Wed

nesd

ay, A

pril

12, 2

023

Angle (Exponential) Modulation

1

Wed

nesd

ay, A

pril

12, 2

023

2

Determine the instantaneous frequency of the signal

The frequency of ф(t) is 5 Hz at t = 0 and increases linearly at a rate of 1 Hz per second.

Wed

nesd

ay, A

pril

12, 2

023

3

Hence, in PM, the instantaneous frequency ωi varies linearly with the derivative of the modulating signal

Wed

nesd

ay, A

pril

12, 2

023

4

Wed

nesd

ay, A

pril

12, 2

023

5

Wed

nesd

ay, A

pril

12, 2

023

6

Wed

nesd

ay, A

pril

12, 2

023

7

Wed

nesd

ay, A

pril

12, 2

023

8

Wed

nesd

ay, A

pril

12, 2

023

9

Wed

nesd

ay, A

pril

12, 2

023

10H. W.

Wed

nesd

ay, A

pril

12, 2

023

11

Wed

nesd

ay, A

pril

12, 2

023

12

If kf is very small (that is, if |kfa(t)| << 1), then all but the first two terms are negligible

Wed

nesd

ay, A

pril

12, 2

023

13

Wed

nesd

ay, A

pril

12, 2

023

14

Wed

nesd

ay, A

pril

12, 2

023

15

The Maximum and Minimum carrier frequencies are ωc + kf mp and ωc - kf mp

The deviation of carrier frequency is ± kf mp.

Wed

nesd

ay, A

pril

12, 2

023

16

Wed

nesd

ay, A

pril

12, 2

023

17

Wed

nesd

ay, A

pril

12, 2

023

18

Wed

nesd

ay, A

pril

12, 2

023

19

Wed

nesd

ay, A

pril

12, 2

023

20

Wed

nesd

ay, A

pril

12, 2

023

21

Wed

nesd

ay, A

pril

12, 2

023

22

bandwidth is unchanged so that B = 15 KHz

Wed

nesd

ay, A

pril

12, 2

023

23

Wed

nesd

ay, A

pril

12, 2

023

24

Wed

nesd

ay, A

pril

12, 2

023

25

Wed

nesd

ay, A

pril

12, 2

023

26

Wed

nesd

ay, A

pril

12, 2

023

27