# Experiment 3: Double Sideband Modulation (DSB)

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1 Experiment 3: Double Sideband Modulation (DSB) This experiment examines the characteristics of the double-sideband (DSB) linear modulation process. The demodulation is performed coherently and its strict requirement for a perfect synchronization to the carrier is discussed. Introduction In communication systems information is transmitted from one place to another using electrical signals (telephone, TV and radio broadcast etc.). Usually the information bearing signals (message signals) are not suitable for transmission due to its propagation qualities (a large wavelength). lso, since these signals generally exist in the same frequency range it is necessary to transmit them using different frequency allocations to avoid interference. One of the methods used to solve these problems is linear modulation, which is merely the frequency translation of the spectrum of the information (or message) signal to a usually much higher frequency. The translated spectrum can be modified before transmission in different forms resulting in different linear modulation schemes. Specifically, there are four linear modulation methods: double-sideband (DSB) (also known as double-sideband with suppressed carrier DSB-SC), amplitude modulation (M) or DSB-LC (large carrier), single-sideband (SSB) and vestigial-sideband (VSB). This experiment examines the characteristics of the DSB modulation.. DSB signal generation The simplest modulation method to implement is DSB, in which the translated spectrum of the message signal is transmitted without further modification. From the real signal frequency translation property of the Fourier transform, the spectrum of the message signal x(t) is translated to the frequency f c by multiplying x(t) with a carrier waveform c cos(2πf c t). The modulated waveform x c (t) is whose spectrum is x c (t) = c x(t) cos(2πf c t) () X c (f) = c 2 [X(f + f c) + X(f f c )] (2) The message signal is usually referred to as the baseband signal and the spectral range that occupies is called the baseband frequency range. In communication systems the baseband signal is limited in frequency to a bandwidth of f x Hz, and the carrier frequency f c is much higher than f x. The spectral components of the baseband signal that occupy the positive side of the frequency axis appear in the range f c to f c + f x in the spectrum of the DSB signal, this portion of the spectrum is called the upper sideband. Similarly, the spectral components of the baseband signal that occupy the negative side of the frequency axis are translated to the lower sideband of the spectrum of the DSB signal in the frequency range f c f x to f c. Hence the (one-sided) spectrum consists of two sidebands that occupy the frequency range f c f x to f c + f x and therefore the bandwidth B T required for transmission is B T = 2f x (3).2 Demodulation of DSB signals In order to recover the message signal from the received DSB signal another frequency translation is required. That is, the spectra of the two sidebands must be translated back to the baseband frequency range. ssuming

2 EE35 E. Cura 2 that the received signal x r (t) has the same form as x c (t) except for an attenuation factor a c / c introduced by the channel x r (t) = a c x(t) cos(2πf c t) the message signal can be recovered from the received signal by multiplying x r (t) with a local carrier waveform (identical to the transmitter carrier scaled by 2) and lowpass filtering the product signal z(t), z(t) = [a c x(t) cos(2πf c t)] 2 cos(2πf c t) = a c x(t) + a c x(t) cos(4πf c t) (4) whose spectrum Z(f) is Z(f) = a c X(f) + a c 2 [X(f 2f c) + X(f + 2f c )] (5) Notice that scaled replicas of the message spectrum appear at the baseband frequency range and at 2f c. Therefore, a lowpass filter with cut-off frequency B, f x < B < 2f c f x is necessary to remove the high frequency components. The output y(t) of the lowpass filter is which is the message signal scaled by a factor a c. y(t) = a c x(t).2. Requirements for coherent demodulation The demodulation process described in the previous section involves the multiplication of the received signal by a local carrier at the receiver. Such demodulation scheme is called synchronous or coherent because a local carrier completely synchronous to the carrier of the DSB signal is required. This is a very strict requirement for practical systems and increases the complexity of the receivers. Lack of synchronism produces distortion in the recovered signal. In fact, a small difference in frequency and/or phase between the carrier of the DSB signal and the local carrier is sufficient to produce great distortion and in some cases a complete loss of the output signal. Suppose that the local carrier have a frequency offset of f and a phase offset of θ. The resulting product signal z(t) in this case is which after lowpass filtering is z(t) = a c x(t) cos(2π ft + θ) + double frequency terms y(t) = a c x(t) cos(2π ft + θ) (6) Notice that even when the frequency of the carriers are identical ( f = ) if they have a phase difference of θ = π/2 the output signal is y(t) =, and the signal is completely lost. In the opposite case, when θ = the output signal is y(t) = a c x(t) cos(2π ft), hence the message signal cannot be recovered due to distortion. 2 Prelab instructions Enclosed in brackets is the number of points assigned to each question/plot.. From Equation (), (a) obtain the expression for x c (t) [] when x(t) = x sin(2πf x t) and (b) plot [3] the DSB signal. The parameters are: c = V, f c = 9 khz, x =5 V, f x =5 Hz, (time span for the plot) T S=4 ms. [4 points total]. 2. Equation (2) describes the spectrum of the DSB signal. Using the same function and parameters as above, (a) obtain the expression for X c (f) [] and (b) plot [3] the one-sided spectrum in the frequency span F S=2 khz, use NF=-3 dbv. [4 points total]. 3. Equation (4) describes the product signal z(t) and Eq. (5) its spectrum Z(f). Using the same function x(t) and parameters as before but changing x = 2.5 V, (a) obtain the expressions for z(t) [] and Z(f) [] and (b) create the corresponding plot [3] in time domain with T S=4 ms and the one-sided spectrum [3] in the frequency span F S=2 khz and NF=-3 dbv. ssume there is no attenuation and set a c = c. [8 points total]

3 EE35 E. Cura 3 4. During the lab, the phase offset θ of Eq. (6) will be introduced in the local carrier by the RC network of Fig. 3. The output of this circuit is node B. Compute the phase shift introduced by this circuit at f = khz. [Hint: Obtain the transfer function H(f) of this circuit and θ(f) = arctan(i[h(f)]/r[h(f)])]. [3 points]. 3 Lab procedure GENERL INSTRUCTIONS: Load the virtual instrument TIMEFREQ.VI by double-clicking the shortcut located in the computer desktop. To avoid damage to the integrated circuits, keep the power supply off during the assembling of the circuits. fter taking each plot make sure to ask your T to verify that your results are correct. This also serves to monitor your progress and performance. Your T have the correct plots from actual circuits so you can compare yours. 3. DSB signal generation In this section DSB signals are generated by multiplying message signals with a carrier. The multiplier chip utilized is the. From its data sheet notice that the product of the two signals is divided by V. Hence two signals with amplitude of V will result in a signal with amplitude (*)/ = V.. Keeping the power supply off, assemble the circuit of Fig.. Use FG as the message signal and FG2 as the carrier signal. Set the following parameters in FG: mplitude=5 V, Frequency=5 Hz, sine wave. For FG2: mplitude= V, Frequency=9 khz, sine wave. Connect channel probe of the oscilloscope to the output of the modulator (at pin 7). 2. Turn on the power supply and capture the DSB signal and its spectrum by executing TIMEFREQ.VI with the following parameters: Channel=, TS=4m (meaning milliseconds), FS=2, Save data=on, a proper file name. [Plot, 5 points]. 3. Change the waveform of FG (the message signal) to triangle and repeat the previous step using the same parameters but different file name. [, 5 points]. 3.2 Coherent demodulation of DSB signals In this section the message signal is recovered by coherent demodulation. The case of a synchronous local carrier at the receiver is implemented here.. Keeping the power supply off, assemble the circuit of Fig. 2. Use FG as the message signal and FG2 as the carrier signal. Set the following parameters in FG: mplitude=5 V, Frequency=5 Hz, sine wave. For FG2: mplitude= V, Frequency=9 khz, sine wave. Connect channel probe of the oscilloscope to observe the product signal (at pin 7 of the second ), and the channel 2 probe to the output of the filter to observe the recovered message signal. 2. Turn on the power supply and capture the product signal and its spectrum by executing TIMEFREQ.VI with the following parameters: Channel=, TS=4m, FS=2, Save data=on, a proper file name. [, 5 points]. 3. Capture the output (recovered message) signal and its spectrum by repeating the previous step with Channel=2 and a different file name. [, 5 points]. 4. Change the following parameters in FG: Frequency= khz, triangle wave, in FG2: Frequency=8 khz. Repeat the previous two steps using TS=2m, FS=5, and different file names. [ and, 5 points each].

4 EE35 E. Cura Synchronization problems of the coherent demodulation In this section the problems associated with lack of synchrony of the local carrier are observed. phase offset is introduced in the local carrier and later the effect of a frequency offset is considered Phase offset in the local carrier. Keeping the power supply off, assemble the circuit of Fig. 3. Use FG as the message signal and FG2 as the carrier signal. Set the following parameters in FG: mplitude= V, Frequency=5 Hz, sine wave. For FG2: mplitude= V, Frequency= khz, sine wave. 2. Connect the channel probe of the oscilloscope to node and the channel 2 probe to node B. Disconnect the synchrony cable from channel 4. Turn the power supply on and press utoscale. 3. Set an attenuation factor of for both channels by pressing ( 2 for channel 2) and selecting in the softmenu Probe. 4. Measure the amplitude peak-to-peak of these two signals by pressing Voltage and selecting Vp-p for each of the two channels. These two voltages should be approximately the same. If they are different to each other, adjust the carrier frequency of FG2 to change the voltage at node B until these voltages are equal. 5. Measure and record the phase difference θ between these two signals by pressing Time, selecting Next Menu twice and then Phase. The phase value displayed in the oscilloscope might be changing constantly, pick an average value, θ =. 6. Connect the synchrony cable from FG to channel 4. Connect node C to node. Connect channel probe of the oscilloscope to observe the product signal (at pin 7 of the second ), and the channel 2 probe to the output of the filter. 7. Capture the output signal with the following parameters: Channel=2, TS=4m, FS=25, Save data=on, a proper file name. [, 5 points]. This is the recovered message signal using a synchronous local carrier, i.e. f = and θ =. This plot is taken as a reference in order to observe the effect of a phase offset in the next step. 8. Disconnect from C and now connect node B to node C. Now the local carrier has a phase offset of θ but the same frequency and amplitude as in the previous step. Capture the product signal and its spectrum by executing TIMEFREQ.VI with the following parameters: Channel=, TS=4m, FS=25, Save data=on, a proper file name. [, 5 points]. Capture the output signal by executing the VI with Channel=2 and a different file name. [P9, 5 points] Frequency offset in the local carrier. Load the virtual instrument DSB.vi by double-clicking the shortcut located in the computer desktop. This VI generates a DSB signal and loads the waveform to the volatile memory of FG. Run the VI by pressing Ctrl-R. No further adjustments to the parameters of FG are required. 2. Keeping the power supply off, assemble the circuit of Fig. 4. Use FG as the received DSB signal and FG2 as the local carrier signal. In FG2 set mplitude = V, frequency = 2 khz, sine wave. 3. Turn on the power supply. Connect the channel probe of the oscilloscope to FG to observe the DSB signal and the channel 2 probe to the output of the filter. Run TIMEFREQ.vi to observe the spectrum of the DSB signal with Channel=, TS=2m, FS=25, Save data=off. This plot is not required for the lab report, but helps to verify that the carrier frequency for this DSB signal is 2 khz and the message signal is a sinusoid of khz.

5 EE35 E. Cura 5 4. Connect the channel probe to observe the product signal (at pin 7 of the ). t this point you should see that the product signal and the output signal change slowly. Set the local carrier frequency (FG2) to 2 Hz and observe the effect of a frequency offset of only Hz on the output and product signals. Since this effect cannot be recorded using the computer write a note describing what you observe. Please shut down properly the computer and the equipment. 4 nalysis This section contains questions regarding the obervations you made during the lab.. Include in your report all the plots obtained during the lab. Make sure to label properly all the plots. The number of points assigned to each plot is specified in the lab procedure. Refer to ppendix B section 3.4 for instructions regarding the plotting of experimental results. 2. From plot, (a) estimate the bandwidth B T of the DSB signal. [2]. Suppose the upper sideband is suppressed before transmission, (b) Could the message signal (a triangle wave) be recovered at the receiver? Justify your answer.[2]. (c) What would be the frequency of the local carrier? [2]. 3. From plot, explain why the component at 5 Hz (the message signal) is about 6 dbv higher than the components (the translated sidebands) at 7.5 khz and 8.5 khz. [2]. 4. Observe from plot that the envelope of the product signal has the shape of the message signal, which is recovered as the output signal in plot. Plot shows that the message signal is a triangle wave, however plot shows a recovered signal that resembles more closely a sine wave, (a) explain why a triangle wave was not recovered. [2]. (b) What modifications should be made to the circuit of Fig. 2 in order to recover the triangle wave? [2]. 5. Plot shows the output signal y(t) when f = and θ =. Estimate its peak amplitude (in volts). Using Eq. (6) and the value of the phase offset θ you measured during the lab, (a) calculate the peak amplitude of the output signal when is affected by the phase offset in the local carrier. [2]. Plot P9 shows the output signal affected by a phase offset, (b) estimate the peak amplitude of this signal and compare it with the theoretical value just found. [2]. 6. Describe the effect of the frequency offset on the output signal that you observed in section [2].

6 2 B message_signal carrier Fig. DSB Modulator modulated_signal message_signal carrier product_signal R Coherent detector R2 C2.u C Lowpass filter output_signal n B Fig. 2 Coherent demodulation of DSB signals message_signal carrier R R9 9. R C5.6k C B.u RC network Coherent detector product_signal R5 C3 R6 output_signal n.u C4 Lowpass filter Fig. 3 Test circuit to observe the effect of a phase offset DSB_signal local_carrier product_signal R2 C6 R3.u C7 output_signal n Coherent detector Lowpass filter Fig. 4 Test circuit to observe the effect of a frequency offset EE35 Communication Systems Lab Experiment 3. Linear modulation:dsb Spring 22 E. Cura Page Size: 2 Revision: - Feb 9, 22 Page of

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