## Q. 2.9

For a tribit input of Q = 0, I = 0, and C = 0 (000), determine the output amplitude and phase for the 8-QAM transmitter shown in Figure 30a.

## Verified Solution

The inputs to the I channel 2-to-4-level converter are I = 0 and C = 0. From Figure 30b, the output is -0.541 V. The inputs to the Q channel 2-to-4-level converter are Q = 0 and C = 0. Again from Figure 30b, the output is -0.541 V.

Thus, the two inputs to the I channel product modulator are -0.541 and sin $ω_{c}t$. The output is

I = (-0.541)(sin $ω_{c}t$) = -0.541 sin $ω_{c}t$

The two inputs to the Q channel product modulator are -0.541 and cos $ω_{c}t$. The output is

Q = (-0.541)(cos $ω_{c}t$) = -0.541 cos $ω_{c}t$

The outputs from the I and Q channel product modulators are combined in the linear summer and produce a modulated output of

summer output = -0.541 sin $ω_{c}t$ -0.541 cos $ω_{c}t$
= 0.765 sin($ω_{c}t$ – 135°)

For the remaining tribit codes (001, 010, 011, 100, 101, 110, and 111), the procedure is the same. The results are shown in Figure 31.
Figure 32 shows the output phase-versus-time relationship for an 8-QAM modulator. Note that there are two output amplitudes, and only four phases are possible.