INTRODUCTION
The slides cover the following topics:
1. Digital to Analog Conversion
2. Types of Digital to Analog Conversion
3. Bit Rate and Baud Rate
4. Amplitude Shift Keying (ASK)
5. Frequency Shift Keying (FSK)
6. Phase Shift Keying (PSK)
7. Constellation Diagrams
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Digital-to-Analog Conversion
Digital-to-analog conversion is the process of changing one of the characteristics of an analog signal based on the information in digital data.
Topics discussed in this section:
Figure 5.1 Digital-to-analog conversion
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Figure 5.2 Types of digital-to-analog conversion
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Note:
Bit rate, N, is the number of bits per second (bps).
Baud rate is the number of signal elements per second (bauds).
In the analog transmission of digital data, the signal or baud rate is less than or equal to the bit rate.
S=Nx1/r bauds
Where r is the number of data bits per signal element.
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Example 5.1
An analog signal carries 4 bits per signal element. If 1000 signal elements are sent per second, find the bit rate.
Solution
In this case, r = 4, S = 1000, and N is unknown. We can find the value of N from
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Example 5.2
An analog signal has a bit rate of 8000 bps and a baud rate of 1000 baud. How many data elements are carried by each signal element? How many signal elements do we need?
Solution
In this example, S = 1000, N = 8000, and r and L are unknown. We find first the value of r and then the value of L.
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Amplitude Shift Keying (ASK)
B = (1+d)S
Figure 5.3 Binary amplitude shift keying
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Figure 5.4 Implementation of binary ASK
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Example 5.3
We have an available bandwidth of 100 kHz which spans from 200 to 300 kHz. What are the carrier frequency and the bit rate if we modulated our data by using ASK with d = 1?
Solution
The middle of the bandwidth is located at 250 kHz. This means that our carrier frequency can be at fc = 250 kHz. We can use the formula for bandwidth to find the bit rate (with d = 1 and r = 1).
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Example 5.4
In data communications, we normally use full-duplex links with communication in both directions. We need to divide the bandwidth into two with two carrier frequencies, as shown in Figure 5.5. The figure shows the positions of two carrier frequencies and the bandwidths. The available bandwidth for each direction is now 50 kHz, which leaves us with a data rate of 25 kbps in each direction.
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Figure 5.5 Bandwidth of full-duplex ASK used in Example 5.4
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Frequency Shift Keying
Figure 5.6 Binary frequency shift keying
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Bandwidth of FSK
B = (1+d)xS + 2Δf
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Example 5.5
We have an available bandwidth of 100 kHz which spans from 200 to 300 kHz. What should be the carrier frequency and the bit rate if we modulated our data by using FSK with d = 1?
Solution
This problem is similar to Example 5.3, but we are modulating by using FSK. The midpoint of the band is at 250 kHz. We choose 2Δf to be 50 kHz; this means
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Coherent and Non Coherent
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Multi level FSK
B = (1+d)xS + (L-1)/2Δf = LxS
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Figure 5.7 Bandwidth of MFSK used in Example 5.6
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Example 5.6
We need to send data 3 bits at a time at a bit rate of 3 Mbps. The carrier frequency is 10 MHz. Calculate the number of levels (different frequencies), the baud rate, and the bandwidth.
Solution
We can have L = 23 = 8. The baud rate is S = 3 Mbps/3 = 1 Mbaud. This means that the carrier frequencies must be 1 MHz apart (2Δf = 1 MHz). The bandwidth is B = 8 × 1M = 8M. Figure 5.8 shows the allocation of frequencies and bandwidth.
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Figure 5.8 Bandwidth of MFSK used in Example 5.6
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Phase Shift Keyeing
B = (1+d)xS
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Figure 5.9 Binary phase shift keying
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Figure 5.10 Implementation of BASK
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Quadrature PSK
Figure 5.11 QPSK and its implementation
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Example 5.7
Find the bandwidth for a signal transmitting at 12 Mbps for QPSK. The value of d = 0.
Solution
For QPSK, 2 bits is carried by one signal element. This means that r = 2. So the signal rate (baud rate) is S = N × (1/r) = 6 Mbaud. With a value of d = 0, we have B = S = 6 MHz.
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Constellation Diagrams
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Figure 5.12 Concept of a constellation diagram
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Example 5.8
Show the constellation diagrams for an ASK (OOK), BPSK, and QPSK signals.
Solution
Figure 5.13 shows the three constellation diagrams.
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Figure 5.13 Three constellation diagrams
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Note
Quadrature amplitude modulation is a combination of ASK and PSK.
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Figure 5.14 Constellation diagrams for some QAMs
1. What is analog transmission? |
2. What are the advantages of analog transmission? |
3. What are the limitations of analog transmission? |
4. How does analog transmission differ from digital transmission? |
5. What are some examples of analog transmission? |
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