# Double Sideband (DSB) and Amplitude Modulation (AM)

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1 Double Sideband (DSB) and Amplitude Modulation (AM) Modules: Audio Oscillator, Wideband True RMS Meter, Multiplier, Adder, Utilities, Phase Shifter, Tuneable LPFs (2), Quadrature Utilities, Twin Pulse Generator, Digital Utilities, Speech, Headphones 0 Pre-Laboratory Reading Double sideband (DSB) is one of the easiest modulation techniques to understand, so it is a good starting point for the study of modulation. A type of DSB, called binary phase-shift keying, is used for digital telemetry. Amplitude modulation (AM) is similar to DSB but has the advantage of permitting a simpler demodulator, the envelope detector. AM is used for broadcast radio, aviation radio, citizens band (CB) radio, and short-wave broadcasting. 0.1 Double Sideband (DSB) Modulation A message signal modulated carrier can be DSB modulated onto a carrier with a simple multiplication. The can be represented by where is the carrier frequency. The Fourier transform of the modulator output is related to the Fourier transform of the message signal by (1) For a real, is symmetric about and is symmetric about. For the present discussion, it is only necessary to consider that part of that lies in the positive half of the frequency axis. The signal content that lies in the frequency domain below is the lower sideband. The signal content that lies in the frequency domain above is the upper sideband. This is the origin of the term double sideband. When studying and testing analog modulation schemes, it is convenient to use a sinusoid as the message signal. This is a good choice for several reasons. First, when testing a system in the laboratory, it is desirable to use a periodic signal since a stable oscilloscope display with continuous signal capture is then possible. Second, the mathematics are usually simpler with a sinusoidal message signal. Third, a sinusoid is easy to generate in the laboratory. After a communication system goes into the field and becomes operational, the message signal would not ordinarily be sinusoidal, of course. (2) 1

2 If is a sinusoid of frequency, the modulated carrier can be written as [ ] [ ] (3) This last expression indicates that when a carrier is DSB modulated by a message sinusoid, the modulated carrier is equivalent to the sum of two sinusoids: one having the difference frequency and the other with the sum frequency. In the frequency domain there is signal content lying on both sides of the carrier frequency. When is a sinusoid, each sideband is one discrete spectral line (on the positive half of the frequency axis). In the general case where is real but not a sinusoid, each sideband is more complicated than a single discrete spectral line. However, it is still true that there are two sidebands: a lower and an upper. In the time domain, a carrier that is DSB modulated by a message sinusoid looks like this: DSB modulated carrier (solid curve) and message sinusoid (dashed curve) A DSB modulated carrier is normally demodulated with a synchronous detector. This means that the modulated carrier is multiplied by a local oscillator and the product is then sent to a lowpass filter. With synchronous detection the frequency and phase of the local oscillator are important. Its frequency must match that of the carrier. The local oscillator phase must approximately match that of the carrier. When the modulated carrier of Eq. (1) is sent to a synchronous detector, the demodulator (detector) output can be written as 2

3 { } { } { } (4) The local oscillator is modeled as. It has a frequency that matches that of the carrier. However, allowance is made for a phase that might not match that of the carrier. The low-pass filtering is represented by { }. message modulator x synchronous detector x LPF carrier local oscillator DSB modulator (left) and synchronous detector as demodulator (right) The message signal is presumably low pass. The term represents a bandpass signal centered at in the frequency domain. The bandwidth of the low-pass filter should be large enough that passes through the filter with little distortion. If the bandwidth of is small compared with (as it will be in this experiment and as it normally is in practice), then a bandwidth for the low-pass filter can easily be selected that passes but blocks. The demodulator output is, in this case, where is the lowpass gain of the filter. There will also be a time delay in going through the filter; this is not indicated in Eq. (5) because it is not important for the present discussion. The filter output is a scaled and delayed version of. A demodulation that produces a scaled and delayed version of the original message is considered successful. An important consideration is the phase difference between the local oscillator and the carrier. The amplitude of the demodulator output is a function of. If, is zero. It is essential that remain close to so that the message not suffer fading at the output of the demodulator. Keeping close to is normally accomplished within the receiver by a circuit that performs carrier synchronization. (5) 3

4 0.2 Amplitude Modulation (AM) If a DC component is added to the message signal before multiplication with a carrier, then the modulation scheme is known as amplitude modulation (AM). The purpose of the DC component is to permit the modulated carrier to be demodulated at the receiver by a means other than synchronous detection. More will be said about this later. message + x DC carrier Modulator for AM The output of the modulator can be written: Where and are constants. [ ] For AM the maximum of the absolute value of the message signal denoted here by ( ). is of importance; this is (6) It is useful to define a normalized message signal as follows: (7) The maximum of the absolute value of is therefore (8) This is what is meant by normalization. The modulator output can be rewritten as [ ] Factoring out of the bracket and defining as the modulation index for AM, the modulator output can then be written 4 (9)

5 [ ] The modulation index of Eq. (9) is always non-negative (that is, positive or 0) since (by definition) and the constants and should always have the same sign. is positive The term is a residual carrier and the term is a DSBmodulated carrier. The ratio of the peak value of the DSB term to the peak value of the residual carrier is In the above, we recognize that is positive. The ratio of the peak value of the DSB term to the peak value of the residual carrier is the modulation index. There are some AM calculations that involve the ratio of the DSB term to the residual carrier. For this class of problem, it is acceptable to forget about the common factor. The important problem of selecting an appropriate value for the modulation index is an example of this class of problem. Therefore, in the analysis that appears below, we sometimes forget about and use the following definition: [ ] (10) There are, of course, problems for which the constant must be considered. One problem of this type is when we must determine if any stage in the transmitter is overloaded (the voltage is so large that the stage is unintentionally operated in a nonlinear regime). As was done with DSB, the next step in this description of AM is to consider a sinusoidal message signal. Eq. (11) satisfies Eq. (8). Three cases are of interest: (11) 100% modulation undermodulation overmodulation The time-domain view of the modulated carrier is shown below for these three cases. It helps when interpreting these figures to consider the quantity. This quantity has a minimum value of 0 for. The minimum value is positive and non-zero for. The minimum value is negative for. (It is assumed here that and therefore that.) 5

6 (100% modulation): AM carrier (solid curve) and message sinusoid (dashed curve) (undermodulation): AM carrier (solid curve) and message sinusoid (dashed curve) (overmodulation): AM carrier (solid curve) and message sinusoid (dashed curve) 6

7 In the laboratory, the modulation index can be set with good accuracy when the message signal is a sinusoid. The rms value of and the rms value of are separately measured. For the of Eq. (11), these rms values are and, respectively. The ratio of these two rms values is: A desired modulation index until the ratio equals message signal. (sinusoid) (12) can be set by adjusting the gain on the (sinusoidal) message signal. It must be emphasized that Eq. (12) is valid only for a sinusoidal There is a technique for estimating the modulation index of an AM carrier that is quite general; it does not require the message signal to be a sinusoid. This technique uses the XY view of an oscilloscope. The multiplier input that is not the carrier is applied to Channel A. In the case of DSB, this is. In the case of AM, this is. To Channel B is applied the output of the multiplier (that is, the modulated carrier). When this is done, one of the following figures is displayed: DSB AM: AM: AM: 100% modulation undermodulation overmodulation Consider first the DSB figure. The modulated carrier is plotted against. At any instant when the message signal is 0, the modulated carrier is also zero. The center of the bowtie represents this point; it is the origin. When takes on the value, the modulated carrier can take on any value between and. The larger, the wider the range of values that the modulated carrier can assume. For AM, the modulated carrier [ ] is plotted against. If, then takes on only non-negative values, so only the right half of the bowtie is present. If, then the minimum value of is a positive and non-zero value. If, then the minimum value of is negative. The nice thing about using the XY view to estimate the modulation index is that this works for any message signal, even an audio signal (from a microphone, for example). The problem of calculating the modulation index for a general audio signal is that it can be difficult even to 7

8 identify and therefore for a signal that appears random. The XY view provides a quick but approximate characterization of the AM. It is worthwhile to consider how an AM carrier looks in the frequency domain. This is done here for the case of a sinusoidal message signal. Eqs. (10) and (11) together can be rewritten as [ ] [ ] (13) It is clear from Eq. (13) that the spectrum of an AM carrier with sinusoidal message signal contains three discrete spectral lines (on the positive half of the frequency axis). The frequencies are:,, and. This is similar to the case of DSB, except for the additional discrete spectral line at, which is known as a residual carrier. Each of the sideband lines has a line height that is different from that of the residual carrier by The unit dbc is the number of decibels relative to the residual carrier. For 100% modulation ( ), each sideband is dbc. Demodulation of an AM carrier is normally done with an envelope detector. An envelope detector, implemented as a rectifier followed by a low-pass filter, extracts the envelope of the modulated carrier. For the modulated carrier of Eq. (10), the envelope is. (14) rectifier LPF Demodulator for AM If, is always non-negative, so the envelope is just. With AC coupling (to remove the DC component) a scaled (and delayed) version of the original message is recovered. With overmodulation ( ), the envelope does not equal. In this case, only a distorted version of the message can be recovered. However, if the overmodulation is slight, then the distortion is slight. 8

9 Ideally, AM should be used with close to. If is significantly greater than, then distortion occurs in envelope detection at the receiver. If is significantly less than, then the system is inefficient because an unnecessarily large fraction of the transmitted power is devoted to the residual carrier, which contains no information about the message. It is the sidebands that contain the information about the message; the residual carrier is only present to make distortionfree envelope detection possible at the receiver. Envelope detection, unlike synchronous detection, requires no carrier synchronization circuit in the receiver. This is why AM was selected over DSB for broadcast radio. The goal was to permit the many receivers of broadcast radio to be simple (and therefore cheap) and reliable. 1 DSB Modulation and Synchronous Detection You will build a DSB modulator. This will be paired with a synchronous detector. 1.1 Sinusoidal Message Initially, you will use a 5-kHz sinusoid as the message signal. Adjust the frequency of the Audio Oscillator to approximately 5 khz and place this message signal at one of the inputs of the Multiplier. It is necessary that the Multiplier be set for DC coupling. Connect a 100-kHz sinusoid (Master Signals) to the second input of the Multiplier. The output of the Multiplier is the modulated carrier. Simultaneously observe the message signal and the modulated carrier on the oscilloscope. Use the TTL output from the Audio Oscillator as an external trigger source. This will stabilize the envelope, but you will see that the fast carrier oscillation inside the envelope is not stabilized. This is a consequence of the fact that the message sinusoid and the 100-kHz sinusoid are not coherently related. (The message sinusoid has a frequency that is only approximately 5 khz; it is not exactly 100 khz divided by 20.) Switch to an XY View (Views > X-Axis > A). Verify that this view gives the correct picture for DSB. Select the Spectrum Mode. Note the frequencies of the two tall spectral lines. Now you will demodulate the DSB carrier. Connect the modulated carrier to an input on a different multiplier. You should use one of the multipliers in the Quadrature Utilities module for this purpose. Place a 100-kHz sinusoid (Master Signals) on the input of a Phase Shifter. Connect the Phase Shifter output to the second input of the (demodulator) multiplier. This second input to the (demodulator) multiplier is known as the local oscillator; its frequency must match that of the carrier if synchronous detection is to work. Connect the output of the (demodulator) multiplier to a Tuneable LPF. Adjust the bandwidth of this filter to approximately 6 khz. 9

10 message modulator x x demodulator LPF carrier stolen carrier phase shifter local oscillator Simultaneously observe the original 5-kHz message sinusoid (coming out of the Audio Oscillator) and the Tuneable LPF output on the oscilloscope. Notice that the demodulator has reproduced the original message, with some scaling and a delay. It should be possible to stabilize simultaneously both sinusoids in the display since they share a common frequency. Observe how the amplitude of the demodulator output varies as you vary the phase delay of the Phase Shifter. Adjust the Phase Shifter such that the local oscillator (at the input of the demodulator multiplier) is in phase with the carrier. In order to make this adjustment, you will want to simultaneously observe the Phase Shifter input (the unmodulated carrier) and the output (the local oscillator) on the oscilloscope. Then measure the amplitude of the demodulator output. Now adjust the Phase Shifter so that the local oscillator is in phase quadrature to the carrier (that is, so that the local oscillator either lags or leads the carrier by ). Now measure the amplitude of the demodulator output. Complete the following table. Phase Offset Demodulator Output Amplitude As you can see, synchronous detection requires that the local oscillator match the carrier in frequency and approximately match it in phase. This is an important issue in receiver design. For the purpose of this laboratory, the receiver has stolen a copy of the (unmodulated) carrier from the transmitter. This is feasible as long as both transmitter and receiver are sitting in the same laboratory. In the field, it is generally impossible for the receiver to steal a copy of the (unmodulated) carrier from the transmitter. Instead, the receiver must perform carrier synchronization. 1.2 Sum-of-Sinusoids Message Generate a message signal that is a sum of sinusoids by the following procedure. First, create a (100/96)-kHz clock by dividing the frequency of a (100/12)-kHz TTL clock (labeled as 8.3 khz on the Master Signals panel) by 8. (The Digital Utilities module provides circuits that divide the frequency of a TTL signal by 4 and by 2.) With the Twin Pulse Generator set for single mode 10

11 (on the PCB), clock this module with the (100/96)-kHz TTL signal. Every low-to-high transition occurring on this clock will generate a narrow pulse on the Twin Pulse Generator output. Rotate the width knob fully counter-clockwise, in order to produce the narrowest possible pulse. Place the Twin Pulse Generator output on the input of a Tuneable LPF. Adjust the bandwidth of this filter to approximately 5 khz. The output of this filter will be used as the message signal. Observe this message signal on both the oscilloscope and the spectrum analyzer. On the oscilloscope, the signal should look like a train of pulses, but these pulses are not rectangular in shape because of the low-pass filtering. In the frequency domain, this signal should look like a set of discrete spectral lines spaced about 1 khz apart and up to approximately 5 khz. This message signal will be referred to as a sum-of-sinusoids. Use the same configuration for the DSB modulator that you used above, except that the 5-kHz message sinusoid should be replaced with the sum-of-sinusoids message signal. Place the message signal on Channel A and the DSB modulator output on Channel B. Switch to an XY view. This should have the characteristic shape of DSB modulation. Simultaneously view the spectrum of the message signal and the spectrum of the modulated carrier. You should observe the double sidebands of the latter. Connect the DSB modulator output to the synchronous detector. Reset the phase offset between the (unmodulated) carrier and local oscillator to. If you wish, you can accomplish this by simply removing the Phase Shifter, replacing it with a cable. Simultaneously observe the message signal (from the transmitter side) and the demodulator output on the oscilloscope. Notice that the demodulator has reproduced the original message, with some scaling and a delay. 1.3 Audio Message Use an audio signal from the Speech module as the message signal. Otherwise, your configuration will remain the same. Place the audio message signal on Channel A and the DSB modulator output on Channel B. Switch to an XY view. This should have the characteristic shape of DSB modulation. Simultaneously view the spectrum of the audio message signal and the spectrum of the modulated carrier. You should observe the double sidebands of the latter. Connect the DSB modulator output to the synchronous detector. The phase offset between the (unmodulated) carrier and the local oscillator should be. Connect the demodulator output to the headphones. Listen to the recovered audio message while varying the bandwidth of the demodulator lowpass filter. Note the smallest bandwidth that still permits a sound of good quality to come from the demodulator. 11

12 2 AM and Envelope Detection You will build an AM modulator. This will be paired with an envelope detector. 2.1 Sinusoidal Message Build a modulator for AM. Use a 5-kHz sinusoid from the Audio Oscillator as the message signal. Use a weighted adder to combine the message signal and a DC component. The DC component will come from the Variable DC panel, and the knob on this panel should be set clockwise from the vertical position, so that a positive DC value is supplied. Connect the output of the Adder to a Buffer Amplifier and the output of this amplifier to a multiplier (set for DC coupling). The other input to the multiplier will be a 100-kHz sinusoid (Master Signals). In the Adder, the gain on each input is negative. The purpose of the Buffer Amplifier, with its negative gain, is to cancel minus signs so that the net gain through Adder and amplifier is positive for both the DC component and the message signal. Care should be taken that the absolute value of the gain is not set too high. If it is too high, saturation (overloading) can result. modulator demodulator message + x rectifier LPF DC carrier Set the modulation index to. You can do this by measuring the rms voltage at the output of Buffer Amplifier. First, measure the rms voltage with only the message signal present. Second, measure the rms voltage with only the DC component present. Adjust one or both gain knobs on the weighted adder until the ratio of the message signal measurement to the DC measurement is approximately See Eq. (12). Simultaneously observe the 5-kHz message signal and the Buffer Amplifier output on the oscilloscope. Then observe the 5-kHz message signal and the modulator output. Use the TTL output from the Audio Oscillator as the trigger source. This will stabilize the display of the envelope but not the fast carrier fluctuations inside the envelope. Place the Buffer Amplifier output on Channel A and the modulator output on Channel B. Switch to an XY view and observe the resulting figure. Switch to the Spectrum Mode and observe the spectrum of the modulated carrier. Measure the line height of the lower and upper sidebands. Use units of dbc (decibels below carrier). 12

13 Connect the modulated carrier to a rectifier and the rectifier output to a Tuneable LPF. Adjust the bandwidth of this filter to approximately 6 khz. The combination of the rectifier and the low-pass filter make an envelope detector. Simultaneously observe the message signal and the rectifier output on the oscilloscope. Then observe the message signal and the envelope detector output on the oscilloscope. For the envelope detector output, set the coupling for AC. (Now that the envelope detection is done, the DC component is no longer needed.) You will have noticed that no local oscillator (and therefore no stolen carrier) is required for envelope detection. For an AM receiver, carrier synchronization is not required; and this simplifies the receiver design. Set the modulation index to the new value of 0.5 and repeat the above measurements. Set the modulation index to the new value of 1.5 and repeat the above measurements. In this case, the 5-kHz message signal will be distorted by the envelope detector. You should increase the bandwidth of the Tuneable LPF (beyond the original bandwidth of 6 khz) in order to get a clear picture of this distortion. Complete the following table Line Height of Upper Sideband (dbc) Predicted Line Height from Eq. (14) 2.2 Sum-of-Sinusoids Message Generate a message signal that is a sum of sinusoids using the same procedure as was done for the DSB experiment. Use the same configuration for the AM modulator that you used above, except that the 5-kHz message sinusoid should be replaced with the sum-of-sinusoids message signal. Place the Buffer Amplifier output on Channel A and the AM modulator output on Channel B. Switch to an XY view. Adjust the relative gains of the weighted adder in the modulator in order to achieve. The XY view will help you make this adjustment. Simultaneously view the message signal and the modulated carrier on the oscilloscope. You can use the TTL signal that clocks the Twin Pulse Generator as the trigger source. This should provide a stable display for the message signal and for the envelope of the modulated carrier. Simultaneously view the spectrum of the message signal and the spectrum of the modulated carrier. 13

14 Connect the AM modulator output to the envelope detector. As above, use a bandwidth of approximately 6 khz for the low-pass filter in the envelope detector. Simultaneously observe the message signal (from the transmitter side) and the demodulator output on the oscilloscope. Notice that the demodulator has reproduced the original message, with some scaling and a delay. 2.3 Audio Message Use an audio signal from the Speech module as the message signal. Otherwise, your configuration will remain the same. Place the Buffer Amplifier output on Channel A and the AM modulator output on Channel B. Switch to an XY view. Adjust the relative gains of the weighted adder in the modulator in order to achieve. The XY view will help you make this adjustment. Connect the AM modulator output to the envelope detector. Connect the demodulator output to the headphones. Listen to the recovered audio message. Repeat the above steps, but setting Repeat the above steps, but setting to a value less than 1 (that is, undermodulation). to a value greater than 1 (that is, overmodulation). Complete the following table, using adjectives like good, okay and poor. Sound Quality of Recovered Message 14

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