# bfsk full form | Generation of BFSK signals | Spectrum of BFSK Signal , Bandwidth , transmitter and receiver

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what is bfsk full form | Generation of BFSK signals | Spectrum of BFSK Signal , Bandwidth , transmitter and receiver block diagram ?
Generation of BFSK                   (U.P. Tech, Sem. Exam; 2005-06) (10 marks)
It may be observed from Table 8.1 that PH(t) is same as b(t) and also PL(t) is inverted version of b(t). The block diagram for BFSK generation is shown in figure 8.14.
* The derivation of this expression has been given sepatately in the end of this chapter.
DIAGRAM
FIGURE 8.14 Block diagram for BFSK generation.
We know that input sequence b(t) is same as PH(t). An inverter is added after b(t) to get PL(t). The level shifter PH(t) and PL(t) are unipolar signals. The level shifter converts the ‘+1’ level to . Zero level is unaffected. Thus, the output of the level shifters will be either (if ‘+1’) or zero (if input is zero). In other words, when a binary ‘0’ is to be transmitted, PL(t) = 1 and PH(t) = 0, and for a binary ‘1’ to be transmitted, PH(t) = 1 and PL(t) = 0. Hence, the transmitted signal will have a frequency of either fH or fL. Further, there are product modulators after level shifter. The two carrier signals 1(t) and 2(t) are used. 1(t) and 2(t) are orthogonal to each other. In one bit period of input signal (i.e., Tb), 1 (t) or 2(t) have integral number of cycles.
Thus, the modulated signal is having continuous phase. Figure 8.15 shows such type of BFSK signal. The adder then adds the two signals.
diagram
FIGURE 8.15 The BFSK signal.
NOTE Here it may be noted that outputs from both the multipliers are not possible at a time. This is because PH(t) and PL(t) are complementary to each other. Therefore, if PH(t) = 1. then output will be only due to upper modulator and lower modulator output will be zero [since PL(t) = 0].
8.7.2. The Spectrum of BFSK Signal
In figure 8.14, the BFSK signal s(t) may be written as,
s(t) = PH (t) cos (2fHt) = PL (t) cos (2fHt)     …(8.30)
This is the expression for BFSK signal. Let us compare this equation with BPSK equation which is written below:
SBPSK(t) = b(t)  cos (2fct)                                  …(8.31)
It may be noted that this equation is identical to BFSK equation. In BPSK equation, b(t) is a bipolar signal where as in BFSK, the similar coefficients PH(t) or PL(t) are unipolar. Hence, let us convert these coefficients in bipolar form as under:
PH(t) = P’H(t)                                        …(8.32)
and                                             PL(t) = P’L(t)                             …(8.33)
where P’H(t) and P’L(t) will be bipolar (i.e., + 1 or – 1).
Substituting these values in equation (8.30), we obtain
EQUATION
or                                               equation
+ P’L (t) cos (2fLt)         …(8.34)

 DO YOU KNOW? FSK is also used extensively in high-frequency radio systems for radio-teletype transmission.

In this equation, the first term represents the single frequency impulse situated at frequency fH. The second term represents the impulse at fL. These are constant amplitude pulses. The last two terms are identical to BPSK equation of equation (8.31).
Here PH‘(t) and P’L(t) are equivalent to b(t). Therefore, these last two terms in equation (8.34) produce the spectrum which are similar to that of BPSK. One spectrum is located at fH and other at fL. Hence, we can write the power spectral density of BFSK as under:
equation
Figure 8.16 illustrates the plot of power spectral density of BFSK signal expressed by equation (8.35).
Also, fH, and fL, are selected such that,
fH – fL = 2fb                                                                                 …(8.36)
With such types of selection, it is obvious from the spectrums in the above figure that the two frequencies fH and fL may be identified properly. The interference between the spectrums is not much with the above assumption.
diagram
Figure 8.16 Illustration of Power spectral density (psd) of a BFSK signal.
8.7.3.   Bandwidth of BFSK Signal
From figure 8.16, it is obvious that the width of one lobe is 2fb. The two main lobes due to fH and fL are placed such that the total width due to both main lobes is 4 fb.
Therefore, we have
Bandwidth of BFSK = 2fb + 2fb
or                             BW = 4fb                                                                            …(8.37)
Now, if we compare this bandwidth with that of BPSK, we note that,
BW (BFSK) = 2 x BW(BPSK)                                     …(8.38)
8.7.4.   BPSK Receiver: Coherent Detection of BFSK
Figure 8.17 shows the block diagram of a scheme for demodulation of BFSK wave using coherent detection technique. The detector consists of two correlators that are individually tuned to two different carrier frequencies to represent symbols ‘1’ and ‘0’. A correlator consists of a multiplier followed by an integrator. Then, the received binary FSK signal is applied to the multipliers of both the correlators. To the other input of the multipliers, carriers with frequency fc1 and fc2, are applied as shown in figure 8.17. The multiplied output of each multiplier is subsequently passed through integrators generating output l1 and l2 in the two paths. The output of the two
diagram
FIGURE 8.17 Block diagram s of BFSK receiver (detect ion of BFSK).
integrators are then fed to the decision making device. The decision making device is essentially a comparator which compares the output. l1 (in the upper path) and output l2 (in the lower path). If the output l1 produced in the upper path (associated with frequency fc1) is greater than the output l2 produced in the lower path (associated with frequency fc2), the detector makes a decision in favour of symbol 1. If the output l1 is less l2, then the decision making device decides in favour of symbol 0 (say). This type of digital communication receivers are also called correlation receivers. As discussed earlier, the detector based upon coherent detection requires phase and timing synchronisation.
8.7.5.   Geometrical Representation of Orthogonal BFSK
As a flatter of fact, orthogonal carriers are used for M-ary PSK and QASK. The different signal points are represented geometrically in 1 2-plane. For geometrical representation of BFSK signals, such orthogonal carriers are required. From figure 8.14, we know that two carriers 1(t) and 2(t) of two different frequencies fH and fL, are used for modulation. To make 1 (t) and  2(t) orthogonal, the frequencies fH and fL must be some integer multiple of band frequency ‘fb‘.
Thus,                                       fH = mfb                                                            …(8.39)
and                                          fL = nfb                                                               …(8.40)
Here;  fb = , then the carriers would be
1(t) =  cos (2mfb t)                                          …(8.41)
and                                 2(t) =  cos (2mfb t)                              …(8.42)
The carriers 1(t) and 2 (t) are orthogonal over the period Tb. We can write equation (8.25) and equation (8.26) as,
sH(t) =    cos (2fH t)
and                              sL(t) =    cos (2fL t)
Here                            fH = fc +
and                              fL = fc +
Using the relations in equations (8.39) to (8.42), we can write above equations as
sH(t) =  . 1(t)                          …(8.43)
and                                              sL(t) =  . 2(t)                                     …(8.44)
diagram
FIGURE 8.18 Illustration of signal space representation of orthogonal BFSK signal.
Thus, based on the above two equations, we can draw the signal space diagram as shown in figure 8.18.
8.7.5.1. Distance Between Signal Points
Note that there are two signal points in the signal space. The distance between these two points may be evaluated as under:
d2 =
or                                             d2 = 2Ps Tb    or   d =       …(8.45)
Since Ps Tb = Eb, we can write above relation (i.e., equation (8.45)) as under:
d =                                                        …(8.46)
As compared to the distance of BPSK, we may observe that this distance is smaller than BPSK.
8.7.6.   Comparison of Three Basic Digital Modulation Techniques
We can compare three basic digital modulation techniques in the form of table 8.3.
Table 8.3.

 S. No. Parameter of comparison Binary ASK Binary FSK Binary PSK 1 Variable characteristic Amplitude Frequency Phase 2 Bandwidth (Hz) (spectral efficiency) 2fb 4fb 2fb 3 Noise immunity low high high 4 Probability of error high low low 5 Performance in presence of noise poor Better tan ASK Best of three 6 System complexity Simple Moderately complex Very complex 7 Bit rate or data rate Suitable upto 100 bits/sec. Suitable upto about 1200 bits/sec. Suitable for high bit rates 8 Demodulation method Envelope detection Envelope detection Coherent detection