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

*(t). An inverter is added after b(t) to get P*

_{H}*(t). The level shifter P*

_{L}*(t) and P*

_{H}*(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}_{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

*(t) = 1. then output will be only due to upper modulator and lower modulator output will be zero [since P*

_{H}*(t) = 0].*

_{L}**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

_{H}t) = P

_{L}(t) cos (2f

_{H}t) …(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

*t) …(8.31)*

_{c}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

*(t) are unipolar. Hence, let us convert these coefficients in bipolar form as under:*

_{L}P

*(t) = P’*

_{H}*(t) …(8.32)*

_{H}and P

*(t) = P’*

_{L}*(t) …(8.33)*

_{L}where P’

*(t) and P’*

_{H}*(t) will be bipolar (i.e., + 1 or – 1).*

_{L}Substituting these values in equation (8.30), we obtain

**EQUATION**

or

**equation**

+ P’L (t) cos (2f

*t) …(8.34)*

_{L}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 f* _{H}*. The second term represents the impulse at f

*. These are constant amplitude pulses. The last two terms are identical to BPSK equation of equation (8.31).*

_{L}Here P

*‘(t) and P’*

_{H}*(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*

_{L}*and other at f*

_{H}*. Hence, we can write the power spectral density of BFSK as under:*

_{L}**equation**

Figure 8.16 illustrates the plot of power spectral density of BFSK signal expressed by equation (8.35).

Also, f

*, and f*

_{H}*, are selected such that,*

_{L}f

*– f*

_{H }*= 2f*

_{L}_{b}…(8.36)

With such types of selection, it is obvious from the spectrums in the above figure that the two frequencies f

*and f*

_{H}*may be identified properly. The interference between the spectrums is not*

_{L}**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**

*. The two main lobes due to f*

_{b}*and f*

_{H}*are placed such that the total width due to both main lobes is 4*

_{L}*f*.

_{b}Therefore, we have

Bandwidth of BFSK = 2

*f*+ 2

_{b}*f*

_{b}or BW = 4

*f*…(8.37)

_{b}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

*l*

_{1}and

*l*

_{2}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.

*l*

_{1}(in the upper path) and output

*l*

_{2}(in the lower path). If the output

*l*

_{1}produced in the upper path (associated with frequency f

_{c1}) is greater than the output

*l*

_{2}produced in the lower path (associated with frequency f

_{c2}), the detector makes a decision in favour of symbol 1. If the output

*l*

_{1}is less

*l*

_{2}, 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

*and f*

_{H}_{L}, are used for modulation. To make

_{1}(t) and

_{2}(t) orthogonal, the frequencies f

*and f*

_{H}*must be some integer multiple of band frequency ‘*

_{L}*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

*t) …(8.41)*

_{b}and

_{2}(t) = cos (2mf

*t) …(8.42)*

_{b}The carriers

_{1}(t) and

_{2 }(t) are orthogonal over the period T

*. We can write equation (8.25) and equation (8.26) as,*

_{b}s

_{H}(t) = cos (2f

*t)*

_{H}and s

_{L}(t) = cos (2f

*t)*

_{L}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:**

d

^{2}=

or d

^{2}= 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.**

S. No. |
Parameter of comparison |
Binary ASK |
Binary FSK |
Binary PSK |

1 | Variable characteristic | Amplitude | Frequency | Phase |

2 | Bandwidth (Hz) (spectral efficiency) | 2f_{b} |
4f_{b} |
2f_{b} |

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 |