Download ENGG 1015 Tutorial - University of Hong Kong

ENGG 1203 Tutorial
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Op Amps
8 Mar
Learning Objectives
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News
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Analyze circuits with ideal operational amplifiers
HW2 (18 Mar 23:55)
Mid term (22 Mar 2:30pm-3:30pm)
Revision tutorial (14 Mar 3:30pm-5:30pm, CBA)
Ack.: MIT OCW 6.01
1
Analysis of a Circuit with Op Amp (I)
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Determine Vo in the following circuit. Assume
that the op-amp is ideal.
2
Solution
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Since V- = V+, V- = 5V. So there must be 1/12A
flowing left through the two 6 ohm resistors.
There must be a corresponding 1/12 A flowing to
the left through the 12 ohm resistor. Vo is then
the sum of V- = 5V and the 1V across the 12
ohm resistor.
3
Analysis of a Circuit with Op Amp (II)
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Determine the current Ix
when V1 = 1V and V2 = 2V.
Determine the voltage VA
when V1 = 1V and V2 = 2V.
Determine a general expression
for VA in terms of V1 and V2.
4
Solution
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When V1 = 1V and V2 = 2V, Ix = 1A
When V1 = 1V and V2 = 2V, VA = 4V
2
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A general expression for VA:
𝑉𝐴 = 𝑉2 + 𝐼𝑥 × 2
𝑉2 − 𝑉1
= 𝑉2 +
×2
1
= 𝑉2 + 2 𝑉2 − 𝑉1
= −2𝑉1 + 3𝑉2
4
2
1
-1
1
5
Multi-stage Non-inverting Amplifier
Vn
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Use a single op-amp and
resistors to make a circuit
that is equivalent to the
following circuit.
𝑉𝑛
𝑅2
= 1+
𝑉𝑖
𝑅1
𝑉𝑜 𝑉𝑜 𝑉𝑛
𝑅3
=
= 1+
𝑉𝑖 𝑉𝑛 𝑉𝑖
𝑅4
=1
𝑅2
1+
𝑅1
𝑅1 𝑅4 +𝑅2 𝑅3 +𝑅2 𝑅4
+
𝑅1 𝑅3
6
Voltage-controlled Current Source
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Use the ideal op-amp model (V+ = V-) to
determine an expression for the output current Io
in terms of the input voltage Vi and resistors R1
and R2.
𝑣𝑥 = 𝑣𝑖 + 𝑣𝑥
𝑅2
⇒ 𝑣𝑥 = 𝑣𝑖
𝑅1
𝑅2
𝑅1 + 𝑅2
vi +vx
vi +vx
vx
𝑣𝑥
1 𝑅2 𝑣𝑖
𝐼𝑜 =
=
𝑣𝑖
=
𝑅2 𝑅2 𝑅1 𝑅1
7
Op Amp Configurations (I)
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Determine R so that Vo = 2 (V1 − V2).
8
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No current in +ve or -ve inputs:
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Ideal op-amp:
9
Op Amp Configurations (II)
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Fill in the values of R1 and R2 required to satisfy the
equations in the left column of the following table. The
values must be non-negative (i.e., in the range [0,∞])
R1
R2
Vo = 2V2 - 2V1
Vo = V2 - V1
Vo = 4V2 - 2V1
10
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𝑉+ =
𝑅2
𝑉2
10𝑘+𝑅2
𝑉𝑜 =
10𝑘+𝑅1
10𝑘+𝑅2
×
= 𝑉− =
𝑅2
10𝑘
× 𝑉2 −
Negative R 
i.e. Impossible
 3rd:
𝑅1
𝑉1
10𝑘+𝑅1
𝑅1
10𝑘
10𝑘
+
𝑉𝑜
10𝑘+𝑅1
× 𝑉1
R1
R2
Vo=2V2-2V1
20kΩ
20kΩ
Vo=V2-V1
20kΩ
20kΩ
Vo=4V2-2V1
Impossible
Impossible
11
Unusual Op Amp Configurations
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What is Vo?
V3+ V1
V3+ V2
V3
Vo = 0
Vo = V1 – V2
12
Motor Control
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Students Kim, Pat, Jody, Chris, and Leon are trying to
design a controller for a display of three robotic mice in
the Rube Goldberg Machine, using a 10V power supply
and three motors.
The first is supposed to spin as fast as possible (in one
direction only), the second at half of the speed of the
first, and the third at half of the speed of the second.
Assume the motors have a resistance of approximately
5Ω and that rotational speed is proportional to voltage.
For each design, indicate the voltage across each of the
motors.
13
Motor Control (Jody’s Design)
P.D. of motor 1 = 10V
P.D. of motor 2 = 0.05V
P.D. of motor 3 = 0V
Wrong design
Eq. R. (Red): 1K+~5  1K
Eq. R. (Blue): 1K//1K//5  ~5
10
0.05
0
14
Motor Control (Chris’s Design)
P.D. of motor 1 = 10V
P.D. of motor 2 = 0.45V
P.D. of motor 3 = 0V
Wrong design
Eq. R. (Red): 100K+~5  100K
Eq. R. (Blue): 1K//100K//5  ~5
10
0.45
0
15
Motor Control (Pat’s Design)
P.D. of motor 1 = 10V
P.D. of motor 3 = 2V
P.D. of motor 2 = 4V
Wrong design
10
4
Eq. R. : 1K // 2K = 2/3K
4
2
2
16
Motor Control (Kim’s Design)
P.D. of motor 1 = 10V
P.D. of motor 3 = 2.5V
P.D. of motor 2 = 5V
Correct design
10
Eq. R. :
100 // 200K = ~100
5
5
2.5
2.5
17
Motor Control (Leon’s Design)
P.D. of motor 1 = 10V
P.D. of motor 3 = 2.5V
P.D. of motor 2 = 5V
Correct design
10
5
5
2.5
2.5
18
Motor Control
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The following circuit is a proportional controller that
regulates the current through a motor by setting the
motor voltage VC to VC = K(Id − Io) where K is the gain
(notice that its dimensions
are ohms), Id is the desired
motor current, and Io is the
actual current through the
motor.
19
Solution
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Consider the circuit inside the dotted rectangle.
Determine V1 as a function of Io.
V+ = 1/2 x Io = VV- = 100/(100+9900) x V1
V1 = 1/2 x Io x 100
Determine the gain K and
desired motor current Id.
KCL at -ve input to right op-amp:
𝑉𝑐 − 2.5 2.5 − 0.5 × 𝐼𝑜 × 100
=
⇒ 𝑉𝑐 = 50 0.1 − 𝐼𝑜
10000
1000
20
Position Controller
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The following figure shows a motor controller. A human
can turn the left potentiometer (the input pot). Then the
motor will turn the right potentiometer (the output pot) so
that the shaft angle of the output pot tracks that of the
input pot.
21
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The dependence of the pot resistances on shaft angle is
given in terms of α, which varies from 0 (most
counterclockwise position) to 1 (most clockwise
position). The resistance of the lower part of the pot is
αR and that of the upper part is (1 − α)R, where R =
1000Ω.
Notice that if αi >αo, then the voltage to the motor (VM+ −
VM−) is positive, and the motor turns clockwise (so as to
increase αo)—i.e., positive motor voltage clockwise
rotation.
22
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Determine an expression for VM+ in terms of αi,
R, and VS.
The output of the voltage divider is
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The op-amp provides a gain of 1, so VM+ = V+.
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23
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The following circuit produces a
voltage Vo that depends on the
position of the input pot.
Determine an expression for
the voltage Vo in terms of αi,
R, R1, R2, and VS.
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The positive input to the op-amp is connected to a
voltage divider with equal resistors so
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The input pot is on the output of the op-amp, so
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In an ideal op-amp, V+ = V− so
24
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The following circuit produces a voltage Vo that depends
on the positions of both pots. Determine an expression
for Vo in terms of αi, αo, R, and VS.
The positive input to the op-amp is connected to pot 1 so
that
The output pot is on the
output of the op-amp, so
In an ideal op-amp, V+ = V− so
25
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Assume that we are provided with a circuit whose output
is αi/αo volts. We wish to determine if it is possible to
design a motor controller of the following form so that the
motor shaft angle (which is proportional to αo) will track
the input pot angle (which is proportional to αi).
Assume that R1 = R3 = R4 = 1000Ω and VC = 0. Is it
possible to choose R2 so that αo tracks αi? If yes, enter
an acceptable value for R2.
26
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Assume that R1 = R3 = R4 = 1000Ω and VC = 0. Is it
possible to choose R2 so that αo tracks αi? If yes,
enter an acceptable value (a number) for R2.
If R3 = R4 then the right motor input is 5V. If αi = αo
then the gain of the left op-amp circuit must be 5 so
that the motor voltage is 0. The gain is R1 + R2/R1,
so R2 must be 4000Ω.
5
1
5
5
1
0
27
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Assume that R1 = R3 = R4 = 1000Ω and VC = 5V. Is
it possible to choose R2 so that αo tracks αi?
If R3 = R4 then the right motor input is 5V. If αi = αo
then V+ = V− = 1 for the right op-amp. We need the
left motor input to be 5V. But if the left motor input is
5V and VC = 5V then V− must also be 5V, which
leads to a contradiction.
5
1
5
5
1
5
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Course Timeline (Tentative)
Lecture
Tutorial Lab
Systems
L1
T1
Digital systems
L1
Combinational
logic
L2
Sequential logic
L3
FSM
L3, L4
ADC/DAC
L4
Circuit
L5
Project
Op Amp
L6
T2, T3
#1, #2
Homework
HW1
HW1
T3, T4
#3, #4
HW1
#4 (DAC), #7,8 (ADC)
T4, T5
HW2
T5
#6
HW2
T6
#5, #8
HW2
……
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Tutorial Schedule (Tentative)
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1/25
2/1
2/8
2/15
2/22
3/1
3/8
3/15
3/22
3/29
Introduction+System
Digital Logic
Digital Logic
N/A
Digital Logic+Circuit
Circuit+Project
Circuit
Revision Tutorial
** Mid Term **
N/A
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4/5
4/12
4/19
4/26
5/3
5/X
Signal
Signal
Signal
N/A
N/A
Computer+Revision
30