(1) Design the circuit to reduce the input voltage by 40%, by using the circuit connected through an ideal Operational Amplifier. (You are free to choose any electric element)
(1) Design the circuit to reduce the input voltage by 40%, by using the circuit connected through an ideal Operational Amplifier. (You are free to choose any electric element)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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![The complete response is the sum of the natural response and the forced response
X = Xn+Xf
Natural response of a first-order circuit
Natural response of a second-order circuit
CASE
Overdamped
Critically damped
Underdamped
az
S1 =
FORCING FUNCTION
K
Kt
K₁²
K sin cot
Ke at
Forced response of a first-order, or a second-order circuit
+ A₁
NATURAL FREQUENCIES
$1,52 = -α± √√² - 0²
$1,$₂=-α
S1, S2 = -x±j√√/0²-a² -α±jood
dx
dt
d²x
dt²
Solution of the Second-Order Differential Equation
d²x
x(t) = xn(t) + xf (t)
a2
dt²
+ a。x = f(t)
+ A1
dx
dt
"xn(t)" = Aest
Xn(t) = Ke-t/t
+ a。x = 0
-a₁ + √²-4a₂a0
242
-
Xn(t) = A₁e³₁ª + A₂e³₂t
ASSUMED RESPONSE
A
At + B
At² +Bt+C
A sin cot + B cos cot
Ae-at
NATURAL RESPONSE, Xn
Ale+Azer
(A₁+A₂t)e-at
(A, cos coat+A₂ sin coat)e
xn(t) = ?
(a₂s² + a₁s+ao) = 0
-α₁ - √²-4a₂a0
242
NATURAL RESPONSE, Xn
A₁ est + A₂e21
-α1
(A₁+A₂t)e
(A₁ cos wat+A₂ sin wat)ext](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff343651e-c46c-419d-8f81-2ed17d4ca38d%2Fa7c9cdc6-00fb-474b-a119-6917a768b5e4%2Fcqjvr8r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The complete response is the sum of the natural response and the forced response
X = Xn+Xf
Natural response of a first-order circuit
Natural response of a second-order circuit
CASE
Overdamped
Critically damped
Underdamped
az
S1 =
FORCING FUNCTION
K
Kt
K₁²
K sin cot
Ke at
Forced response of a first-order, or a second-order circuit
+ A₁
NATURAL FREQUENCIES
$1,52 = -α± √√² - 0²
$1,$₂=-α
S1, S2 = -x±j√√/0²-a² -α±jood
dx
dt
d²x
dt²
Solution of the Second-Order Differential Equation
d²x
x(t) = xn(t) + xf (t)
a2
dt²
+ a。x = f(t)
+ A1
dx
dt
"xn(t)" = Aest
Xn(t) = Ke-t/t
+ a。x = 0
-a₁ + √²-4a₂a0
242
-
Xn(t) = A₁e³₁ª + A₂e³₂t
ASSUMED RESPONSE
A
At + B
At² +Bt+C
A sin cot + B cos cot
Ae-at
NATURAL RESPONSE, Xn
Ale+Azer
(A₁+A₂t)e-at
(A, cos coat+A₂ sin coat)e
xn(t) = ?
(a₂s² + a₁s+ao) = 0
-α₁ - √²-4a₂a0
242
NATURAL RESPONSE, Xn
A₁ est + A₂e21
-α1
(A₁+A₂t)e
(A₁ cos wat+A₂ sin wat)ext
![• Problem 1. Please answer the following questions, as directed in the questions.
(1) Design the circuit to reduce the input voltage by 40%, by using the circuit connected through
an ideal Operational Amplifier. (You are free to choose any electric element)
(2) By using the models of the ideal Operational amplifier, Design the linear algebraic circuit as
shown below.
1
3Y
■
Consider Z as Vout and x, y as Vin 1, Vin 2 (You are3 free to choose any electric element, but it
should also include the operational amplifier)
www
R₁
T
Vin m
R₁
Brief catalog of the Operational Amplifier circuits
(Based on the ideal operational amplifier)
(a) Inverting amplifier
U10-M
R₁
U₂0-M
R₂
Unw
R₁
R₁
Ovout= R₁
Vout=-
www
R₁
- Vout
R₁
R₁
R₁
R₁1+ R₂₂+. Rn
Z = -2x +
Vin
(d) Summing amplifier
Vin
-
R₁
R₁
3
R₁
Vout + Vin
(b) Noninverting amplifier
R/K₁
R₂/K₂
010-
U20-W
RJK3
V30-W
R₂/(1-(K₁ + K₂ + K3))
www
Vin
(c) Voltage follower (buffer amplifier)
R(K4-1)
-Ovout Vin
Ovout= K4(K₁v1 + K₂V2 + K303)
(e) Noninverting summing amplifier](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff343651e-c46c-419d-8f81-2ed17d4ca38d%2Fa7c9cdc6-00fb-474b-a119-6917a768b5e4%2Frnhaj7i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:• Problem 1. Please answer the following questions, as directed in the questions.
(1) Design the circuit to reduce the input voltage by 40%, by using the circuit connected through
an ideal Operational Amplifier. (You are free to choose any electric element)
(2) By using the models of the ideal Operational amplifier, Design the linear algebraic circuit as
shown below.
1
3Y
■
Consider Z as Vout and x, y as Vin 1, Vin 2 (You are3 free to choose any electric element, but it
should also include the operational amplifier)
www
R₁
T
Vin m
R₁
Brief catalog of the Operational Amplifier circuits
(Based on the ideal operational amplifier)
(a) Inverting amplifier
U10-M
R₁
U₂0-M
R₂
Unw
R₁
R₁
Ovout= R₁
Vout=-
www
R₁
- Vout
R₁
R₁
R₁
R₁1+ R₂₂+. Rn
Z = -2x +
Vin
(d) Summing amplifier
Vin
-
R₁
R₁
3
R₁
Vout + Vin
(b) Noninverting amplifier
R/K₁
R₂/K₂
010-
U20-W
RJK3
V30-W
R₂/(1-(K₁ + K₂ + K3))
www
Vin
(c) Voltage follower (buffer amplifier)
R(K4-1)
-Ovout Vin
Ovout= K4(K₁v1 + K₂V2 + K303)
(e) Noninverting summing amplifier
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