Generation of DSBSC Waves:

DSBSC (Double Sideband Suppressed Carrier) wave is a variant of the DSB (Double Sideband) wave, where the carrier component of the modulated signal is removed or suppressed, resulting in a more efficient use of the available bandwidth. The generation of a DSBSC wave involves two main steps: modulation and carrier suppression.

Generation of DSBSC Waves

1. Modulation: 

The first step in generating a DSBSC wave is to modulate the carrier signal with the modulating signal using an amplitude modulator. The amplitude modulator varies the amplitude of the carrier signal in proportion to the instantaneous amplitude of the modulating signal, producing a modulated signal that contains two identical sidebands centered around the carrier frequency.

Mathematically, the modulated signal can be represented as:

s(t) = Ac * m(t) * cos(2πfct)

where s(t) is the modulated signal, Ac is the amplitude of the carrier signal, m(t) is the modulating signal, fc is the carrier frequency, and cos(2πfct) is the carrier waveform.

2. Carrier Suppression: 

The second step in generating a DSBSC wave is to remove or suppress the carrier component of the modulated signal. This can be achieved using a frequency-selective device such as a bandpass filter or a Hilbert transformer.

A bandpass filter can be used to remove the carrier frequency and retain only the sidebands. The bandpass filter is designed to pass frequencies within the bandwidth of the modulated signal, while attenuating frequencies outside this range. The result is a DSBSC signal that contains two identical sidebands but no carrier component.

Alternatively, a Hilbert transformer can be used to generate a 90-degree phase-shifted version of the modulated signal. The phase-shifted signal can then be combined with the original modulated signal to cancel out the carrier component. This method is known as the single-sideband suppressed-carrier (SSBSC) modulation, which is a variant of the SSB modulation technique.

In summary, the generation of a DSBSC wave involves the modulation of a carrier signal with a modulating signal using an amplitude modulator, followed by the removal or suppression of the carrier component using a frequency-selective device. The resulting DSBSC signal contains only the two sidebands of the modulated signal and is more bandwidth-efficient than the original DSB signal.

Balanced 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,

Balanced Modulator

𝑠1(𝑡) = 𝐴𝑐[1 + 𝑘𝑎𝑚(𝑡)] cos(2𝜋𝑓𝑐𝑡)
𝑠2(𝑡) = 𝐴𝑐[1 − 𝑘𝑎𝑚(𝑡)] cos(2𝜋𝑓𝑐𝑡)
Subtracting 𝑠2(𝑡) from𝑠1(𝑡)
𝑠(𝑡) = 𝑠1(𝑡) − 𝑠2(𝑡)
𝑠(𝑡) = 2𝑘𝑎𝑚(𝑡) 𝐴𝑐cos(2𝜋𝑓𝑐𝑡)
Hence, except for the scaling factor 2ka, the balanced modulator output is equal
to the product of the modulating wave and the carrier.

Ring Modulator

Ring modulator is the most widely used product modulator for generating DSBSC wave and is shown below.

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.

Therefore the ring modulator output is given by

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 centred at fc.