SJSU EE 160 Lab: Experiment 1 Page 1 of 11 EE 160: Principles of Communication Systems Experiment 1: Harmonics and intermodulation I. INTRODUCTION a. Objectives i. Gain familiarity with the operation of the spectrum analyzer ii. Study harmonic generation with a nonlinear device (diode) iii. Evaluate experimentally the input third order intercept point (IIP3) of an amplifier using a two-tone test procedure iv. Measure the spectra of periodic signals b. Required reading (follow the links in the web page) i. Spectrum Analyzer Basics (Agilent) ii. HP 8590 Spectrum Analyzer user’s manual: All of section 2 and section 3, pages 3-1 to 3-3 iii. Digital Waveform Generator user’s manual iv. Digital Oscilloscope user’s manual c. List of parts i. Spectrum analyzer coupling and attenuation circuit (ATT-SA) 1. 1 kΩ resistor 2. 56 Ω resistor 3. 0.1 uF monolithic ceramic capacitor ii. Two-sinusoidal adder 1. Two 1 kΩ resistors iii. Amplifier two-tone test 1. LF347 (or equivalent) quad op amp 2. Three 1 kΩ resistors 3. Two 10 kΩ resistors iv. Cosine waveform clipper 1. 1 kΩ resistor 2. Switching diode: 1N914 or 1N4148 II. THEORY This experiment serves three fundamental purposes: First, familiarize the student with the spectrum analyzer (SA) by identifying and resolving sinusoidal signals of relatively close center frequencies. Second, use the SA in measuring harmonics generated by a non-linearity. Finally, use a two-tone test in determining the nonlinear (third-order) characteristic of an amplifier.SJSU EE 160 Lab: Experiment 1 Page 2 of 11 A periodic waveform f(t) with period T can be expressed as an exponential Fourier series ∑∞∞==)(ntωjnnoectf where 0022fTππω== and f0 the fundamental frequency. The Fourier coefficients cn can be computed as ∫=TjnnetfTc0dtt 0)(1ω Note that the integral may be taken over any interval of length T. The power in the n-th harmonic (for n>0) is proportional to 2||2=nncP The total harmonic distortion (THD) is defined as 212=212=||||==ccPPTHDnnnn∑∑∞∞ and is typically expressed as a percentage. Sequence Pn can be plotted in a graph as a one-sided power line spectrum. The spectrum analyzer displays this spectrum with the lines broadened by the finite bandwidth resulotion of the analyzer’s variable frequency bandpass filter. When the spectrum analyzer is properly adjusted, the amplitude of each displayed spectral peak indicates the corresponding Pn. II. 1 The coupling-attenuation (ATT-SA) circuit Of fundamental importance in the EE 160 lab is the ATT-SA circuit. Its function is to limit the input signal levels, block any DC components and match the input 50 Ω impedance of the spectrum analyzer. A diagram of the ATT-SA circuit is shown in Fig. 1.SJSU EE 160 Lab: Experiment 1 Page 3 of 11 Figure 1: Coupling-attenuator circuit (ATT-SA) As the ATT-SA will be used in future experiments, you must build it on an end of the breadboard and leave it permanently until the end of the semester. Please notice that all input signals to the spectrum analyzer shall be applied through the ATT-SA. III. INSTRUMENTS AND MATERIAL Follow the procedure on pages 2-13 to 2-15 of the spectrum analyzer user’s manual to learn how to make basic measurements. Make sure that you follow through the entire procedure. In particular, from section 2 you shall understand how to set the start and stop frequencies, adjusting the amplitude reference level and using markers to determine the dB ratio of two spectral components. Also read the user’s manual of the digital oscilloscope from the web page. IV. PRE-LAB WORK Read the handout given in class on nonlinear devices and harmonics. In particular, the section that deals with measuring the input third-order intercept point (IIP3) of a non-linearity based on a two sinusoidal input. This procedure is known as the two-tone test. Triangle Wave Either look up in your textbook or derive an exponential Fourier series coefficient formula for the symmetric triangular wave given by To Input of Spectrum Analyzer 1 kΩ 0.1 μF 56 Ω ATT-SA R1 R2 C From Output of Circuit Under TestSJSU EE 160 Lab: Experiment 1 Page 4 of 11 ,2||,||41)(TtifTttf ≤−= as shown in Figure 2. Then evaluate the harmonic power ratio Pn/P1 (n = 2, 3, 4, and 5) in dB. Also, compute the THD due to the second through fifth harmonics (only). Figure 2. Symmetric Triangular Wave. Variable Duty Cycle Rectangular Wave Similarly, look up or derive an exponential Fourier coefficient formula for the square wave with duty cycle α (0 < α < 1): ⎪⎩⎪⎨⎧≤<≤+=2||2,02||,1)(TtTTttfαα shown in Figure 3. Figure 3. Variable Duty Cycle Rectangular Wave tSJSU EE 160 Lab: Experiment 1 Page 5 of 11 From this formula, determine the duty cycle values α at which the second, third, and fourth harmonics vanish. For each of these three duty cycles, compute the harmonic power ratios Pn/P1 (dB) and the THD (only for n = 2, …., 5). Note that the harmonic power ratios for a “unipolar” (0 to +1) rectangular wave are identical to those for a “bipolar” (-1/2 to +1/2) rectangular wave with the same duty cycle. Their spectra differ only in the DC component, which cannot be measured with a spectrum analyzer. Clipped Cosine Wave Figure 4 shows a clipped cosine wave defined by: {})cos()cos(,0max)(0θω−=ttf where 0 < θ < π. This waveform corresponds to the portion of a cosine wave with phase between -θ and + θ. Note that the peak amplitude of this clipped wave increases monotonically with θ. Figure 4. Clipped Cosine Wave. Look up or derive an exponential Fourier coefficient formula for this periodic waveform. These coefficients will depend on θ as well as the period T. For n = 1 through 5, plot Pn(θ) vs. θ over the range 0 < θ < π. (you may use MATLAB to generate these plots.) From your plots, find theSJSU EE 160 Lab: Experiment 1 Page 6 of 11 value(s) of θ at which each Pn reaches local maximum and minimum values. For some values of n you will see more than one sharp dip or “null” in the plots. In the lab you will work with a simple circuit that generates a good approximation to this clipped sine wave. A practical application of this circuit is the generation of specific harmonics. For example, to design a frequency doubler, you might choose the value of θ that yields the maximum P2, or you might choose a θ that produces a minimum P3 while