LABORATORY EXPERIMENT #1
THE OSCILLOSCOPE

ABSTRACT
The purpose of this lab was to become familiar with the EE 390 communication laboratory equipment available in the lab, particularly the Agilent 54621A digital oscilloscope. In this lab, electrical signals were measured using the oscilloscope in both time domain and frequency domain. Two electrical signals were displayed- a 1 kHz, 2.78VPP as well as a 2 kHz, 278mVPP. In this lab, methods of improving measurement accuracy, dealing with floor noise and averaging were all explored. Overall this lab was a useful tool in understanding the lab equipment.

RESULTS AND DISCUSSION:
PART 1 - QUESTION 1
i) A 1 kHz, 2.78 VPP sinusoid wave is displayed with trigger level at 200 mV (rising edge). See Fig.1

Fig.1: Time Domain Representation of Signal
Power dissipated in the load:
P_load=〖V_rms〗^2/R , where V_rms=V_amp/√2 and V_amp=V_PP/2
So, V_amp=(2.78 "V" )/2=1.39 "V" and V_rms=(1.39 "V" )/√2=0.9829 "V"
Hence, P_load=((〖0.9829 "V" )〗^2)/(50 "Ω" )=19.32 "mW"

ii) When we set the triggering level to 1.5V, the resulting signal displayed is an unstable one. The reason for this is because the trigger level must be on the rising or falling edge. iii) A 1 kHz, 2.78 VPP sinusoid wave is displayed and the accuracy of the measurement is calculated. The volts/division is equal to 500 mV. See Fig.2

Fig.2: Accuracy of Time Domain Representation of Signal error = 2% Vfs , where Vfs= (number of spaces) x (volts/division)
So, Vfs = 8 x 500 mV = 4 V
Hence, error = 2% x 4 V = 80 mV
Thus, Accuracy = 2.78±0.08VPP

iv) The embedded functions on the oscilloscope are explored to improve the quality of the measurement. One of these functions was to use the ‘fine’ volts/Div to display the signal across the entire screen of the oscilloscope. As a result a more accurate measurement can be made. See Fig.3

Fig. 3: Higher Accuracy Waveform
We can calculate the accuracy of this waveform to confirm improvement in our result. error = 2% Vfs , where Vfs= (number of spaces) x (volts/divison)
So, Vfs = 8 x 348 mV = 2.784 V hence, error = 2% x 4 V = 55.68 mV
Thus, Accuracy = 2.78±0.06VPP
Here, we can see that our accuracy improved from 2.78±0.08VPP to 2.78±0.06VPP, a 25% improvement in the error.
Other methods for improving the quality of the measurement are to use ‘averaging’ and ‘bandwidth’. Both methods help to enhance the quality of the received signal by averaging and by reducing the noise via noise rejection, high frequency rejection. Hence, a clearer and sharper sinusoidal waveform is displayed. See Fig. 4 and Fig. 5

Fig.4: Enhanced Representation of Signal using ‘Averaging’

Fig.5: Enhance Representation of Signal using ‘Bandwidth’
v) A 2 kHz, 2.78 mVPP sinusoid wave is displayed with trigger level at 20.00 mV (rising edge). To get the display we first attenuated the signal by setting attenuator to 40dB scale. See Fig.6

Fig.6: Time Domain Representation of Attenuated non-enhanced Signal (noisy)
The embedded functions of the oscilloscope, such as ‘averaging’, ‘high frequency rejection’, and noise rejection, are used to clean up and enhance the quality of the signal. See Fig. 7

Fig7: Time Domain Representation of enhanced Attenuated Signal (de-noised)
PART 2 - QUESTION 2
i) A 1 kHz, 2.78 VPP sinusoid wave is displayed and the ‘Math’ function is explored.
a) For amplitude we are using the magnitude cursor and to measure frequency we are using the time cursor. See Fig.8

Fig.8: Frequency Domain Representation of Signal
Frequency domain power:
Power[dBm] = 10*log⁡[(RMS Magnitude of Sinusoidal Component)^2 ]+13 = Display Reading [V_(RMS,dB) ]+13dB=64.0 dB+13 dB=77 dB
Time domain power:
P(dBm)=x^dB+13.01 dB= -190 mdB+13.01 dB=12.82 dB
P=〖10〗^((P(dBm)/10))= 〖10〗^((12.82/10))=19.14 mW

The percentage difference between the time domain and the frequency domain is:
"% difference"=(19.32 "mW " -19.14 "mW" )/19.32" mW" ×100%=0.932%
The percentage difference between power in time domain to power in frequency domain is 0.932%.

b) Using the cursor, the noise floor is found, which is used to calculate the signal to noise ratio (SNR).
i) Noise floor using averaging:

Fig.9: Noise Floor using Averaging
Noise floor = -64.2 dB, SNR = (- 190 mdB)/(-64.2 dB)= 0.00296 ii) Noise floor using averaging with 4 samples:

Fig.10: Noise Floor using Averaging with 4 samples

With 4 sample averaging: Noise floor = -65.0 dB, SNR = (- 190 mdB)/(-65.0 dB)=0.002923 iii) Noise floor using averaging with 16 samples: Fig.11: Noise Floor using Averaging with 16 samples
With 16 sample averaging: Noise floor = -65.8 dB, SNR = (- 190 mdB)/(-65.8 dB)=0.002888 iv) Noise floor using averaging with 64 samples:

Fig.12: Noise Floor using Averaging with 64 samples
With 64 sample averaging: Noise floor = -65.8 dB, SNR = (- 190 mdB)/(-65.8 dB)= 0.002888
After averaging with 16 samples there is not a significant change in the noise signal. Any amount of averaging will not have a significant improvement on the SNR for small signals.

PART 3 - QUESTION 3

a) When the vertical scale is set too low in the time domain the signal magnitude is not being properly captured and is extending past the display. This is causing incorrect readings on the scope. In the frequency domain this has caused an improper display of the frequency domain (something similar to the sinc function) and is also showing incorrect reading on the scope.

Fig.13: Frequency Representation (20mV/div) Time Domain

Fig.14: Frequency Representation (20mV/div) Frequency Domain

PART 4 - QUESTION 4

Fig.15: Pseudo Random Binary Sequence (PRBS)
a) The signal bit rate is 40 kHz and the period is 25×〖10〗^(-6) s.
b) These values are the result of the function generator as the function generator is sending the sync pulse to the bit generator and with each pulse the function generator is sending another 5 random bits.

Evaluating the lab, it was found that we obtained a useful insight of the equipment that was available. It offered a detailed summary of how to measure signals in the time and frequency domains. Also it showed how it is easy to describe and display signals by attenuation and comparing them in the time domain. Measurements that were taken throughout the lab, both in the frequency and time domains agrees within error as expected. At this time there are no recommendations as to how to improve the lab since it was simply an introductory lab on how to use the equipment.

CONCLUSION:
As expected we were able to gain valuable experience in the lab which guided us on how to use the equipment available. We conclude that the lab was a success since all the measurements were taken without significant difficulty. The Power in time domain was 19.32 mW and in frequency domain was 19.14 mw, a difference of 0.932%. The accuracy was improved using embedded functions of the oscilloscope from 2.78±0.08VPP to 2.78±0.06VPP, a 25% improvement in the error. The signal to noise ratio using averaging was 0.00296. This was further improved to 0.002888 using averaging with more samples (64 samples). Finally, the signal bit rate was found to be 40kHz and the period was 25 µs.