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

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 P_H(t) is same as b(t) and also P_L(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 P_H(t). An inverter is added after b(t) to get P_L(t). The level shifter P_H(t) and P_L(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, P_L(t) = 1 and P_H(t) = 0, and for a binary ‘1’ to be transmitted, P_H(t) = 1 and P_L(t) = 0. Hence, the transmitted signal will have a frequency of either f_H or f_L. 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., T_b), 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 P_H(t) and P_L(t) are complementary to each other. Therefore, if P_H(t) = 1. then output will be only due to upper modulator and lower modulator output will be zero [since P_L(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) = P_H (t) cos (2f_Ht) = P_L (t) cos (2f_Ht)     …(8.30)
This is the expression for BFSK signal. Let us compare this equation with BPSK equation which is written below:
S_BPSK(t) = b(t)  cos (2f_ct)                                  …(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 P_H(t) or P_L(t) are unipolar. Hence, let us convert these coefficients in bipolar form as under:
P_H(t) = P’_H(t)                                        …(8.32)
and                                             P_L(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 (2f_Lt)         …(8.34)

In this equation, the first term represents the single frequency impulse situated at frequency f_H. The second term represents the impulse at f_L. These are constant amplitude pulses. The last two terms are identical to BPSK equation of equation (8.31).
Here P_H‘(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 f_H and other at f_L. 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, f_H, and f_L, are selected such that,
f_H – f_L = 2f_b                                                                                 …(8.36)
With such types of selection, it is obvious from the spectrums in the above figure that the two frequencies f_H and f_L 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 2f_b. The two main lobes due to f_H and f_L are placed such that the total width due to both main lobes is 4 f_b.
Therefore, we have
Bandwidth of BFSK = 2f_b + 2f_b
or                             BW = 4f_b                                                                            …(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 f_c1 and f_c2, 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 f_c1) is greater than the output l₂ produced in the lower path (associated with frequency f_c2), 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 f_H and f_L, are used for modulation. To make ₁ (t) and  ₂(t) orthogonal, the frequencies f_H and f_L must be some integer multiple of band frequency ‘f_b‘.
Thus,                                       f_H = mf_b                                                            …(8.39)
and                                          f_L = nf_b                                                               …(8.40)
Here;  fb = , then the carriers would be
₁(t) =  cos (2mf_b t)                                          …(8.41)
and                                 ₂(t) =  cos (2mf_b t)                              …(8.42)
The carriers ₁(t) and ₂ (t) are orthogonal over the period T_b. We can write equation (8.25) and equation (8.26) as,
s_H(t) =    cos (2f_H t)
and                              s_L(t) =    cos (2f_L t)
Here                            f_H = f_c +
and                              f_L = f_c +
Using the relations in equations (8.39) to (8.42), we can write above equations as
s_H(t) =  . ₁(t)                          …(8.43)
and                                              s_L(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 P_s T_b = E_b, 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.