load > 5.612/.0298 = Ω
510.2 μa

26. Current & Voltage Values are Incorrect
5v in & 10 Ω Load?
|Vcc| = 25v
Av = 10,000
1.020 ma
-.1020v
LM741 can sink
35 – 40 ma
10K Ω
1.020 ma - 5v
-11/49*5v = v
5K Ω +
I_load
I_load =
1.122/10 = 112 mA
LM741 can't sink this!!
10 Ω
-.1020v
10K Ω
1K Ω
102.0 μa
102.0 μa
Current & Voltage Values are Incorrect

27. 5v in? Operating outside OpAmp's Comfort Zone?
Voltages & Currents may not be as expected.
Here sunk current maxes out at
40 mA.
269.8 μA
3.651 V
10K Ω
269.8 μA - 5v V
vout
1 Ω
5 Ω
10 Ω 5v
40 mA
5K Ω + A
10 Ω V
10K Ω
1K Ω
36.00 μA
36.00 μA

28. 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 Vp = Vn
Circuit gain Vout/Vin super high?
Indication system is possibly unstable - +
vout
1 Ω
5 Ω
10 Ω
vin
|Vcc| = 25v
Av = 10,000