EE-4022 Experiment 2 Amplitude Modulation (AM)

Transcription

1 EE-4022 MILWAUKEE SCHOOL OF ENGINEERING 2015 Page 2-1 Student objectives: EE-4022 Experiment 2 Amplitude Modulation (AM) In this experiment the student will use laboratory modules to implement operations (signal addition and multiplication) on basic signals (DC, sinusoidal message, and sinusoidal carrier) to generate an AM signal having specified parameters. The laboratory modules will perform operations that match those in the AM signal equation. The modules to be used are from the Telecommunications Instructional Modeling System (TIMS). The student will determine the AM modulation index from the observed AM waveform or its associated trapezoidal pattern, and will adjust signaling parameters to change the modulation index. The frequency spectrum of the AM signal is also observed on the oscilloscope and compared to the expected spectrum. To illustrate the operation of a demodulator for an AM signal, a simple envelope detector circuit is constructed and tested. Published resources: TIMS-301 User Manual (Issue No. 1.6, October 2004) describes each basic TIMS module. Communication Systems Modelling with TIMS, Vol. A1 Fundamental Analog Experiments by Tim Hooper (Issue No. 4.9, 2005) Instructor s Manual to accompany Communication Systems Modelling with TIMS includes notes on the TIMS experiments Equipment needed: Oscilloscope (e.g., Agilent MSO-X-3014A Mixed Signal Oscilloscope (100 MHz, 4 Gsa/s)) Multimeter (e.g., Agilent 34401A Digital Multimeter) TIMS system with the following modules: o Audio Oscillator o Variable DC module o Adder o Master Signals generator o Multiplier o PC-Based Instrument Inputs (earlier TIMS called this Scope Selector) if desired For the AM demodulator: Breadboard, wires, 1N914 signal diode, 10k resistor, 0.01μF capacitor. Background: Background information on Amplitude Modulation (AM) signals is provided in Appendix I. Prelaboratory investigation: 1. Review information on AM signals in the course textbook and in Appendix I. 2. Assume that a message signal or modulating signal in an AM system is a sine wave signal at a frequency of 1 khz. Assume that the carrier frequency is 100 khz. Assume that the unmodulated carrier amplitude is 2 volts peak-to-peak. If A is the peak value of the unmodulated carrier, then 2A is the peak-to-peak value (see Figure 1 below). Refer to the maximum and minimum p-p carrier voltages for the modulated signal, labeled as P and Q respectively on Figure 1 below. Note that the average p-p carrier amplitude is 2A = (P+Q)/2, and the modulation index is μ = (P - Q) / (P + Q). Derive

2 EE-4022 MILWAUKEE SCHOOL OF ENGINEERING 2015 Page 2-2 expressions for P and Q, each as a function of A and μ. Using those expressions, determine P and Q for the 2V peak-to-peak carrier if μ = Sketch the AM signal waveform having the parameters given in the previous step. Your sketch should be similar to Figure 1, except that your sketch should include numerical values and units on both axes. 4. Make a sketch of the frequency spectrum of the AM signal described in the previous step. On the sketch, indicate rms voltage magnitudes for each component in the frequency spectrum. For each component, show its rms magnitude both as a voltage in volts (V) and as a dbv quantity. P = max. p-p carrier voltage 2A = unmodulated p-p carrier voltage 2A Q = min. p-p carrier voltage Envelope AM signal Figure 1. AM signal waveform and p-p carrier voltage variations Laboratory investigation: Part A. Generating an AM signal using TIMS modules 1. Connect the TIMS modules as shown on Figure 2. Note that the Audio Oscillator provides a sinusoidal message signal, and the Audio Oscillator output is to trigger the Agilent oscilloscope. It is suggested that the Audio Oscillator output, the Adder output, and the Multiplier output (all shown on Figure 2) are each routed to a separate oscilloscope input. Set the Multiplier switch to DC. 2. Use the Frequency Counter to set the Audio Oscillator to approximately 1 khz. 3. Adjust the control on the Variable DC module so that the DC signal at its output measures (using the DMM) approximately -2V. (The exact voltage value is not critical because the gain control on the Adder module will further adjust the DC level. Note that if the control on the Variable DC module is turned in one direction (clockwise), the module output has a positive DC voltage, and if the control is turned in the other direction (counter-clockwise) then the module output has a negative voltage. Note also that the Adder module reverses the polarity of each of its inputs.) 4. Adjust the two controls on the Adder module so that the Adder output (that is, the [A + B cos (ω M t)] waveform) observed on the oscilloscope has a +1V DC level plus a 1 volt peak (that is, 2 V p-p)

3 EE-4022 MILWAUKEE SCHOOL OF ENGINEERING 2015 Page 2-3 sinusoidal wave at 1 khz. (Be sure to use DC coupling on the scope inputs.) [Suggestion: Use the Meas feature on the oscilloscope to measure Pk-Pk and average levels. The MSO-X 3014A scope indicates Average - Full Screen abbreviated Avg - FS as the average value over the full screen.] If this Adder output is the low frequency signal a(t) in equation (1) in Appendix I, then what modulation index is represented by the adjustments made in this step? 5. Capture and store a scope image showing both the Adder output waveform (that is, the [A + B cos (ω M t)] waveform) and the Multiplier output (that is, the AM signal). The Multiplier output should be similar to Figure AI-1 in Appendix I. To scope inputs as appropriate Figure 2. TIMS model for the AM modulator block diagram shown on Figure AI-2 6. Measure the largest peak-to-peak amplitude of the AM signal (referred to as P on Figure 1 above and on Figure AI-3 in Appendix I). Compare this to the expected value of P from prelaboratory step Adjust the G control on the Adder module (see Figure 2), which will adjust the modulation index μ, until the peak-to-peak amplitude for the AM signal (for the largest peaks) is 3V. Use cursors to measure the trough-to-trough voltage for the AM signal (referred to as Q on Figure 1 above). Use measured P and Q values, and equation (4) in Appendix I, to determine a measured value for the modulation index. 8. With approximately 5 cycles of the sinusoidal message displayed on the oscilloscope, display the frequency spectrum of the AM signal (suggested frequency span is from 97.5 khz to khz), and measure the levels of the three components. 9. Adjust the G control on the Adder module (see Figure 2), which will adjust the modulation index μ, to achieve (i) a modulation index of 0.75, and (ii) a modulation index of 1.5. Capture each AM waveform displayed on the scope. (See Figure 3.)

4 EE-4022 MILWAUKEE SCHOOL OF ENGINEERING 2015 Page The modulation trapezoid: Adjust the G control on the Adder to result in approximately 50 percent modulation, determined from measured P and Q values, and equation (4) in Appendix I. With the Audio Oscillator output connected to scope channel 1 and the Multiplier output connected to scope channel 2, change the scope to an X-Y mode (using the Horiz switch on the scope and then pressing the Time Mode soft-key and selecting XY). Observe the trapezoid, which should be similar to that shown on Figure 4. Adjust the sensitivities of the Channel-1 and Channel-2 scope inputs to fill most of the screen. Press Run/Stop to freeze the image, and use cursors to measure P and Q. Then adjust the G control on the Adder module, and observe the effect on the trapezoid when μ is adjusted. μ = 1.5 μ = 1 μ = 0.75 Figure 3. AM signal envelopes for various modulation indices

5 EE-4022 MILWAUKEE SCHOOL OF ENGINEERING 2015 Page 2-5 Figure 4. AM trapezoid for modulation index of 0.5 Part B. Envelope Detector for AM Demodulation 1. Construct on a breadboard the demodulator circuit shown on Figure 5. Connect the AM signal at the Multiplier output to the input of the AM Demodulator, and connect the output of the AM Demodulator to the scope channel 1 input (while observing the AM signal waveform connected to scope channel 2). Adjust the G control on the Adder to result in approximately 30% modulation, determined from measured P and Q values. Store an image of the demodulator output shown with the AM signal, and observe any peculiarities of the demodulator output waveform. 1N914 Figure 5. Envelope Detector Circuit for AM Demodulation Report Suggestions: Compare measurements to predictions as appropriate. Comment on the waveform observed at the demodulator output and suggest modifications to the demodulator that would improve the output waveform.

6 EE-4022 MILWAUKEE SCHOOL OF ENGINEERING 2015 Page 2-6 APPENDIX I. Background on Amplitude Modulation (AM) App-I-1. History In the early days of wireless, communication was carried out by telegraphy, the radiated signal being an interrupted radio wave. Later, the amplitude of this wave was varied in accordance with (that is, modulated by) a speech message (rather than an on/off signal from a telegraph key), and the message was recovered from the envelope of the received signal. The radio wave was called a carrier, since it carried the speech information. The process and the signal were called amplitude modulation, or AM for short. In the context of radio communications, near the end of the 20th century, few modulated signals contained a significant component at the carrier frequency. However, despite the fact that for many communication systems a carrier is not radiated, the need for such a signal at the transmitter (where the modulated signal is generated), and in some cases at the receiver, remains fundamental to the modulation and demodulation process respectively. The use of the term carrier to describe this signal has continued to the present day. Many present-day radio broadcasting transmissions do have a carrier component. By transmitting this carrier the design of the demodulator at the receiver is greatly simplified, and this allows significant cost savings. The most common method of AM generation uses a class C modulated amplifier ; such an amplifier is not available in the BASIC TIMS set of modules. It is well documented in textbooks. This is a high level method of generation, in that the AM signal is generated at a power level ready for radiation. It is still in use in broadcasting stations around the world, ranging in powers from a few tens of watts to many megawatts. Unfortunately, textbooks that describe the operation of the class C modulated amplifier tend to associate properties of this particular method of generation with those of AM, and AM generators, in general. This gives rise to many misconceptions. The worst of these is the belief that it is impossible to generate an AM signal with a depth of modulation (or modulation index) exceeding 100% without giving rise to serious RF distortion. You will see in this experiment that there is no problem in generating an AM signal with a modulation index exceeding 100%, and without RF distortion. App-I-2. Theory A multiplier circuit can multiply two input signals: a higher frequency carrier signal v C(t) and a lower frequency signal, a(t). For AM, the lower frequency signal consists of a DC level added to a low frequency message waveform. For testing purposes a sine wave signal is used as the message waveform, and the lower frequency signal is a(t) = [A + B cos (2πf M t)] = A [1+ μ cos (ω M t)] (1) where μ = B/A is the modulation index (or depth of modulation). The carrier signal is v C (t) = cos (2πf Ct) = cos (ω Ct). Consider what happens when these two signals are multiplied, as shown on the block diagram of Figure AI- 2. The output of the multiplier will be called v AM(t): V AM (t) = a(t) v C (t) V AM (t) = [A + B cos (2πf Mt)] cos (2πf Ct) (2) V AM (t) = A cos (2πf Ct) + (B/2) cos [2π(f C + f M)t] + (B/2) cos [2π(f C - f M)t]

7 EE-4022 MILWAUKEE SCHOOL OF ENGINEERING 2015 Page 2-7 V AM (t) = A cos (2πf Ct) + (μa /2) cos [2π(f C + f M)t] + (μa /2) cos [2π(f C - f M)t] (3) For any particular AM signal and message signal, the value of μ is a constant, called the depth of modulation or modulation index. Typically μ < 1. The modulation index, expressed as a percentage, is 100 μ. However, there is no inherent restriction on the size of μ in equations (1) and (3). The parameters ω M and ω C are angular frequencies in rad/s, where ω M2π is a relatively low, message frequency, as an example in the range from 300 Hz to 3000 Hz; and ω C /2π is a relatively high, carrier frequency. In TIMS the carrier frequency is generally 100 khz. Notice that the signal a(t) in eqn. (1) contains both a DC component and an AC component. It is the DC component that gives rise to the term at ω C - the carrier - in the AM signal. The AC term B cos ω M t is generally thought of as the message, and is sometimes written as m(t). Thus: a(t) = DC + m(t) Figure AI-1 below illustrates what the oscilloscope will show if displaying the AM signal with 100% modulation. Figure AI-1. Message signal and AM signal with 100% modulation A block diagram representation of eqn. (2) is shown on Figure AI-2 below.

8 EE-4022 MILWAUKEE SCHOOL OF ENGINEERING 2015 Page 2-8 For the first part of the AM experimentation with TIMS, you will model eqn. (2) by the arrangement of Figure AI-2. The modulation index will be set to 100% (μ = 1). You will adjust the signal parameters for other values of μ, including cases where μ > 1. m(t) = B cos (ωmt) A vc (t) vc (t) = cos (ωct) Figure AI-2. Block diagram for AM signal generator corresponding to equation (2) App-I-3. Modulation index The condition when μ = 1 is also referred to as 100% modulation. To have μ = 1 requires that the amplitude of the DC term (which is A) within the a(t) signal is equal to the peak amplitude of the AC term (which is B). This means that their ratio is unity at the output of the Adder (see Figure AI-2), which forces μ to a value of exactly unity. The value of μ can be measured directly from the AM display, using the following equation with P and Q values as defined on Figure AI-3. μ = (P Q) / (P + Q) (4) Figure AI-3. Message and AM signal showing P and Q parameters (with 50% modulation as an example)

9 EE-4022 MILWAUKEE SCHOOL OF ENGINEERING 2015 Page 2-9 Note that on Figure AI-3 the shape of the outline, or envelope, which defines the upper boundary of the carrier cycles for the AM waveform (lower trace), is exactly that of the message waveform (upper trace). On the scope, you can shift the vertical position of the message signal (upper trace) down so that it aligns with the envelope of the AM signal (lower trace). Now examine the effect of varying the value of the modulation index μ. This is done by varying the message amplitude with the Adder gain control G. for all values of μ less than (μ = 1), the envelope of the AM is the same shape as that of the message. for values of μ > 1 the envelope is NOT a copy of the message shape. It is important to note that, for the condition μ > 1, there is no envelope distortion relative to the envelope that is expected, however the envelope does not have the shape of the message signal. (See Figure 3.) APPENDIX II. Tutorial questions 1. There is no difficulty in relating the formula of eqn. (4) to the waveforms of Figure 3 for values of μ less than unity. But the formula is also valid for μ > 1, provided the magnitudes P and Q are interpreted correctly. By varying μ, and watching the waveform, can you see how P and Q are to be interpreted for μ > 1? 2. Explain how the arrangement in Lab Investigation step 10 generates the trapezoid of Figure 4, and how a triangle shape is generated as a special case. 3. Derive eqn. (4), which relates the magnitude of the parameter μ to the peak-to-peak and trough-to-trough amplitudes of the AM signal. 4. If the AC/DC switch on the Multiplier front panel is switched to AC, what will the output of the model of Figure 2 become? 5. An AM signal, having 100% modulation from a single tone message, has a peak-to-peak amplitude of 4 volts (when its amplitude is largest). What would an RMS voltmeter read if connected to this signal? 6. What difference would there be to the AM signal from the Multiplier if the opposite polarity of a DC voltage had been taken from the VARIABLE DC module?

10 EE-4022 MILWAUKEE SCHOOL OF ENGINEERING 2015 Page 2-10 APPENDIX III. Generating an AM signal using an Arbitrary Waveform Generator (Optional) Background: Many function generators and arbitrary waveform generators, such as the Agilent/HP 33120A, are capable of generating modulated waveforms. That is, they have a built-in modulator function. The Agilent/HP 33120A Arbitrary Waveform Generator: has built-in AM and FM modulator functions; allows the carrier frequency and the frequency of the internal information signal to be independently adjusted; allows the internal information signal (also called the modulation source) to be selected as a sine wave, square wave, triangle wave, ramp signal, periodic arbitrary signal, or noise signal; and when using AM modulation, allows the use of an external information signal (or modulation source) instead of the internal information signal. Laboratory investigation: Generating an AM signal using an Arbitrary Waveform Generator (AWG) 1. Connect the output of the Arbitrary Waveform Generator (AWG) to the oscilloscope, and set the generator to provide a 100-kHz sine wave having an amplitude of 2V p-p. This is the unmodulated carrier signal. Use the blue Shift button on the AWG to switch on AM modulation. Note that when AM modulation is switched on, this can cause the signal amplitude to jump to a new value, even if the modulation is set to 0%. If necessary, readjust to 2V p-p (unmodulated). 2. Use Shift-Freq to adjust the modulating (information) signal frequency to 1 khz, and Shift-Level to adjust the level of the AM modulation to 50%. This corresponds to a modulation index of 0.5 or 50%. 3. Adjust the scope horizontal sweep rate to display 500 μs per division. With AUTO triggering, the trigger level can be adjusted to a level near the signal s positive peak to achieve a more stable display. Press the scope Run/Stop button to freeze a single sweep. Use the cursors to measure the maximum peak-to-peak carrier voltage (called P on Figure 1 above) and the minimum peak-to-peak carrier voltage (called Q on Figure 1 above), and calculate the measured modulation index as μ = (P - Q) / (P + Q). 4. While the scope is displaying the AM signal waveform, use the scope s Math-FFT function to simultaneously display the frequency spectrum of the AM waveform. Store an image of the waveform and spectrum, and measure the level of each component in the spectrum. 5. On the AWG, change the modulation level to 100%, and repeat the previous step. Change the modulation level to 120%, and repeat the previous step. Then reset the modulation index to 50%. 6. Change the shape of the information signal, from a sine wave to a triangle wave, by pressing Shift-Enter on the AWG (which turns on the MENU), and then pressing V, V, >, >, and ENTER. Adjust the scope controls for the frequency spectrum display so that you can see at least two components on each side of the carrier, and store an image of the waveform and spectrum.