Generation of AM waves

An amplitude modulated (AM) wave can be generated using a modulating signal and a carrier wave. The modulating signal is typically a low-frequency audio signal, and the carrier wave is a high-frequency sine wave.

There are different ways to generate an AM wave, but one common method is by using a nonlinear device such as a diode or transistor. The nonlinear device is used to vary the amplitude of the carrier wave in response to the modulating signal. This process is known as nonlinear modulation.

The basic circuit for generating an AM wave using a diode is shown below:

AM wave generation using a diode

In this circuit, the modulating signal is applied to the diode, which acts as a variable resistor. As the modulating signal varies, the resistance of the diode changes, causing the amplitude of the carrier wave to vary. The output of the circuit is the modulated signal.

Another method for generating an AM wave is by using a balanced modulator circuit. The balanced modulator circuit uses two diodes and a transformer to modulate the carrier wave. The modulating signal is applied to one of the diodes, and the other diode is used to produce the carrier wave. The transformer is used to combine the modulated carrier wave and the unmodulated carrier wave.

The basic circuit for generating an AM wave using a balanced modulator is shown below:

AM wave generation using a balanced modulator

In this circuit, the modulating signal is applied to one of the diodes, and the other diode is used to produce the carrier wave. The transformer is used to combine the modulated carrier wave and the unmodulated carrier wave.

Other methods for generating an AM wave include using a varactor diode, which is a special type of diode that can change its capacitance in response to an applied voltage, and using a phase-locked loop (PLL), which is a circuit that can generate a stable carrier wave and modulate it using a modulating signal.

There are two methods to generate AM waves
1. Square-law modulator
2. Switching modulator

Square-law modulator: -

Square-law modulator

 A Square-law modulator requires three features: a means of summing the carrier and modulating waves, a nonlinear element, and a band pass filter for extracting the desired modulation products. Semi-conductor diodes and transistors are the most common nonlinear devices used for implementing
square law modulators. The filtering requirement is usually satisfied by using a single or double tuned filters.When a nonlinear element such as a diode is suitably biased and operated in a restricted portion of its characteristic curve, that is ,the signal applied to the diode is relatively weak, we find that transfer characteristic of diode-load resistor combination can be represented closely by a square law :
V0 (t) = a1Vi (t) + a2 Vi2(t) ……………….(i)
Where a1, a2 are constants
Now, the input voltage Vi (t) is the sum of both carrier and message signals 

i.e., Vi (t) =Accos 2fct+m (t) ……………. (ii)
Substitute equation (ii) in equation (i) we get
V0 (t) =a1Ac [1+kam (t)] cos2fct +a1m (t) +a2Ac2cos22fct+a2m2 (t) ………..(iii)
Where ka =2a2/a1
Now design the tuned filter /Band pass filter with center frequency fc and pass band frequency width 2W.We can remove the unwanted terms by passing this output voltage V0(t) through the band pass filter and finally we will get required AM signal.
V0 (t) =a1Ac [1+2a2/a1 m (t)] cos2fct
Assume the message signal m (t) is band limited to the interval –W  f  W
The Fourier transform of output voltage VO (t) is given by
VO (f) = a1AC/2[(f-fc) + (f+fc)] +a2 AC [M (f-fc) + M (f+fc)]

Switching Modulator: -

Assume that carrier wave C (t) applied to the diode is large in amplitude, so that it swings right across the characteristic curve of the diode .we assume that the diode acts as an ideal switch, that is, it presents zero impedance when it is forward-biased and infinite impedance when it is reverse-biased. We may thus approximate the transfer characteristic of the diode-load resistor combination by a piecewise-linear characteristic.

Switching Modulator

The input voltage applied Vi (t) applied to the diode is the sum of both carrier and message signals.
Vi (t) =Accos 2fct+m (t) …………….(i)
During the positive half cycle of the carrier signal i.e. if C (t)>0, the diode is forward biased, and then the diode acts as a closed switch. Now the output voltage Vo (t) is same as the input voltage Vi (t) . During the negative half cycle of the carrier signal i.e. if C (t) <0, the diode is reverse biased, and then
the diode acts as a open switch. Now the output voltage VO (t) is zero i.e. the output voltage varies periodically between the values input voltage Vi (t) and zero at a rate equal to the carrier frequency fc.
i.e., Vo (t) = [Accos 2fct+m (t)] gP(t)……….(ii)
Where gp(t) is the periodic pulse train with duty cycle one-half and period Tc=1/fc and which is given by gP(t)= ½+2/ [(-1)n-1/(2n-1)]cos [2fct(2n-1)]…………(iii)
Now design the tuned filter /Band pass filter with center frequency fc and pass band frequency width 2W.We can remove the unwanted terms by passing this output voltage V0(t) through the band pass filter and finally we will get required AM signal.
V0 (t) =Ac/2[1+kam (t)] cos2fct
Assume the message signal m(t) is band limited to the interval –W  f  W The Fourier transform of output voltage VO (t) is given by
VO (f) = AC/4[(f-fc) + (f+fc)] +AC/ [M (f-fc) + M (f+fc)]
The AM spectrum consists of two impulse functions which are located at fc & -fc and weighted by Aca1/2 & a2Ac/2, two USBs, band of frequencies from fc to fc +W and band of frequencies from -fc-W to –fc, and two LSBs, band of frequencies from fc-W to fc & -fc to -fc+W.