# Quadrature Amplitude Modulation (QAM)

## Quadrature Amplitude Modulation (QAM)

The quadrature amplitude modulation (QAM) is similar to DSB-SC. The only difference is that QAM sends two message signals over the same spectrum .

Let the two message signals be x_{1}(t) and x_{2}(t) .

One of them is sent in phase i.e. by multiplying it with cos ω_{c}t and the other one x_{2}(t) is sent in quadrature by multiplying it with sinω_{c}t .

Finally the two signals are added to obtain the QAM signals as shown in fig.1 .

Fig.1 : Generation of QAM Signal

Hence, the QAM signal is mathematically represented as below :

V_{QAM}(t) = x_{1}(t) cos ω_{c}t + x_{2}(t) sinω_{c}t

The coherent detection is used at the receiver to recover the signal x(t) back .

The QAM signal at the receiver input is multiplied by locally generated carrier and the product is passed through a low pass filter .

If we multiply V_{QAM}(t) by cos ω_{c}t, then we can recover x_{1}(t) whereas multiplying V_{QAM}(t) by sinω_{c}t can recover x_{2}(t) as under :

If we pass this signal through a LPF, then, only the first term will be passed through to the output .

Therefore,

Thus, we recover x_{1}(t) if V_{QAM}(t) multiplied with cosω_{c}(t) .

Similarly, if sinω_{c}(t) is multiplied with V_{QAM}(t) then, we get,

If this is passed through a LPF, only the second term will be allowed to pass through .

Hence,

Thus, we recover x_{2}(t), if V_{QAM}(t) is multiplied with sinω_{c}t .

Fig.2 shows the block diagram of QAM receiver. QAM performs like SSB . The QAM system is easy to install .

Fig.2 : QAM Receiver

But, if the locally generated carriers at the receiver have some phase error, then, it will cause a serious problem .