EE 207 - Lab #10 Evaluating the Harmonics of Periodic Waveforms Using the Tektronix TDS 3052 Digital Oscilloscope (thanks to Dr. Nehrir for this lab) Objective: This experiment will introduce the spectrum analysis feature of the Tektronix TDS 3052 Digital oscilloscope, using this feature to verify the relative amplitude of the harmonic components of several common periodic signals. Prelab: Determine the rms magnitude of the fundamental (n=1) of a square wave, a sawtooth wave, a symmetric triangle wave, and a half-wave rectified sine wave, all with peak-to-peak amplitude A = 1 and frequency f = 1 kHz. Then find the magnitude for all harmonics less than 12 kHz relative to the fundamental, in dB (this is how the oscilloscope will conveniently provide the output data). RMS amplitude for each harmonic is found according to: 1 1 2 2 An cn an bn 2 Cn 2 2 The relative magnitude in dB is defined as follows: Ai (Relative) [dB] = 20 log10 (Ai/ A1) For example: 4 For a unit amplitude square wave, c , n odd. The rms amplitude of the n nS 4 fundamental is A1 0.9 . The third harmonic amplitude, relative to the 2S fundamental is A3 =A1/3. Therefore, A3 (Relative) = 20 log10(1/3) = -9.542 dB 8 For a unit amplitude triangle wave, cn , n odd. The rms amplitude of the n2S 2 8 fundamental is A1 0.573 . The third harmonic amplitude, relative to the 2S 2 fundamental is A3 =A1/9. Therefore, 2 A3 (Relative) = 20 log10(1/3 ) = -19.08 dB Make a table, like the one shown below, in your notebook. Enter the calculated values before you come to the lab and enter the measured values as you measure them in the lab. Frequency Square wave Sawtooth wave Triangle Wave Half-wave retified (kHz) sine wave Calculated Measured Calculated Measured Calculated Measured Calculated Measured RMS 1 0.9 .573 1 0 0 0 0 0 0 0 0 2 ----- ----- 3 -9.54 -19.1 4 5 dB 6 7 8 9 10 11 Lab: 1. Turn on the Oscilloscope and the function generator. Set the function generator to a 1 kHz square wave. 2. Press Math function and select FFT. 3. Set FFT source to Ch1(or Ch2). 4. Set FFT Vertical scale to dbV RMS. 5. Set FFT window (Pass band window) to Hanning. 6. Use Cursors to observe the vertical bars on the screen of the oscilloscope corresponding to the harmonics of the square wave. 7. Position one of the vertical bars so that it is centered at the top of the first (fundamental) pulse. This is our reference for the rest of the measurements. 8. Move the other vertical bar to the harmonic you want to measure relative to the fundamental. (The reading next to symbol ' gives the difference between the reference and the place of measurement, which you need to record in the table above, under the measured column. The reading next to the symbol @ gives the current place of measurement). 9. Move the second vertical bar to top of each pulse and record the reading in the table. 10. Change the waveform on the function generator to a triangle wave and repeat steps 7 to 9. 11. Change the waveform to a ramp and repeat steps 7-9. 12. Time permitting, construct the small-signal half wave rectifier circuit shown below to create a half-wave rectified sine wave. The lab instructor will have diodes available for you to use. Report: In your notebook, compare the measured and calculated values of the magnitude of each frequency component of the waveforms you worked with in the lab, and draw conclusions. Compare to your Matlab analysis for these same waveforms. Your written report should include your Matlab analysis from Lab 9 as well as your experimental observations from Lab 10. Small-Signal Half-Wave Rectifier Circuit.