ALL 9 CHAPTERS COVERED
SOLUTIONS MANUAL
, Contents
Chapter 1 1
Chapter 2 57
Chapter 3 155
Chapter 4 274
Chapter 5 384
Chapter 6 467
Chapter 7 572
Chapter 8 675
Chapter 9 765
, Chapter 1
1.1 Suppose the input to an amplifier is xa (t) = sin(2πF0 t) and the steady-state output is
ya (t) = 100 sin(2πF0 t + φ1 ) − 2 sin(4πF0 t + φ2 ) + cos(6πF0 t + φ3 )
(a) Is the amplifier a linear system or is it a nonlinear system?
(b) What is the gain of the amplifier?
(c) Find the average power of the output signal.
(d) What is the total harmonic distortion of the amplifier?
Solution
(a) The amplifier is nonlinear because the steady-state output contains harmonics.
(b) From (1.1.2), the amplifier gain is K = 100.
(c) From (1.2.4), the output power is
d20 1 2
d1 + d+ 22 + d23
Py = +
4 2
= .5(1002 + 22 + 1)
= 5002.5
(d) From (1.2.5)
100(Py − d21 /2)
THD =
Py
100(5002.5 − 5000)
=
5002.5
= .05%
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1
, √
1.2 Consider the following signum function that returns the sign of its argument.
1 , t>0
∆
sgn(t) = 0 , t=0
−1 , t < 0
(a) Using Appendix 1, find the magnitude spectrum
(b) Find the phase spectrum
Solution
(a) From Table A2 in Appendix 1
1
Xa (f ) =
jπf
Thus the magnitude spectrum is
Aa (f ) = |Xa(f )|
1
=
|jπf |
1
=
π|f |
(b) The phase spectrum is
φa (f ) = 6 Xa (f )
= −6 jπf
π
= −sgn(f )
2
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
2
SOLUTIONS MANUAL
, Contents
Chapter 1 1
Chapter 2 57
Chapter 3 155
Chapter 4 274
Chapter 5 384
Chapter 6 467
Chapter 7 572
Chapter 8 675
Chapter 9 765
, Chapter 1
1.1 Suppose the input to an amplifier is xa (t) = sin(2πF0 t) and the steady-state output is
ya (t) = 100 sin(2πF0 t + φ1 ) − 2 sin(4πF0 t + φ2 ) + cos(6πF0 t + φ3 )
(a) Is the amplifier a linear system or is it a nonlinear system?
(b) What is the gain of the amplifier?
(c) Find the average power of the output signal.
(d) What is the total harmonic distortion of the amplifier?
Solution
(a) The amplifier is nonlinear because the steady-state output contains harmonics.
(b) From (1.1.2), the amplifier gain is K = 100.
(c) From (1.2.4), the output power is
d20 1 2
d1 + d+ 22 + d23
Py = +
4 2
= .5(1002 + 22 + 1)
= 5002.5
(d) From (1.2.5)
100(Py − d21 /2)
THD =
Py
100(5002.5 − 5000)
=
5002.5
= .05%
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
1
, √
1.2 Consider the following signum function that returns the sign of its argument.
1 , t>0
∆
sgn(t) = 0 , t=0
−1 , t < 0
(a) Using Appendix 1, find the magnitude spectrum
(b) Find the phase spectrum
Solution
(a) From Table A2 in Appendix 1
1
Xa (f ) =
jπf
Thus the magnitude spectrum is
Aa (f ) = |Xa(f )|
1
=
|jπf |
1
=
π|f |
(b) The phase spectrum is
φa (f ) = 6 Xa (f )
= −6 jπf
π
= −sgn(f )
2
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
2
