1. Quiz 3
ANGEL->Lessons->Quizzes

2. Modulation and Demodulation

3. Reading for next class Ch. 11
Reminder: group research assignment 1 (resubmission) due on Wednesday at 11:59pm

4. Radio telescopes used in radio astronomy
Arecibo Observatory, Puerto Rico
(305 meter in diameter, world's largest single-aperture telescope)
Very Large Array, New Mexico
(27*25-meter radio telescopes)

5. As in movies Goldeneyes (1995, 17th in the James Bond series)

6. Why Do We Need A Large Radio Telescope like This?
Difficulties in low frequency communications
Many astronomical objects emit radiation at radio frequency (RF)
RF is much small than the frequency of visible lights
RF: 3KHz – 300 GHz

7. Why Do We Need A Large Radio Telescope like This?
Antenna size: the same magnitude of the wavelength of a signal
Low frequency signals require large antennas.
Example: f = 1MHz
f *l = c (speed of light)

8. Another example
Audio/music signal: 3KHz
What is its wavelength?

9. We need a NEW way to transmit and receive low frequency signals easily!

10. Modulation and Demodulation
Modulation: use a high frequency signal to carry information about a low-frequency signal (e.g., sound waves).
Demodulation: recreate the low-frequency signal from the high frequency signal.

11. More Motivation for Modulation
Interference
Signals occupy similar frequency bands
Many people talking at the same time
Modulation: allow different signals to be transmitted simultaneously with a single device
Radio and TV channels: different frequencies.

12. Methods for Modulation
In essence, a sender must change one of the characteristics of the carrier
Amplitude modulation
Frequency modulation
Phase shift modulation
y = A sin(2p f t + f)

13. Amplitude Modulation (AM)
The amplitude of a carrier is modified in proportion to the information signal.
The frequency of the carrier is fixed.
carrier
information

14. Example The original signal: sin(x) The carrier: sin(35x)
Multiplication
sin(x) * sin(35x)

15. Problems of Amplitude Modulation
Power level to zero
Practical systems do not allow for a modulated signal to approach zero
In practice, modulation only changes the amplitude of a carrier slightly
Keeping the carrier wave near maximum

16. Example The carrier: sin(35x) The signal: sin(x)
AM with a modulation index a
[ a * sin(x) + mi ] * sin (35x)
a = 0.3, mi =1

17. Modulation of Digital Signals
A different term: shift keying
Instead of a continuum of possible values, digital shift keying has a fixed set
Mapping to the power levels of a digital signal

18. Amplitude Shift Keying: Example
Carrier: 2 sin(2p 4 t)
Digital input signal:
Modulated carrier:
2V  level “1”
1V  level “0”

19. Exercise: ASK
Consider the input signal with 3 levels shown above. Assume we want to use the following sine wave as the carrier.
10 sin(2p 2 t)
And we want to use the following ASK scheme
15V  level ‘1’
10V  level ‘0’
5V  level ‘-1’
Please draw the resulting waveform after modulation.

20. Frequency Modulation (FM)
Signal amplitude can be easily affected by the environment.
Signal frequency, however, is quite stable.
In FM, frequency changes according to the signal.

21. Frequency Shift Keying: Example
Carrier: 2 sin(2p 4 t)
Digital input signal:
Modulated carrier:
8Hz  level “1”
4Hz  level “0”

22. Exercise: FSK
Consider the input signal with 3 levels shown above. Assume we want to use the following sine wave as the carrier.
10 sin(2p 2 t)
And we want to use the following FSK scheme
3Hz  level ‘1’
2Hz  level ‘0’
1Hz  level ‘-1’
Please draw the resulting waveform after modulation.

23. Efficiency Issues of ASK and FSK
Must capture the amplitude or frequency information of the carrier
Require at least one cycle of a carrier wave to send a single bit
Transmission capacity is limited by the carrier frequency!
A single sine wave circle
One amplitude
One frequency
Can be shifted with multiple phases!

24. Phase Shift Keying (PSK)
Almost every real world modem use PSK to send more bits.
PSK changes the phase of the carrier wave abruptly.
Each such change is called a phase shift
On a sine wave, each point correspond to a phase (angle)
90°
180°
360° 0°
270°

25. Calculating the Phase Shift
Example:
The first change:
Point A’s phase: 90°
Point B’s phase: 270°
Phase change: 270° - 90° = 180°
The second change:
360° - 180° = 180°
The third change?
90°
180°
360° 0°
270° A B A B B A

26. Calculating the Phase Shift
Step 1: Identify the two points A & B involved in this phase shift
Step 2: Find the phase of A & B
Step 3: phase shift = B’s phase – A’s phase

27. Phase Shift and a Constellation Diagram
How to encode data into phase shifts?
A sender and receiver can agree on the number of bits per second
Use different phase shifts to denote the data bits.
A constellation diagram is used to express the exact assignment of data bits to specific phase changes

28. Constellation Diagram
Example: Assume 4 bits / cycle:
1 bit / shift
2-PSK

29. Exercise: PSK
Assume we want to use the following sine wave as the carrier.
sin(2p t)
And we want to use the 2-PSK to send four bits “0101” in one second. Please draw the resulting waveform after modulation.

30. Phase Shift and Constellation Diagram
2 bit / shift
4-PSK
Phase Shift
45°
135°
215°
305°
Bit Value 00 01 10 11

31. Phase Shift and a Constellation Diagram
In theory, it is possible to increase the data rate by decreasing the angular difference between phases
4-PSK  8-PSK
90°  45°
16-PSK: 22.5°
Noise and distortion limit the ability of practical systems to distinguish among arbitrarily small differences in phase changes.

32. Quadrature Amplitude Modulation (QAM)
ASK + PSK
In a constellation diagram, we use distance from the origin as a measure of amplitude
16QAM

33. 67. 5 ° shifted away from the original signal, but only 22
67.5 ° shifted away from the original signal, but only 22.5 ° from the previous signal
45 ° shifted away from the original signal

34. MODEM: MOdulator + DEModulator
Usually within the same device
Each location needs both a modulator to send data and a demodulator to receive data.
Most communication systems are full duplex.