Quiz 3 ANGEL->Lessons->Quizzes

Modulation and Demodulation

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

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)

As in movies Goldeneyes (1995, 17th in the James Bond series) https://www.youtube.com/watch?v=MH2qnn4D0kY

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

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)

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

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

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.

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. https://www.google.com/get/spectrumdatabase/

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)

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

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

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

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

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

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

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.

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.

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

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.

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!

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°

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

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

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

Constellation Diagram Example: Assume 4 bits / cycle: 1 1 0 0 1 bit / shift 2-PSK

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.

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

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.

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

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

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.