Amplitude Modulators
Two basic amplitude modulation principles are discussed. They are square law modulation and switching modulation.
Square law modulator
When the output of a device is not directly proportional to input throughout the operation, the device is said to be non-linear. The Input-Output relation of a non-linear device can be expressed as
When the in put is very small, the higher power terms can be neglected. Hence the output
is approximately given by 
When the output is considered up to square of the in put, the device is called a square law device and the square law modulator is as shown in the figure 2.7.
Figure 2.7: Square law modulator
Consider a non linear device to which a carrier c(t)= Ac cos(2πfc t) and an information signal m(t) are fed simultaneously as shown in figure 2.7. The total input to the device at any instant is
Frequency band centered at fc with a deviation of ± W , Hz.
The required AM signal with a carrier frequency fc can be separated using a band pass filter at the out put of the square law device. The filter should have a lower cut- off frequency ranging between 2W and ( fc -W) and upper cut-off frequency between ( fc +W) and 2 fc
Therefore the filter out put is
The output AM signal is free from distortion and attenuation only when ( fc − W )> 2W or fc > 3W .
Switching modulator
Consider a semiconductor diode used as an ideal switch to which the carrier signalc(t ) = Ac cos(2πfct) and information signal m(t) are applied simultaneously as shown figure 2.8.
Figure 2.8: Switching modulator
The total input for the diode at any instant is given by
When the peak amplitude of c(t) is maintained more than that of information signal, the operation is assumed to be dependent on only c(t) irrespective of m(t). When c(t) is positive, v2=v1since the diode is forward biased. Similarly, when c(t) is negative, v2=0 since diode is reverse biased. Based upon above operation, switching response of the diode is periodic rectangular wave with an amplitude unity and is given by
The diode output v2 consists of
a dc component at f =0.
Information signal ranging from 0 to w Hz and infinite number of frequency bands centered at f, 2fc, 3fc, 4fc, ---------
The required AM signal centered at fc can be separated using band pass filter. The lower cutoff-frequency for the band pass filter should be between w and fc-w and the upper cut-off frequency between fc+w and 2fc. The filter output is given by the equation
Demodulation of AM: -
Demodulation is the process of recovering the information signal (base band) from the incoming modulated signal at the receiver. There are two methods.
Square law demodulator
Consider a non-linear device to which the AM signal s(t) is applied. When the level of s(t) is very small, output can be considered upto square of the input.
The device output consists of a dc component at f =0, information signal ranging from 0-W Hz and its second harmonics and frequency bands centered at fc and 2fc.
The required information can be separated using low pass filter with cut off frequency ranging between W and fc-w.
The filter output is given by
The dc component (first term) can be eliminated using a coupling capacitor or a transformer. The effect of second harmonics of information signal can be reduced by maintaining its level very low. When m(t) is very low, the filter output is given by
When the information level is very low, the noise effect increases at the receiver, hence the system clarity is very low using square law demodulator.
Envelop detector
It is a simple and highly effective system. This method is used in most of the commercial AM radio receivers. An envelop detector is as shown below.
During the positive half cycles of the input signals, the diode D is forward biased and the capacitor C charges up rapidly to the peak of the input signal. When the input signal falls below this value, the diode becomes reverse biased and the capacitor C discharges through the load resistor RL.
The discharge process continues until the next positive half cycle. When the input
signal becomes greater than the voltage across the capacitor, the diode conducts again and the process is repeated.
The charge time constant (rf+Rs)C must be short compared with the carrier period, the capacitor charges rapidly and there by follows the applied voltage up to the positive peak when the diode is conducting.
That is the charging time constant shall satisfy the condition,
On the other hand, the discharging time-constant RLC must be long enough to ensure that the capacitor discharges slowly through the load resistor RL between the positive peaks of the carrier wave, but not so long that the capacitor voltage will not discharge at the maximum rate of change of the modulating wave.
That is the discharge time constant shall satisfy the condition,
where ‘W’ is band width of the message signal.
The result is that the capacitor voltage or detector output is nearly the same as the envelope of AM wave.
Advantages of AM: Generation and demodulation of AM wave are easy. AM systems are cost effective and easy to build.
Disadvantages: AM contains unwanted carrier component, hence it requires more transmission power. The transmission bandwidth is equal to twice the message bandwidth.
To overcome these limitations, the conventional AM system is modified at the cost of increased system complexity. Therefore, three types of modified AM systems are discussed.
DSBSC (Double Side Band Suppressed Carrier) modulation:
In DSBC modulation, the modulated wave consists of only the upper and lower side bands. Transmitted power is saved through the suppression of the carrier wave, but the channel bandwidth requirement is the same as before.
SSBSC (Single Side Band Suppressed Carrier) modulation:
The SSBSC modulated wave consists of only the upper side band or lower side band. SSBSC is suited for transmission of voice signals. It is an optimum form of modulation in that it requires the minimum transmission power and minimum channel band width. Disadvantage is increased cost and complexity.
VSB (Vestigial Side Band) modulation:
In VSB, one side band is completely passed and just a trace or vestige of the other side band is retained. The required channel bandwidth is therefore in excess of the message bandwidth by an amount equal to the width of the vestigial side band. This method is suitable for the transmission of wide band signals.
Double Side Band Suppressed Carrier Modulation
DSBSC modulators make use of the multiplying action in which the modulating
signal multiplies the carrier wave. In this system, the carrier component is eliminated and both upper and lower side bands are transmitted. As the carrier component is suppressed, the power required for transmission is less than that of AM.
If m(t) is the message signal and DSBSC modulated wave s(t) is given by
Consequently, the modulated signal s(t) under goes a phase reversal , whenever the message signal m(t) crosses zero as shown below.
The envelope of a DSBSC modulated signal is therefore different from the message signal and the Fourier transform of s(t) is given by
For the case when base band signal m(t) is limited to the interval –W<f<W as shown in figure below, we find that the spectrum S(f) of the DSBSC wave s(t) is as illustrated below. Except for a change in scaling factor, the modulation process simply translates the spectrum of the base band signal by fc. The transmission bandwidth required by DSBSC modulation is the same as that for AM.
Figure: Message and the corresponding DSBSC spectrum
Ring modulator: -
Ring modulator is the most widely used product modulator for generating DSBSC wave and is shown below.
Figure: Ring modulator
The four diodes form a ring in which they all point in the same direction. The diodes are controlled by square wave carrier c(t) of frequency fc, which is applied longitudinally by means of two center-tapped transformers. Assuming the diodes are ideal, when the carrier is positive, the outer diodes D1 and D2 are forward biased where as the inner diodes D3 and D4 are reverse biased, so that the modulator multiplies the base band signal m(t) by c(t). When the carrier is negative, the diodes D1 and D2 are reverse biased and D3 and D4 are forward, and the modulator multiplies the base band signal –m(t) by c(t). Thus the ring modulator in its ideal form is a product modulator for square wave carrier and the base band signal m(t). The square wave carrier can be expanded using Fourier series as
From the above equation it is clear that output from the modulator consists entirely of modulation products. If the message signal m(t) is band limited to the frequency band − w < f < w , the output spectrum consists of side bands centered at fc.
Balance modulator (Product modulator)
A balanced modulator consists of two standard amplitude modulators arranged in
a balanced configuration so as to suppress the carrier wave as shown in the following block diagram. It is assumed that the AM modulators are identical, except for the sign reversal of the modulating wave applied to the input of one of them. Thus, the output of the two modulators may be expressed as,
Hence, except for the scaling factor 2ka, the balanced modulator output is equal to the product of the modulating wave and the carrier.
Demodulation of DSBSC modulated wave by Coherent detection
The message signal m(t) can be uniquely recovered from a DSBSC wave s(t) by
first multiplying s(t) with a locally generated sinusoidal wave and then low pass filtering the product as shown.
Figure: Coherent detector
It is assumed that the local oscillator signal is exactly coherent or synchronized, in both frequency and phase, with the carrier wave c(t) used in the product modulator to generate s(t). This method of demodulation is known as coherent detection or synchronous detection.
The first term in the above expression represents a DSBSC modulated signal with a carrier frequency 2fc, and the second term represents the scaled version of message signal. Assuming that the message signal is band limited to the interval − w < f spectrum of v(t) is plotted as shown below.
Figure: Spectrum of output of the product modulator
From the spectrum, it is clear that the unwanted component (first term in the expression) can be removed by the low-pass filter, provided that the cut-off frequency of the filter is greater than W but less than 2fc-W. The filter output is given by
Thus the spectrum of the DSBSC modulated wave, for the case of sinusoidal modulating wave, consists of delta functions located at − fc ± f m and fc ± f m .
Assuming perfect synchronism between the local oscillator and carrier wave in a coherent detector, the product modulator output contains the high frequency components and scaled version of original information signal. The Low Pass Filter is used to separate the desired message signal.
Costas Receiver (Costas loop)
Costas receiver is a synchronous receiver system, suitable for demodulating DSBSC waves. It consists of two coherent detectors supplied with the same input signal, that is the incoming DSBSC wave s(t ) = Ac cos(2πfct )m(t ) but with individual local oscillator signals that are in phase quadrature with respect to each other as shown below.
Figure: Costas receiver
The frequency of the local oscillator is adjusted to be the same as the carrier frequency fc. The detector in the upper path is referred to as the in-phase coherent detector or I- channel, and that in the lower path is referred to as the quadrature-phase coherent detector or Q-channel. These two detector are coupled together to form a negative feed back system designed in such a way as to maintain the local oscillator synchronous with the carrier wave. Suppose the local oscillator signal is of the same phase as the carrier wave c(t ) = Ac cos(2πfc t ) used to generate the incoming DSBSC wave. Then we find that the I-channel output contains the desired demodulated signal m(t), where as the Q- channel output is zero due to quadrature null effect of the Q-channel. Suppose that the local oscillator phase drifts from its proper value by a small angleφ radiations. The I- channel output will remain essentially unchanged, but there will be some signal appearing at the Q-channel output, which is proportional to sin(φ ) ≅ φ for small φ . This Q-channel output will have same polarity as the I-channel output for one direction of local oscillator phase drift and opposite polarity for the opposite direction of local oscillator phase drift. Thus by combining the I-channel and Q-channel outputs in a phase discriminator (which consists of a multiplier followed by a LPF), a dc control signal is obtained that automatically corrects for the local phase errors in the voltage-controlled oscillator.
