TNE30003 Group 1 Lab1 Report1

TNE30003: Communication Principles - Group 1_Lab 1 Report

Lab 1 : Signals in Time Domain and Frequency Domain

Introduction :

To better understand the transition from time domain to frequency domain, a series of different waveforms in both domains were observed using the TIMS unit and the Tektronix Oscilloscope ,and their characteristics were recorded. Preliminary work were carriied out prior to the carried out of the experiment upon which results were compared and verified with mathematical proofs.

Experiment 1 : Single Sinusoid (Single Tone)

Procedures:1.1. The "TIMS" unit was powered up by using the switch at the back. 1.2. The Tektronix Oscilloscope (TDS2002 or TDS1002B) was connected to the PC using the USB cable provided. The OpenChoice Desktop software was openned to capture the waveform on the oscilloscope display or waveform data. 1.3. On the "TIMS" unit, the 2 kHz (sin µt) message found on the “Master Signals” module was connected, to input A-CH1 of the “Scope Selector”. Making sure the toggle switch is set to A,CH1 of the scope selector was connecetd to CH1 of the DSO via the coaxial cable provided .1.4. The time domain signal was observed and recorded, characteristics such as frequency and amplitude were noted. (Note: the probe setting on the DSO is 1X). 1.5. The frequency domain information was obtained by using the Tektronix Oscilloscope, as per 1.5.1. the spectrum was captured and recorded, noting the characteristics like peaks and frequencies. 1.5.1. the “Math Menu” button on the oscilloscope was pressed and set the “Operation” to FFT. This will display the spectrum of the sinusoid. The position of the impulse was adjusted using “SEC/DIV” control and you can use the “Cursor” button to make your measurements. 1.6. The 2 kHz message was disconneted and the 100 kHz Carrier was connected with steps 1.3 to 1.5 repeated.

Question 01Compare your predictions (based on the preliminary work) with the experimental results (indicate the differences). Comment on differences (indicate why they are different).

Peak to Peak Voltage Amplitudepredicted 4.00 2.00Experimental (2kHz) 4.00 2.08Experimental (100kHz) 4.40 2.12

There is a slight difference for both the 2kHz and 100kHz waveform.. This might be due to noise or power loss to heat in the equipment. With regard to the peak-to-peak voltage, the tuning is done manually using the knob. The internal noise generated by the components might have caused the interference. And the wire connection from the modules to the oscilloscope might have been loosely connected causing a delay. All these factors could have contributed to the difference in the experimental values with the theoretical ones.

Group 1: SYED AHMED HUSSAINSYED AHMED HUSSAIN LILANKA KUSHAN UDAWATTA KINISI MARAMA TIKOICINA


Fig 1.1: 2KHz Time Domain Waveform

Fig 1.2: 100KHz Time Domain Waveform

Question 02

What is the relationship between the strength of the impulse (peak indicated on the spectrum based on Step 1.5) and the amplitude of the sinusoid (based on Step 1.4 - are they the same)?

Strength of impulse for 2kHz wave :2.004Strength of impulse for 100kHz wave : 1.828For 2kHz,Vrms= 10^(3.03/20)=1.4174Vp= Vrms x =2.004For 100kHz,Vrms= 10^(3.03/20)=1.4174Vp= Vrms x =2.004Amplitude of the 2kHz sinusoid: 2.00Amplitude of the 100kHz sinusoid: 2.00



The strength of impulse and the amplitude of the waves are about the same value for the 2kHz and the 100kHz wave.

The following are the captured signals for the 2kHz and 100kHz respectively:

Fig 1.3: 2kHz Frequency Domain Signal

Fig 1.3: 100kHz Frequency Domain Signal



Experiment 2 : Addition of Two Sinusoids

Procedures2.1. Connected the 2kHz signal to input A of the “Adder” module.2.2. Connected input B to ground (GND). 2.3. Connected the output of the “Adder”(GA+gB) to input A-CH1 of “Scope Selector” or the PC-Based Instrument Inputs. 2.4. Adjusted the G control so that the output of the adder is 4Vpp sine wave.2.5. Disconnected the ground from the B input.2.6. Connected the output of the “Audio Oscillator” module to the analogue input of the “Frequency Counter” module. Using the Δf control on the audio oscillator module, adjusted the audio oscillator output to 5 kHz. And then applied the 5 kHz signal to input B of the “Adder” module. Grounding input A of the “Adder”. 2.7. Adjusted the g control so that the output of the adder is a 4Vpp sine wave. 2.8. Removed the ground from input A of the “Adder” module reconnecting the 2 kHz message signal. 2.9. Observed and recorded the resultant waveform in both the time and frequency domains, noting all the important characteristics.

Question: 1. Compare your predictions (based on the preliminary work – Part 2) with the experimental results (indicate the differences). Comment on differences (indicate why they are different).

Part 2(i) Preliminary work: The results that were expected if the two sinusoids were to be combined:y(t) = 2sin(2π×2E3t ) + 2sin(2π×5E3t)

Figure 2.1: Resultant of both waveforms. Figure. 2.2:



The result was obtained in the lab using an adder module in TIMS for time domain was as follows:

Figure 3So the experiment proved the expectation correct.

The next part asked to draw frequency domain of the waves. From the equations the frequency and their amplitudes could easily be obtained: y(t) = 2sin(2π×2E3t) + 2sin(2π×5E3t)

The results obtained in the labs for frequency domain were as follows:

The results obtained in frequency domain showed that results were approximately similar to those expected.If the dB were to be converted to V peak values using the equation: dB = 20log (Vrms)Then V peak for 2.25 dB = 1.83 V and 2.65 dB = 1.91 VThese little inaccuracies might be the results of computation related to FFT. Initially there some hassle to obtain the correct frequency domain so we had to repeat the whole procedure again in order to obtain the more appropriate result.



Experiment 3: Product of Two Sinusoids

Procedure3.1. Connected the two signals used in Experiment 2 above to the “Multiplier” module.

3.2. Observed and recorded the resultant waveform in both the time and frequency domains.

In this part of the experiment, two sinusoids of frequencies 2 KHz and 5 KHz are multiplied using the ‘Multiplier’ module to determine the product of the two sinusoids. The amplitudes and the frequencies of the resultant waveforms are recorded in the Time domain and the Frequency domain.

Observation and Results

Time-Domian Product WaveformPreliminary Predictions Experimental Observations



Frequency-Domain Product waveformPreliminary Predictions Experimental Observations

The two analog inputs used to produce the waveform were

Error: Reference source not found and Error: Reference source not found

The signal mathematically reduced to help us draw the waveform was

Results

Peak to Peak Voltage/V

Peak Amplitude/V

Preliminary Results 8.00 4.00Experimental Results 4.28 2.16

The observed Time domain waveform is identical to the predicted waveform in the preliminaries, but the Amplitude and the Peak to Peak voltages did not agree with the preliminaries. The results observed are almost half the value predicted of the preliminaries.The signal from the multiplier is scaled down by a factor of 0.5 by the TIMS unit to prevent overloading. This resulted in the results observed during the experiment to be scaled down by a factor of 0.54, which explains for the reduction of the Amplitude and Peak to Peak voltages.Frequency domain observation of the waveform proves to show intended results which agrees with the preliminaries. The two peaks are at 3.00 KHz and 7.10 KHz. The peak at 7.10 KHz is a 0.1 KHz over the prediction of the peak at 7.00 KHz in the preliminaries, but is acceptable as the intended result.



Experiment 04 : Square Wave

Procedures

4.1. Connected the TTL output (square wave) of the “Audio Oscillator” to the “Scope Selector”. 4.2. Adjusted the frequency of the square wave to 2 kHz. 4.3. Then the maximum frequency span of the spectrum was set to approximately 25kHz.

The table below is showing both the theoretical and experimental values of the square waveform.

Preliminary Work Experimental ResultFrequency 2 kHz 2.024 kHzPeak to Peak Voltage 4.00 V 4.32 VPeriod 500 µs 494 µs

Experimental Preliminary Resultsn Frequency(kHz) Magnitude(dB) Magnitude(V) Magnitude(V)0 0 01 2 5.4515 2.649 2.532 4 03 6 -6.9485 0.636 0.854 8 05 10 -9.348499 0.482 0.516 12 07 14 -12.9485 0.319 0.368 16 09 18 -15.7485 0.23 0.2810 20 011 22 -18.5485 0.167 0.2312 25 0



Question

Compare your predictions (based on the preliminary work) with the experimental results (indicate the differences). Discuss whether this is a “perfect” square wave.

The preliminaries gave peak voltage of 4 V, frequency of 2 kHz and magnitude of 2.55 V. But the experiment that we carried out in the lab gave the following results,

The time domain had a peak voltage of 4.32 V and frequency of 2.024 kHz. The frequency spectrum had a magnitudes of the square wave showed a

significant differences in magnitudes. But the trend was similar to the preliminaries.

It can be seen that the results of the two are not similar. This may be due to noise effect on the experimental equipment or miscalculations of the preliminaries.No, this is not a perfect square wave. Actually in reality it is impossible to generate a perfect square wave. This is because there are physical limitations to the device used to generate it. Examples of these limitations include resistance in the wiring used in the device’s circuitry which will delay the change in voltage levels.

Captured waveforms in Time and Frequency Domain:

Figure 4.1: Time Domain Waveform - Square Wave



Figure 4.2: Frequency Domain Signal

Conclusion:

In this laboratory exercise there were some differences in the theoretical values and experimental values but not in large scale which could have been caused by human errors in taking readings, setting up of equipment, procedures in adjusting the waveforms, malfunction of the equipment or cards slots where the Adder, Multiplier and Oscillator modules are seated. The difference in the amplitudes was mainly due the sensitivity of the knob of the DSO, but is very difficult to adjust the vertical parameters using the DSO knob in real life.

At the conclusion of the laboratory, our group gained a lot of knowledge on the different type of signals generated and also did gain experience on handling the equipment, notably the TIMS unit.


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TNE30003 Group 1 Lab1 Report1