Lecture (Mar 30, 2000)

1
Lecture (Mar 30, 2000)

• Digital Modulation
• Data Rates/ Channel Capacity

2
Summary of Last Lecture

• Ohms Law relates current and voltage (VIR)
• The laws of electricity and magnetism are
  summarized in 4 fundamental equations called
  Maxwells Equations
• Electromagnetic waves are the foundation of
  communication
• travel at the speed of light

3
Electromagnetic Waves
Transmitter
Receiver
Wave
Signal Voltage
Signal Voltage
Antenna
Antenna

• Received voltage is nearly identical to the
  transmitted voltage
• Electromagnetic Waves can propagate through air
  or cables
• The process of converting bits to signal voltages
  is called digital modulation
• The process of extracting bits from signal
  voltages is called digital demodulation.

4
Ideas of Modulation

• How would I use electromagnetic waves to transmit
  bits?
• Idea Designate a certain signal shape for 1
  and another signal shape for 0. The receiver
  of the signal could then look at the shape (or
  signature) and determine the value of the bit
• The amount of time each signal shape lasts is
  called the Baud Period (Tbaud) and is measured in
  seconds

5
Modulation Signals
Signal Voltage for 1
Time
Tbaud
Signal Voltage for 0
Tbaud
Time
6
Modulation Example
Digital Modulator
Signal Voltage
Bits
Example Input bits 1101 Resulting Signal
1
1
0
1
Signal Voltage
Time
Tbaud
7
Demodulation Example
Digital Demodulator
Signal Voltage
Bits
Demodulated Bits
1
1
0
1
Received Signal Voltage
Time
Tbaud

• Demodulator must synchronize (know where to
  start)
• Demodulator must know Tbaud
• Bits are determined by looking at signal shapes

8
What is the Data (Baud) Rate?

• Identifies the amount of bits transmited in one
  second
• R 1 / Tbaud
• Measured in bits per second (bps)

9
Examples

• What is Tbaud if R 1200 bits per second?
• Answer Tbaud 1/R 0.000833 seconds
• What is R if Tbaud 0.05 seconds?
• Answer R 1/Tbaud 20 bits per second

10
Communication Elements
Transmitter
Channel
Receiver

• Modulator
• Antenna

• Atmosphere
• Ethernet Cable
• Telephone Line

• Antenna
• Demodulator

• How many bits per second can reliably be
  transmitted over a channel?

11
Channel Capacity

• Denoted by C
• Measures the amount of data that can be reliably
  transmitted over a channel
• Given in bits per second (bps)

12
The capacity of a channel is given by
C B log2 ( 1 SNR )
Definitions

• B Bandwidth of Channel (Hz)
• SNR Signal to Noise Ratio (Dimensionless)
• SNR is the ratio of the power of the signal
  (Watts) to the power of the noise (Watts)
• log2 denotes logarithm to the base 2

Observations

• As the SNR increases, the capacity increases
• As the Bandwidth increases, the capacity increases

13
Channel Capacity Theorem

• Information can reliably be transmitted over a
  channel if the data rate R is less than or equal
  to the channel capacity C
• R ltC

14
Do Example 8.4 in Text
15
Do Problem 8.5 in Class