# Electronic Engineering

## Electronic Engineering

• Submitted By: hungpeepee
• Date Submitted: 10/23/2013 5:31 AM
• Category: Technology
• Words: 58785
• Page: 236
• Views: 96

APPENDIX A
Exercises EA.1 Given Z 1 = 2 − j 3 and Z 2 = 8 + j 6, we have:

Z 1 + Z 2 = 10 + j 3 Z 1 − Z 2 = −6 − j 9

Z 1 Z 2 = 16 − j 24 + j 12 − j 2 18 = 34 − j 12
2 − j 3 8 − j 6 16 − j 12 − j 24 + j 2 18 Z1 / Z2 = × = = −0.02 − j 0.36 8+ j6 8− j6 100
EA.2

Z 1 = 15∠45 o = 15 cos( 45 o ) + j 15 sin( 45 o ) = 10.6 + j 10.6 Z 2 = 10∠ − 150 o = 10 cos( −150 o ) + j 10 sin( −150 o ) = −8.66 − j 5 Z 3 = 5∠90 o = 5 cos(90 o ) + j 5 sin(90 o ) = j 5
Notice that Z1 lies in the first quadrant of the complex plane.

EA.3

Z 1 = 3 + j 4 = 32 + 4 2 ∠ arctan( 4 / 3) = 5∠53.13o
Notice that Z2 lies on the negative imaginary axis. Z 2 = − j 10 = 10∠ − 90 o Notice that Z3 lies in the third quadrant of the complex plane.

Z 3 = −5 − j 5 = 52 + 52 ∠(180 o + arctan( −5 / − 5)) = 7.07 ∠225 o = 7.07 ∠ − 135 o
EA.4

Notice that Z1 lies in the first quadrant of the complex plane.

Z 1 = 10 + j 10 = 10 2 + 10 2 ∠ arctan(10 / 10) = 14.14∠45 o = 14.14 exp( j 45 o )
Notice that Z2 lies in the second quadrant of the complex plane.

Z 2 = −10 + j 10 = 10 2 + 10 2 ∠(180 o + arctan( −10 / 10))
= 14.14∠135 o = 14.14 exp( j 135 o )

685

EA.5

Z 1Z 2 = (10∠30 o )(20∠135 o ) = (10 × 20)∠(30 o + 135 o ) = 200∠(165 o ) Z 1 / Z 2 = (10∠30 o ) /(20∠135 o ) = (10 / 20)∠(30 o − 135 o ) = 0.5∠( −105 o )
Z 1 − Z 2 = (10∠30 o ) − (20∠135 o ) = (8.66 + j 5) − ( −14.14 + j 14.14)
= 22.8 − j 9.14 = 24.6∠ − 21.8o

Z 1 + Z 2 = (10∠30 o ) + (20∠135 o ) = (8.66 + j 5) + ( −14.14 + j 14.14)
= −5.48 + j 19.14 = 19.9∠106o

Problems PA.1

Given Z 1 = 2 + j 3 and Z 2 = 4 − j 3, we have:

Z1 + Z2 = 6 + j 0 Z 1 − Z 2 = −2 + j 6 Z 1 Z 2 = 8 − j 6 + j 12 − j 2 9 = 17 + j 6
Z1 / Z2 =
2 + j 3 4 + j 3 − 1 + j 18 = = 0.04 + j 0.72 × 4 − j3 4 + j3 25

PA.2

Given that Z 1 = 1 − j 2 and Z 2 = 2 + j 3, we have:

Z1 + Z2 = 3 + j 1 Z 1 − Z 2 = −1 − j 5 Z1 Z2 = 2 + j 3 − j 4 − j 2 6 = 8 − j 1
Z1 / Z2 =
1 − j2 2 − j3 − 4 − j 7 = = −0.3077 − j 0.5385 × 2 + j3 2 − j3 13

686...