Bandwidth
The required bandwidth for analog transmission of digital data is proportional to the signal rate except for FSK, in which the difference between the carrier signals needs to be added. We discuss the bandwidth for each technique.
Carrier Signal
In analog transmission, the sending device produces a high-frequency signal that acts as a base for the information signal. This base signal is called the carrier signal or carrier frequency. The receiving device is tuned to the frequency ofthe carrier signal that it expects from the sender. Digital information then changes the carrier signal by modifying one or more of its characteristics (amplitude, frequency, or phase). This kind of modification is called modulation (shift keying).
Amplitude Shift Keying
In amplitude shift keying, the amplitude of the carrier signal is varied to create signal elements. Both frequency and phase remain constant while the amplitude changes.
144 CHAPTER 5 ANALOG TRANSMISSION
BinaryASK (BASK)
Although we can have several levels (kinds) of signal elements, each with a different amplitude, ASK is normally implemented using only two levels. This is referred to as binary amplitude shift keying or on-offkeying (OOK). The peak amplitude of one signallevel is 0; the other is the same as the amplitude ofthe carrier frequency. Figure 5.3 gives a conceptual view ofbinary ASK.
Figure 5.3 Binmy amplitude shift keying
Amplitude Bit rate: 5
1 signal element
o
1 signal element
1
I signal element
1 s Baud rate: 5
I signal element
o
I signal element
I I Time I I I I
r=:= 1 S=N B=(I +d)S
Bandwidth for ASK Figure 5.3 also shows the bandwidth for ASK. Although the carrier signal is only one simple sine wave, the process of modulation produces a nonperiodic composite signal. This signal, as was discussed in Chapter 3, has a continuous set of frequencies. As we expect, the bandwidth is proportional to the signal rate (baud rate). However, there is normally another factor involved, called d, which depends on the modulation and filtering process. The value ofd is between 0 and 1. This means that the bandwidth can be expressed as shown, where 5 is the signal rate and the B is the bandwidth.
B =(1 +d) x S
The formula shows that the required bandwidth has a minimum value of 5 and a maximum value of 25. The most important point here is the location ofthe bandwidth. The middle ofthe bandwidth is whereIe the carrier frequency, is located. This means if we have a bandpass channel available, we can choose ourIe so that the modulated signal occupies that bandwidth. This is in fact the most important advantage ofdigitalto-analog conversion. We can shift the resulting bandwidth to match what is available.
Implementation The complete discussion of ASK implementation is beyond the scope ofthis book. However, the simple ideas behind the implementation may help us to better understand the concept itself. Figure 5.4 shows how we can simply implement binary ASK. Ifdigital data are presented as a unipolar NRZ (see Chapter 4) digital signal with a high voltage of I V and a low voltage of 0 V, the implementation can achieved by multiplying the NRZ digital signal by the carrier signal coming from an oscillator. When the amplitude of the NRZ signal is 1, the amplitude of the carrier frequency is
SECTION 5.1 DIGITAL-TO-ANALOG CONVERSION 145
Figure 5.4 Implementation ofbinaryASK
o
Carrier signal I
I 0 I
held; when the amplitude ofthe NRZ signal is 0, the amplitude ofthe carrier frequency IS zero.
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 ifwe modulated our data by using ASK with d =I?
Solution The middle ofthe bandwidth is located at 250 kHz. This means that our carrier frequency can be atfe =250 kHz. We can use the formula for bandwidth to find the bit rate (with d =1 and r =1).
B =(l +d) x S=2 x N X! =2 XN =100 kHz ...... N =50kbps r
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 of25 kbps in each direction.
Figure 5.5 Bandwidth offull-duplex ASKused in Example 5.4
I' B = 50 kHz '11 B = 50 kHz 'I ~"~~~ ~,~Jf: L 200 (225) (275) 300
Multilevel ASK
The above discussion uses only two amplitude levels. We can have multilevel ASK in which there are more than two levels. We can use 4,8, 16, or more different amplitudes for the signal and modulate the data using 2, 3, 4, or more bits at a time. In these cases,
146 CHAPTER 5 ANALOG TRANSMISSION
r = 2, r =3, r =4, and so on. Although this is not implemented with pure ASK, it is implemented with QAM (as we will see later).
Frequency Shift Keying
In frequency shift keying, the frequency ofthe carrier signal is varied to represent data. The frequency of the modulated signal is constant for the duration of one signal element, but changes for the next signal element if the data element changes. Both peak amplitude and phase remain constant for all signal elements.
Binary FSK (BFSK)
One way to think about binary FSK (or BFSK) is to consider two carrier frequencies. In Figure 5.6, we have selected two carrier frequencies,f} and12. We use the first carrier if the data element is 0; we use the second ifthe data element is 1. However, note that this is an unrealistic example used only for demonstration purposes. Normally the carrier frequencies are very high, and the difference between them is very small.
Figure 5.6 Binaryfrequency shift keying
Amplitude
Bit rate: 5 r=l S=N B=(1+d)S+2t-.j
1 signal 1 signal 1signal 1 signal 1 signal element element element element element Is It h I' 21-.! -I o+-~--1-L....JL..--l--..I...-_ o
IlIl1
Baud rate: 5
As Figure 5.6 shows, the middle ofone bandwidth isJI and the middle ofthe other ish. BothJI and12 are il/apart from the midpoint between the two bands. The difference between the two frequencies is 211f
Bandwidth for BFSK Figure 5.6 also shows the bandwidth of FSK. Again the carrier signals are only simple sine waves, but the modulation creates a nonperiodic composite signal with continuous frequencies. We can think of FSK as two ASK signals, each with its own carrier frequency Cil orh). If the difference between the two frequencies is 211j, then the required bandwidth is
B=(l+d)xS+2iij
What should be the minimum value of211/? In Figure 5.6, we have chosen a value greater than (l + d)S. It can be shown that the minimum value should be at least S for the proper operation ofmodulation and demodulation.
SECTION5.1 DIGITAL-TO-ANALOG CONVERSION 147
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 ifwe 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 2~f to be 50 kHz; this means
B =(1 +d) x S + 28f =100 -. 2S =50 kHz S = 25 kbaud N;;;; 25 kbps
Compared to Example 5.3, we can see the bit rate for ASK is 50 kbps while the bit rate for FSK is 25 kbps.
Implementation There are two implementations of BFSK: noncoherent and coherent. In noncoherent BFSK, there may be discontinuity in the phase when one signal element ends and the next begins. In coherent BFSK, the phase continues through the boundary of two signal elements. Noncoherent BFSK can be implemented by treating BFSK as two ASK modulations and using two carrier frequencies. Coherent BFSK can be implemented by using one voltage-controlled oscillator (VeO) that changes its frequency according to the input voltage. Figure 5.7 shows the simplified idea behind the second implementation. The input to the oscillator is the unipolar NRZ signal. When the amplitude of NRZ is zero, the oscillator keeps its regular frequency; when the amplitude is positive, the frequency is increased.
Figure 5.7 Implementation ofBFSK
1 o 1 o
_lD1_I_I_I_-;"~1 veo I~
Voltage-controlled oscillator
Multilevel FSK
Multilevel modulation (MFSK) is not uncommon with the FSK method. We can use more than two frequencies. For example, we can use four different frequenciesfIJ2,!3, and14 to send 2 bits at a time. To send 3 bits at a time, we can use eight frequencies. And so on. However, we need to remember that the frequencies need to be 2~1 apart. For the proper operation of the modulator and demodulator, it can be shown that the minimum value of 2~lneedsto be S. We can show that the bandwidth with d =0 is
B;;;; (l +d) x S +(L - 1)24{ -. B =LxS
148 CHAPTER 5 ANALOG TRANSMISSION
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 MHz/3 =1000 Mbaud. This means that the carrier frequencies must be 1MHz apart (211f =1MHz). The bandwidth is B=8 x 1000 =8000. Figure 5.8 shows the allocation offrequencies and bandwidth.
Figure 5.8 Bandwidth ofMFSK used in Example 5.6
'I r~~'¥'::L
is 13.5 MHz
I h 12.5 MHz
Bandwidth = 8 MHz
II 6.5 MHz
I' -(.-----.."--,,I~~~lf5~~1 I:I--Ji~~l~;~r'·'·t':~ h h 14 j~ 15 16 7.5 8.5 9.5 HI 10.5 11.5 MHz MHz MHz MHz MHz MHz
Phase Shift Keying
In phase shift keying, the phase ofthe carrier is varied to represent two or more different signal elements. Both peak amplitude and frequency remain constant as the phase changes. Today, PSK is more common than ASK or FSK. However, we will see Sh0l1ly that QAM, which combines ASK and PSK, is the dominant method of digitalto-analog modulation.
Binary PSK (BPSK)
The simplest PSK is binary PSK, in which we have only two signal elements, one with a phase of0°, and the other with a phase of 180°. Figure 5.9 gives a conceptua