Introduction to Electronics: AM Radio Modulation and Demodulation using Diodes, Assignments of Electrical and Electronics Engineering

Download Introduction to Electronics: AM Radio Modulation and Demodulation using Diodes and more Assignments Electrical and Electronics Engineering in PDF only on Docsity! EE 461G Introduction to Electronics Homework # 5 Due Tuesday February 22, 2005 Read sections 3.3.1 and 3.3.2 in chapter 3 in Horenstein. Also read sections A.1, A.2, A.3, and A.4 in appendix A of Horenstein. In Horenstein do 3.34 and 3.37. Problem 1 An important application of diodes is in detectors for amplitude modulated (AM) radio waves. Amplitude modulation involves multiplication and the modulated signal is given by   carriersignalcarriercarriersignalAM VVAVVVAV 1 Here A is a constant gain related to the modulation index, Vcarrier is a high frequency sine wave called the carrier which is to be modulated by the signal voltage Vsignal to produce the modulated output VAM. Note that multiplication is a nonlinear operation and that amplitude modulation is a nonlinear operation. In AM radio the carrier is about 1MHz and the signal is a voice signal with frequency content of around 100Hz. The gain A is chosen so that the peak value of (A Vsignal) is less than 1. Figure 1.1 shows a 10V peak 100kHz carrier modulated by a 1V peak 100Hz signal with an A = 0.75. TIME +2.734e-304 V(5) +2.116e-304 D(TIME) +1.901e-305 D(V(5)) +5.563e-309 100kHz carrier modulated with a 100Hz signal with A = 0.75 Time (s) (V) -20.000 -10.000 0.0 +10.000 +20.000 0.0 +5.000m +10.000m +15.000m +20.000m Fig. 1.1 The equation for the AM signal is )000,1002sin(10)000,1002sin(10)1002sin(75.0 tttVAM   Using trigonometric identities this becomes )000,1002sin(10)100,1002sin(75.3)900,992sin(75.3 tttVAM   This new signal contains three frequencies, all of which are very close to or equal to the carrier frequency. In demodulation we want to remove the carrier and recover the original signal. The AM demodulator (also called the detector) can be constructed using a diode rectifier circuit with a capacitor filter. This type of demodulator, also called an envelope detector, is shown in Fig. 1.2. Vsignal + - Rfilt Vmod + - D Modulated carrier Cfilt Fig. 1.2 Schematic of a diode envelope detector for demodulating AM. Note if Rfilt was infinite this circuit would simply be a peak detector and the voltage on the capacitor Cfilt would be the peak of the modulated signal. Because of the resistor, the capacitor has a path to discharge and the voltage on the capacitor can decrease. The circuit must be designed so that at the carrier frequency the capacitor voltage cannot change significantly (acts like a peak detector) but at the lower signal frequency the capacitor can discharge easily. Let the carrier be 10V peak at a frequency equal to 100kHz, let the signal be 1V peak at a frequency equal to 100Hz, let A = 0.75, and Rfilt = 1k. a) What is the constraint on C so that at the 100kHz carrier frequency the capacitor voltage cannot change significantly? b) What is the constraint on C so that at the 100Hz signal frequency the capacitor can discharge easily? c) From parts a) and b) choose a value of C for your circuit. d) Build a Spice model as in Fig. 1.3 to test your demodulator. You will need a nonlinear dependent voltage source available in the more devices menu of B2 Spice to create your modulated signal. After you place the nonlinear dependent source in your schematic double click on it to open a window where you can type in your nonlinear equation. You would type v=0.75*v(5)*v(6)+v(5) for example. You must have the v on the left hand side of the equal sign and you must use node numbers. e) You are to simulate your circuit for two cycles of the 100Hz signal. What must your tceiling and your tstop be? f) Plot your modulated signal (as in Fig. 1.1) and your demodulated signal. g) Your demodulated signal is offset above zero. What kind of circuit could be used to get it centered on zero? For your own information why do you think I chose a 100kHz carrier rather than a more realistic 1MHz carrier? I gave you the value of Rfilt. Think about the issues involved in choosing its value.