# 5 Amplitude Modulation

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1 5 Amplitude Modulation 5.1 Summary This laboratory exercise has two objectives. The first is to gain experience in actually programming the USRP to act as a transmitter or a receiver. The second is to investigate classical analog amplitude modulation and the envelope detector. 5.2 Background Amplitude Modulation Amplitude modulation (AM) is one of the oldest of the modulation methods. It is still in use today in a variety of systems, including, of course, AM broadcast radio. In digital form it is the most common method for transmitting data over optical fiber [1]. If m(t) is a baseband message signal with a peak value m p, and A c cos(2πf c t) is a carrier signal at carrier frequency, f c, then we can write the AM signal g(t) as g(t) = A c [1 + μ m(t) m p ] cos(2πf c t) (18) where the parameter μ is called the modulation index and takes values in the range 0 < μ 1 (0 to 100%) in normal operation. For the special case in which m(t) = m p cos(2πf c t) where f m is the frequency of the message, we can write equation (1) as g(t) = A c [1 + μ cos(2πf m t)] cos(2πf c t) = A c [cos(2πf c t) + μ 2 [cos(2π[f c f m ]t) + cos(2π[f c + f m ]t)]] (19) In the above expression the first term is the carrier, and the second and third terms are the lower and upper sidebands, respectively. Fig. 42 and Fig. 43 is a plot of a 20 khz carrier modulated by a 1 khz sinusoid at 100% and 50% modulation. Fig. 42: AM Signal: Modulation Index = 1 49

2 Fig. 43. AM Signal: Modulation Index = 0.5 When the AM signal arrives at the receiver, it has the form r(t) = A r [1 + μ m(t) m p ] cos(2πf c t + θ) (20) where the angle θ represents the difference in phase between the transmitter and receiver carrier oscillators. We will follow a common practice and offset the receiver s oscillator frequency f O from the transmitter s carrier frequency, f c. This provides the signal r 1 (t) = A r [1 + μ m(t) m p ] cos(2πf IF t + θ) (21) where the so-called intermediate frequency (IF) is given by f IF = f c f o. The signal r 1 (t) can be passed through a bandpass filter to remove interference from unwanted signals on frequencies near f c. Usually the signal r 1 (t) is amplified since A r < A c due to signal attenuation as it moves through the transmission medium. Demodulation of the signal r 1 (t) is most effectively carried out by an envelope detector. An envelope detector can be implemented as a rectifier followed by a lowpass filter. The envelope A(t) of r 1 (t) is given by A(t) = A r [1 + μ m(t) m p ] = A r + μa r m p m(t) (22) 50

3 5.3 Pre-Lab Transmitter The task is to add blocks as needed to produce an AM signal, and then to pass the AM signal into the while loop to the Write Tx Data block. A template for the transmitter has been provided in the file AM_Tx_Template.vi (Fig. 44). This template contains six interface controls, two waveform graphs to display your message signal and scaled amplitude modulated signal, and message generator controls set to produce a message signal consisting of three tones. The three tones are initially set to 1, 2, and 3 khz, but these frequencies can be changed using the message generator front-panel controls. Fig. 44: AM_Tx_Template Front Panel Tx Programming Notes: a) Observe that the baseband signal g (nt) is actually two baseband signals. By long-standing tradition, the real part g I (nt) is called the in-phase component of the baseband signal, and the imaginary part g Q (nt) is called the quadrature component of the baseband signal. The AM signal that you will generate in this lab project uses only the in-phase component, with And g I (nt) = A c [1 + μ m(t) m p ] (23) g Q (nt) = 0 (24) 51

4 You will explore other modulation methods in subsequent lab projects that use both components. The baseband signal is expressed as The signal transmitted by the USRP is g (nt) = g I (nt) + j g Q (nt) (25) g(nt) = A c g I (nt) cos(2πf c t) + A c g Q (nt) cos(2πf c t) (26) These values are entered in the Tx Front Panel (Fig. 44) in the following fields f c is the carrier frequency. Sampling interval T is the reciprocal of the IQ rate. Note that the signal g(t) produced by the USRP is a continuous-time signal; the discrete-tocontinuous conversion is done inside the USRP. b) The message generator creates a signal that is the sum of a set of sinusoids of equal amplitude. You can choose the number of sinusoids to include in the set, you can choose their frequencies, and you can choose their common amplitude. The initial phase angles of the sinusoids are chosen at random, however, and will be different every time the VI runs. Get the data values of the generated signal by using the Get Waveform Components VI (Fig. 45) for amplitude modulation operations. Fig. 45: Get Waveform Components VI c) Set up a MathScript Node (Fig. 46) with data values of the generated signal {m}, maximum value of the generated signal {mp}, and modulation index {mu} as inputs. Use Array Max and Min VI (Fig. 47) to get the maximum value of the generated signal, and the Modulation Index control provided to set the modulation index {mu}. Use equations (23), (24), and (25) to set up the text-based script to get the baseband signal {b]. 52

5 Fig. 46: MathScript Node Fig. 47: Array Max and Min VI d) There is one practical constraint imposed by the D/A converters in the USRP: The maximum magnitude of the transmitted signal g (nt) needs to have a maximum scaled value of 1. Set up a text-based script by dividing the baseband signal {b} by the maximum of its absolute value {max(abs(b))} to get the scaled baseband signal {A}. e) The USRP is designed to transmit using a quadrature modulation approach. So in order to use the radio to transmit an AM signal, it is necessary to represent the signal as a complex sequence. The quadrature modulation then transmits the real and complex sequences using two orthogonal waveforms. The real part is sent using a cosine carrier and the complex part using a sine function as the carrier. Set up a text-based script to convert the scaled amplitude modulated signal from 1D double {A} to 1D complex double form {G}. The 1D complex double form is attained by multiplying the 1D double form by { e (j 0) }. f) Set up both the forms of the scaled baseband signal as outputs of the MathScript Node. Plot the scaled baseband signal {A} by using the Baseband Signal waveform graph provided, and input the complex form {G} to the niusrp Write Tx Data VI (Fig. 48) to be transmitted. 53

6 Fig. 48: niusrp Write Tx Data VI g) Save your transmitter in a file whose name includes the letters AM_Tx and your initials. Note: Modulation with the carrier occurs after the baseband signal is sent to the buffer for transmission. To visualize the amplitude modulated signal, you may plot the waveform received at the receiver end Receiver A template for the receiver has been provided in the file AM_Rx_Template.vi (Fig. 49). This template contains the six interface controls and two waveform graphs to display the received amplitude modulated signal and the demodulated baseband output. Fig. 49: Reciever VI Front Panel Rx Programming Notes: a) Plot the received amplitude modulated signal from the niusrp Fetch Rx Data VI (Fig. 50) using the Rx AM Signal waveform graph provided. 54

7 Fig. 50: niusrp Fetch Rx Data VI b) Get the data values of the signal received from the niusrp Fetch Rx Data VI (Fig. 50)by using a Get waveform components VI (Fig. 45) so as to perform filtering operations. c) To remove unwanted interferences around carrier frequency, design a fifth order Chebyshev band-pass filter (Fig. 51) with a high cutoff frequency of 105 khz, a low cutoff frequency of 95 khz, pass-band ripple of 0.1 db, and a sampling frequency equal to the actual IQ rate obtained from the niusrp Configure Signal VI. Fig. 51: Chebyshev Filter VI d) Extract the real part of the complex filtered signal from the output of the Chebyshev bandpass filter using the Complex to Real/Imaginary VI (Fig. 52). The real part is expressed as shown in equation (21). Fig. 52: Complex to Real/Imaginary VI 55

8 e) Use Absolute Value VI to take the absolute value of the real part of the filtered signal for full-wave rectification. Fig. 53: Absolute Value VI f) To filter out high frequencies to complete envelope detection, design a second order Butterworth low-pass filter (Fig. 54) with a low cutoff frequency of 5 khz, and a sampling frequency the same as the actual IQ rate obtained from the niusrp Configure Signal VI. Fig. 54: Butterworth Filter VI g) Build a waveform from the data values of the output of the low-pass filter designed above by using a Build Waveform VI, setting the sampling time interval same as that of the received waveform. Plot the waveform obtained with the Baseband Output waveform graph provided. h) Save your receiver in a file whose name includes the letters AM_Rx and your initials. 56

11 5.4.1 Worksheet: The Effect of Varying the Modulation Index 1. Set the transmitter to use one of the three tones. Please note that using more than one tone will make it very hard to make the observations. 2. Set the Start Frequency to 1 khz. 3. Set the transmitter VI modulation index to the first value in Table VIII. 4. Start the transmitter VI. 5. Observe the demodulated signal i.e. Baseband Output waveform on the receiver VI. Note the peak to peak voltage in Table VIIITable IX. 6. Stop the receiver VI. Update the modulation index to the next value in Table VIII and repeat steps 4 through 6 until the table is complete. Table VIII Modulation Index Observations Modulatio n Index 0.1 Amplitud e (Peak to Peak) V peak-to-peak m =

13 5.5 Lab Write-up Performance Checklist Amplitude Modulation Short Answer Questions 1. What is the relation between the message bandwidth and the IF and baseband filter bandwidths? 2. What is the effect of varying the modulation index? 3. What is the effect of varying the transmitter and receiver gain? Performance Measures Task Standards Sat/Unsat Hardware Setup Working setup for all with Loopback-cable. Running VIs Data Collection Successful transmission and reception of tones. Collect data to answer Short Answer Questions. Discussion Did all configurations perform as expected? Did you have any difficulties completing the lab? Did your TA provide enough guidance? Do you have any recommendations to improve the lab? 61

14 5.6 References [1] Lab 2: Amplitude Modulation, Bruce A. Black, Rose-Hulman Institute of Technology, July

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