Chapter 2

Q. 2.5

For the QPSK modulator shown in Figure 17, construct the truth table, phasor diagram, and constellation diagram.



Verified Solution

For a binary data input of Q = 0 and I = 0, the two inputs to the I balanced modulator are -1 and sin ω_{c}t, and the two inputs to the Q balanced modulator are -1 and cos ω_{c}t. Consequently, the outputs are

I balanced modulator = (-1)(sin ω_{c}t) = -1 sin ω_{c}t
Q balanced modulator = (-1)(cos ω_{c}t) = -1 cos ω_{c}t

and the output of the linear summer is

-1 cos ω_{c}t – 1 sin ω_{c}t = 1.414 sin(ω_{c}t – 135°)

For the remaining dibit codes (01, 10, and 11), the procedure is the same. The results are shown in Figure 18a.