ASK Signal | application of ask modulation | demodulation | amplitude shift keying example

amplitude shift keying example , ASK Signal | application of ask modulation | demodulation bandwidth circuit ?
Generation of ASK Signal
(i)         Description and Working Operation
            ASK signal may be generated by simply applying the incoming binary data (represented in unipolar form) and the sinusoidal carrier to the two inputs of a product modulator (i.e., balanced modulator). The resulting output will be the ASK waveform. This is shown in figure 8.4. Modulation causes a shift of the baseband signal spectrum.
(ii)        Power Spectral Density (psd)
The ASK signal, which is basically the product of the binary sequence and the carrier signal, has a power spectral density (PSD) same as that of the baseband on-off signal but shifted in the frequency domain by ± f_c. This is shown in figure 8.5. It may be noted that two impulses occur at ± f_c.
(iii)       Bandwidth of BASK
            The spectrum of the ASK signal shows that it has an infinite bandwidth. However for practical purpose, the bandwidth is often defined as the bandwidth of an ideal bandpass filter centered at f_c whose output contains about 95°% of the total average power content of the ASK signal. It may be proved that according to this criterion the bandwidth of the ASK signal is approximately 3/T_b Hz. The bandwidth of the ASK signal can however, be reduced by using smoothed versions of the pulse waveform instead of rectangular pulse waveforms.
diagram
FIGURE 8.4 Generation of binary ASK waveform
diagram
FIGURE 8.5 Power spectral density of ASK signal.
8.5.3. BASK Reception : Coherent Detection or Demodulation of Binary ASK Signal
(i)         Working Operation
            The demodulation of binary ASK waveform can be achieved with the help of coherent detector as shown in figure 8.6. It consists of a product modulator which is followed by an integrator and a decision-making device. The incoming ASK signal is applied to one input of the product modulator. The other input of the product modulator is supplied with a sinusoidal carrier which is generated with the help of a local oscillator. The output of the product modulator goes to input of the integrator. The integrator operates on the output of the multiplier for successive bit intervals and essentially performs a low-pass filtering action. The output of the integrator goes to the input of a decision-making device.
DIAGRAM
FIGURE 8.6 Coherent detection of binary ASK signals.

Now, the decision-making device compares the output of the integrator with a preset threshold. It makes a decision in favour of symbol 1 when the threshold is exceeded and in favour of symbol 0 otherwise. The coherent detection makes the use of linear operation. In this method we have assumed that the local carrier is in perfect synchronisation with the carriers used in the transmitter. This means that the frequency and phase of the locally generated carrier is same as those of the carriers used in the transmitter.
(ii)        Synchronization Requirement
            The following two forms of synchronisation are required for the operation of coherent (or synchronous detector):
(i)         Phase synchronisation which ensures that carrier wave generated locally in the receiver is locked in phase with respect to one that is employed in the transmitter.
(ii)        Timing synchronisation which enable proper timing of the decision making operation in the receiver with respect to switching instants (switching between 1 and 0) in the original binary data.
8.5.4.   Salient Feature of BASK
            The advantage of using BASK is its simplicity. It is easy to generate and detect.
8.5.5. Drawback
            But the drawback of BASK is that it is very sensitive to noise, therefore, it finds limited application in data transmission. It is used at very low bit rates, upto 100 bits sec.
8.5.6.   Bit Error Rate (BER) or Probability of Error
            As a matter of fact, bit error rate (BER) or probability of error is a very important paramter. This paramter is used to judge the performance of a digital communication system. It is represented by P_e. P_e must be as small as possible.
NOTE : The expression for P_e of a BASK signal has been derived separately later on, in this chapter.
8.6       BINARY PHASE SHIFT KEYING (BPSK)
(i)         Definition
Bianry phase shift keying (BPSK) is the most efficient of the three digital modulation, i.e., ASK. FSK and PSK. Hence, bianry phase shift keying (BPSK) is used for high bit rates. In BPSK. phase of the sinusoidal carrier is changed according to the data bit to be transmitted. Also, a bipolar NRZ signal is used to represent the digital data coming from the digital source.
(ii)        Expression for BPSK
            In a binary phase shift keying (BPSK), the binary symbols ‘1’ and ‘0’ modulate the phase of the carlier. Let us assume that the carrier is given as,
s(t) = A cos (2f_ct)                                         …(8.4)
Here ‘A’ represents peak value of sinusoidal carrier. For the standard 1Ω load resistor, the power dissipated would be,
P =  A²
or                                                    A =                                               …(8.5)
Now, when the symbol is changed, then the phase of the carrier will also be changed by an amount of 180 degrees (i.e.,  radians).
Let us consider, for example,
For symbol ‘1’ we have
s₁(t) =  cos (2f_ct)                                              …(8.6)
If next symbol is ‘0’, then we have
For symbol ‘0’, we have
s₂(t) =  cos (2f_ct + )                           ..(8.7)
Now, because cos ( + ) = – cos , therefore, the last equation can be written as
s₂(t) = –  cos (2f_ct)                                            …(8.8)
With the above equation, we can define BPSK signal combinely as,
s₂(t) = b(t)  cos (2f_ct)                            …(8.9)
where                          b(t) = + 1 when binary ‘1’ is to be transmitted.
– 1 when binary ‘0’ is to be transmitted
(iii)       Binary Sequency and its Equivalent Signal b(t)
Figure 8.7 illustrates binary signal and its equivalent signal b(t).
NOTE It may be observed from figure 8.7(b) that the signal b(t) is a NRZ bipolar signal. In fact, this signal directly modulates the carrier signal cos (2fc t).
diagram
FIGURE 8.7 (a) Binary sequence, (b) The corresponding bipolar signal b(t) .
8.6.1.   Generation of BPSK Signal
            BPSK signal may be generated by applying carrier signal to a balanced modulator. The binary data signal (0s and 1s) is converted into a NRZ bipolar signal by an NRZ encoder. Here, the bipolar signal b(t) is applied as a modulating signal to the balanced modulator.
Figure 8.8 shows the block diagram of a BPSK signal generator.
A NRZ level encoder converts the binary data sequence into bipolar NRZ signal.
diagram
FIGURE 8.8 Generation of BPSK.
Table 8.1. shows input digital and corresponding bipolar NRZ signal.

 
In above table,
(i)         P = , where, E_b is the signal energy and Tb is the bit duration
(ii)        Also, _c = 2f_c,
8.6.2.   Reception of BPSK Signal : Coherent Detection
            Figure 8.9 shows the block diagram of the scheme to recover baseband signal from BPSK signal. The transmitted BPSK signal is given as
s(t) = b(t),  cos (2f_ct)
DIAGRAM
FIGURE 8.9 Reception of baseband signal in BPSK signal.
This signal undergoes the phase change depending upon the time delay from transmitter end to receiver end. This phase change is, usually, a fixed phase shift in the transmitted signal.
Let us consider that this phase shift is 0. Because of this, the signal at the input of the receiver can be written as
s(t) = b(t),  cos (2f_ct + )                                 …(8.10)
Now, from this received signal, a carrier is separated because this is coherent detection. As shown in the figure 8.9, the received signal is allowed to pass through a square law device. At the output of the square law device, we get a signal which is given as
cos² (2fct + )
Here, it may be noted that we have neglected the amplitude, since we are only interested in the carrier of the signal.
Again, we know that
cos²  =
Therefore, we have
EQUATION
Here,  represents a DC level. This signal is then allowed to pass through a bandpass filter (BPF) whose passband is centred around 2f_e. Bandpass filter removes the DC level of   and at the output. we obtain.
cos 2(2f_ct + )
This signal is having frequency equal to 2f_c. Hence, it is passed through a frequency divider by two. Thus, at the output of frequency divider, we get a carrier signal whose frequency is f_c i.e., cos (2f_ct + ).
The synchronous (i.e., coherent) demodulator multiplies the input signal and the recovered carrier. Hence, at the output of multiplier, we get
b(t) cos(2f_ct+) x cos (2fct + ) = b(t) cos² (2f_ct + )
= b(t) x  [1 + cos2 (2f_ct + ]
= b(t) [1 + cos 2 (2f_ct + ]           …(8.11)
This signal is then applied to the bit synchronizer and integrator. The integrator integrates the signal over one bit period. The bit synchronized takes care of starting and ending times of a bit. At the end of bit duration T_b, the bit synchronizer closes switch S₂ temporarily. This connects the output of an integrator to the decision device. In fact, it is equivalent to sampling the output of integrator. The synchronizer then opens switch S₂ and switch S₁ is closed temperorily. This resets the integrator voltage to zero. The integrator then integrates next bit. Let us assume that one bit period `T_b‘ contains integral number of cycles of the carrier. This means that the phase change occurs in the carrier only at zero crossing. This has been shown in figure 8.10. This BPSK waveform has full cycles of sinusoidal carrier.
DIAGRAM
FIGURE 8.10 The BPSK waveform.
Also, in the k^th bit interval, we can write output signal as under:
EQUATION
This equation gives the output of an interval for k^th bit. Hence, integration is performed from (k – 1)T_b to kT_b. Here, T_b is the one bit period. We can write the above equation as under.
equation
where  dt = 0, since average value of sinusoidal waveform is zero if integration is done over full cycles. Hence, we can write above equation as,
equation
or                                                           equation                                                   …(8.12)
The last eqaution shows that the output of the receiver depends on input.
Thus,                                       s₀(kT_b) α b(kT_b)
Depending upon the value of b(kT_b), the output s₀(kT_b) is generated in receiver.
This signal is then applied to a decision device which decides whether transmitted symbol was zero or one.

8.6.3.   The Spectrum of BPSK Signals
            Type of we know that the waveform b(t) is a NRZ binary waveform. In this waveform, there are rectangular pulses of amplitude ± V_b. If we assume that each pulse is ± around its centre, then it becomes easy to find Furrier trans-form of such pulse. The Fourier transform of this type of pulse is given as,
X(f) =                                    …(8.13)
For a large number of such positive and negative pulses, the power spectral density S(f) is expressed as
S(f) =                                        …(8.14)
Here,  denotes average value of X(f) due to all the pulses in b(t). And T_s is symbol duration. Substituting value of X(f) from equation (13.13) in equation (8.14), we get
 
EQUATION
For BPSK, because only one bit is transmitted at a time, therefore, symbol and bit durations are same i.e., T_b = T_s. Then the last equation becomes,
equation
* Here, f_b  = .
This equation gives the power spectral density (psd) of baseband signal b(t). The 131’SK signal is generated by modulating a carrier by the baseband signal b(t). Due to modulation of the carrier of frequency f_c, the spectral components are translated from f to f_c + f and f_c – f. The magnitude of these components is divided by half.
Therefore, from equation (8.15) we can write the power spectral density of BPSK signal as under:
Equation
It may be noted that this equation consists of two half magnitude spectral components of same frequency ‘f‘ above and below f_c. Let us assume that the value of ± V_b = + . This means that the NRZ signal is having amplitudes of + and . Then the last equation becomes,
equation
This equation gives power spectral density (psd) of BPSK signal for modulating signal b(t) having amplitudes equal to ± .
Further, we know that the modulated signal is given as
s(t) = +   cos (2f_ct)                                           [∵ A = ]
If b(t) = ± , then the carrier becomes,
(t) =  cos (2f_ct)                         …(8.17)
Equation (8.15) describes power spectral density (psd) of the NRZ waveform. For one rectangular pulse, the shape of S(f) will be a sine pulse as shown in figure 8.11.
equation
FIGURE 8.11 Plot of power spectral density (psd) of NRZ baseband signal.
It may be observed from this figure that the main lobe ranges from – f_b to f_b*. Because we have taken ± V_b = +  in equation (8.15), therefore, the peak value of the main lobe is PT_b. Now let us consider the power spectral density (psd) of BPSK signal expressed by equation (8.16).
Figure 8.12 shows the plot of this equation. This figure, thus, clearly shows that there are two lobes, one at f_c and other at – f_e. The same spectrum of figure 8.11 has been placed at +f_c and – f_c. However, the amplitudes of main lobes are  in figure 8.12.
DIAGRAM
FIGURE 8.12 Plot of power spectral density of BPSK signal.
Hence, they are reduced to half. The spectrum of S(f) as well as S_BPSK(f) extends overall the frequencies.