#### introduction:

Modulation is a process in which we moves a message signal into a specific frequency band that is dictated by physical channel. In communication system there are two types of communications (Base-band communication) that do not use modulation and (Carrier communication) that use modulation.

#### base-band communications:

The term base-band defines the bandwidth in which our message is transfers before modulation while in base-band communication message signal are directly transmitted without any modification because usually audio and video formats contain low frequency that can not be transmitted over wireless links. To transmit them we use coaxial cables and twisted pairs of copper wires. Disadvantage of Base-band is it leave much of the channel spectrum unused.

#### carrier communication:

Communication that uses modulation to shift the frequency spectrum of a signal is known as carrier communication. There are three types of carrier modulation Amplitude modulation, Phase modulation and Frequency modulation while amplitude modulation is linear and other two are non-linear and similar. Phase modulation and Frequency modulation collectively known as angle modulation.

#### Amplitude modulation & angle modulation:

From now we most commonly use a term m(t) which is message signal that is transmitted from sender to receiver and its Fourier transform is M(f) and we know that Fourier transform have a very strong property called frequency-shifting property. This thing can be done by multiplying it by sinusoid of frequency.

s1(t) = m(t) Cos 2 π ft

If we convert it into frequency domain then it is

S1(f) = 0.5 M(f – fc) + 0.5 M(f + fc)

This multiplication infact allowing changes in the amplitude of the sinusiod. There is another relation of sinusoid

s(t) = A(t) cos[ωct + Φ(t)]

We can see three variables in the sinusoid: amplitude, frequency and phase

Relations:

1- In amplitude modulation: Amplitude is proportional to message.

2- In frequency modulation: Frequency is proportional to message.

3- In phase modulation: Phase is proportional to message.

#### double-sideband amplitude modulation:

Amplitude modulation is characterized by an information-bearing carrier amplitude a(t) that is a linear function of baseband signal m(t). If the carrier amplitude A is made directly proportional to the modulating signal m(t), then modulated signal is m(t)cosωct.

m(t) ⇔ M(f)

then,

m(t) cos2π ft ⇔ 0.5 [M(f + fc) + M(f – fc)]

remember that M(f + fc) is M(f) shifted to the left by fc and M(f – fc) is M(f) shifted to right by fc. Disadvantage of AM is if our original signal is of BHz after AM our bandwidth is 2BHz and our modulated signal spectrum is centered at ωc is composed of two parts a portion lies above ωct is upper-sideband and portion lies below ωc is lower-sideband.

so, this is a modulation with double sideband for this reason we called this scheme Double-Sideband Suppressed Carrier.  We already studied this http://www.electricalengineering4u.com/2018/12/20/amplitude-modulation/

#### demodulation:

To recover the original signal from modulated signal is called demodulation. There are two types of demodulation

1- Synchronous or Coherent Demodulation

In this type we multiply our modulated signal with high frequency carrier and then pass through low pass filter we do not get 100% original signal but mostly obtained. In this case we obtain half of the original signal.

2- Non-coherent Demodulation

In this method we pass our modulated signal from rectifier and then through LPF.

#### envelope detector:

Another difference between DSB-SC and DSB-AM is we got envelope in DSB-AM and envelope did not form in DSB-SC.

fig (a)                                fig (b)

so , fig a is DSBAM and fib b is DSBSC we can see envelope formation in fig a.

Condition for Envelope Detection:

A + m(t) ≥ 0      –(a)

What is meant my eq(a)? This equation states that our message signal always in positive region e.g if m(t) a signal

according to the condition we have to increase m(t) amplitude when all signal is in positive region if by increasing amplitude our signal remain in negative region so our envelope with form. A is basically a DC shift in our post http://www.electricalengineering4u.com/2018/12/20/amplitude-modulation/  dc shift is 1V.

let’s understand this thing by generating negative signal and carrier inside it. In this figure-1 our message is completely in +-region.