Envelope Detector : We can define envelope detector simply as the output of the detector follows the envelope of modulated signal. By using a parallel RC circuit with a diode we can detect envelope. Let’s see how it works

For the positive cycle diode is forward bias and capacitor start charging and we know when capacitor start charging and we obtain a rising curve for negative cycle diode act as open circuit and capacitor starts discharging through resistor R at a slow rate for next positive cycle same procedure repeats. Remember during each positive cycle capacitor charges up to peak voltage of the input signal and decays slowly. Thus the output voltage closely follows the envelope of the input AM signal.The slow capacity discharge via the resistor R allows the capacity voltage to follow a declining envelope.

NOTE: All the side-bands which we studied earlier they all are in time domain lets see frequency domain representation of DSBSC. While the upper part is DSBSC signal and second part is its Fourier transform. In this figure we can see two side bands right-one is upper-sideband and left-one is lower-sideband while its total bandwidth is 2B Hz.

#### single sideband (ssb) modulation:

The bandwidth of amplitude modulation is 2BHz. It means that it take double bandwidth so now our task is to make a modulation system that take single sideband to transmit. Single sideband contain only single sideband for this it remove LSB or USB so there is only one message transmit that’s why only one band is use so it is 1BHz.

SSB = (message × carrier) + (message with 90° of phase shift × carrier with 90° of phase shift)

As we stated above that we remove LSB or USB for this we use Hilbert transform because Hilbert transform is use to remove LSB or USB.

Hilbert Transform: An ideal phase shifter that shifts the phase of every positive spectral component by -π/2 without changing any component amplitude.

Before transform:

After transform:

Equations of Hilbert transform:

mh(t) = m(t) * (t)

Mh(f) = -j sgn(f) M(f)

Common methods of generating SSB

1-Phase shift

2-Selective filtering

3-Weavers

SSB Phase Shift Modulator:

An SSB phase shift modulator can be built using

1-Two balanced modulators M1 and M2

2-Two 90° phase shifting method