Question

4.1. Preliminary work Derive an expression for the output of the product detector from the block diagram in Figure 4-1 Product Detector assuming that the input is a single tone modulated DSBSC signal. Also show the effect on the output if the local carrier is out of phase from the modulated carrier by 45 degree.

4. DSB-SC (Suppressed Carrier) Detection Demodulation of DSB-SC signals is achieved by using a product detector as shown in Figure 4-1 Product Detector below. The frequency of the local carrier at the receiver site must match the local carrier at the transmitter site exactly in both frequency aned phase. y(t) LPF Xa(t) cos(oet) Figure 4-1 Product Detector 4.1. Using the DSB-SC system of the previous section, remove the envelope detector box and replace it with a product detector 4.2. Connect the output of the "Multiplier" from section 3.3 to input Y of a second "Multiplier". Apply the same 100 kHz (sin carrier, as for modulation, into input X of the second "Multiplier". Observe and record the output of the second "Multiplier" both in the time and frequency domains in Results 4-2 14 Student id Name: Group: 4.3. If you are using the picoScope set the maximum frequency to 312 kHz and the voltage range to lV on the spectrum analyser. You may want to use the zoom function to magnify a section of the spectrum. 4.4. Connect the output of the second "Multiplier" to the input of the "60kHz LPF" module and turn the gain knob fully clockwise. Observe and record the output of the LPF in both the time and frequency domains in Results 4-3. You want to adjust the gain c ontrol to remove any d distortion 4.5. Optional Challenge (strongly recommended): Use the "Phase Shifter module to vary the phase of the carrier in the product detector. Observe the effect of varying the carrier phase on the recovered signal Explain your results.

Answer 1

General form of DSB signal is y(t) = m(t) cos omega_c t z(t) = y(t) middot cos omega_c t = m(t) cos omega_c t middot cos omega_c t cos^2 theta = 1 + cos 2 theta/2 = m(t) cos^2 omega_c t z(t) = m(t)[1 + cos 2 omega_c t/2] z(t) = m(t)/2 + m(t) cos 2 omega_c t/2 LPF is used to eliminate higher frequency components therefore X_f(t) = m(t)/2 when local carrier = cos (omega_c t + theta) z(t) = m(t) middot cos omega_c t middot cos(omega_c + theta) z(t) = m(t)/2[cos(2 omega_c t + theta) + cos theta) + cos theta] output of CPF z(t) = m(t)/2 cos theta Given theta = 450 = m(t)/2 cos (45 degree) = > z(t) = m(t)/2 squareroot 2