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ECE 405: Digital Data Communications Laboratory Report 01

Felipe Meneguitti Dias A20358366 September 2, 2015

Contents 1 Objective

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2 Introduction

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3 Experiment

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4 Audio example

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5 Questions

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Objective

Analyze the addition of two signals related to phase difference and gain difference.

Figure 1: Signal sum block diagram

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Introduction

For the experiment we used the TIMS, a telecommunications modeling system, with three modules: AUDIO OSCILLATOR, PHASE SHIFTER and ADDER. The AUDIO OSCILLATOR is responsible for generating the signal. The PHASE SHIFTER applies a phase difference between the input and output. The ADDER sums the signals.

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Experiment

The experiment was conducted in this way: 1) Connect the AUDIO OSCILLATOR output to the frequency counter of the TIMS panel; 2) Setting the frequency to approximately 1kHz; 3) Connect the AUDIO OSCILLATOR output to the external trigger of the OSCILLOSCOPE; 3) Connect the AUDIO OSCILLATOR output to the PHASE SHIFTER input; 4) Connect the PHASE SHIFTER output to one of the inputs of the ADDER; 5) Connect the AUDIO OSCILLATOR output to the other ADDER input; 6) Connect the ADDER output to the OSCILLOSCOPE; After doing these steps, we set the signal gains to be equal. By performing a phase shift we can see the signal vary from 0 to 2*GAIN in the oscilloscope.

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Figure 2: Experiment diagram

Figure 3: Vector sum

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Audio example

We realized that the system can cancel the input if an appropriate phase shift is applied. We tested this result using an audio signal. At first, we connected an audio signal to the HEADPHONE AMPLIFIER and heard the sound. We used the LPF in an attempt to cancel the noise, but it didn’t work (the sound heard changed a little bit). Then we used our “cancellation system”, and the noise heard was clearly decreased, but it wasn’t canceled completely. This is because the system itself adds noise to the signal, so the noise can’t be canceled perfectly.

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Figure 4: Null signal

Figure 5: Signal twice bigger

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Figure 6: Experiment Configuration

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Questions

Q1) Refer to the phasor diagram of Figure 3. If the amplitudes of the phasors V1 and V2 were within 1% of each other, and the angle α 1◦ within 180◦ , how would you describe the depth of null ? How would you describe the depth of null you achieved in the experiment? You must be able to express the result numerically. A1: Considering V1 = 1V, V2 = 0.99V, θ1 = 0◦ and θ2 = 179◦ X1 = (1cos0)ˆ x X2 = (0.99cos179)ˆ x + (0.99sin179)ˆ y Y = x1 + x2 = (1cos0 + 0.99cos179)ˆ x + (0.99sin179)ˆ y Y = (1 + -0.989)ˆ x + (0.0173)ˆ y Y = (0.011)ˆ x + (0.0173)ˆ y In the experiment, the null was so close to zero that we were unable to evaluate it. Q2) Why was not the noise nulled at the same time as the 1 kHz test signal? A2: The noise has many different frequency components. The PHASE SHIFTER applies a different phase shift to different frequencies, so there isn’t going to be a noise cancellation. Q3) Describe a method (based on this experiment) which could be used to estimate the harmonic distortion in the output of an oscillator. A3: We could analyze the spectrum of the system after the cancellation (output of the ADDER), and compare it with the pure signal generated. Q4) Suppose you have set up the system of Figure 2, and the output has been successfully minimized. What might happen to this minimum if the frequency

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of the AUDIO OSCILLATOR was changed (say by 10%). Explain. A4: Because the PHASE SHIFTER applies different phase shift to different frequencies, if w1 = 1.1w2 , the cancellation would not remain. Q5) Figure 1 shows an INVERTING AMPLIFIER, but Figure 2 has a PHASE SHIFTER in its place. Could you have used a BUFFER AMPLIFIER (which inverts the polarity) instead of the PHASE SHIFTER ? Explain. A5: We could have used a BUFFER AMPLIFIER instead of a PHASE SHIFTER if x1 and x2 had the same initial phase (y = Acos(wt + θ) − Acos(wt + θ) = 0). However, any small initial phase difference would compromise the cancellation, so an inverting amplifier could work, but it wouldn’t be as effective as the PHASE SHIFTER.

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