MARMARA UNIVERSITY

FACULTY OF ENGINEERING

ELECTRICAL & ELECTRONICS ENGINEERING DEPARTMENT

EE 555

ELECTRONICS LABORATORY

EXPERIMENT REPORT 2

OSCILLOSCOPE AND FUNCTION GENERATOR

Author : F.Kemal BAYAT 009885006 Experiment Partners : F.Kemal BAYAT 009885006 & Kemal BAYAT 009885006 Experiment Date : 10th October, 2011 Submission Date : 17th October, 2011

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INTRODUCTION

-Objectives of this experiment are to learn and practice fundamental measurement equipments (oscilloscope and function generator), as well as to observe limitations of these devices.

DEVICES & EQUIPMENTS - Tektronix Digital Oscilloscope - Function Generator - Capacitors (10nF and 30nF) - Resistor (4.7kΩ)

- Breadboard - Multimeter

METHODS

- To Measure phase difference between two waves with same frequency; one method is to read the time value between them. Reading time value gives chance to calculate corresponding phase angle in degrees. For this method,

read time / period = phase shift / 360° ratio is available.

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- Another way for determining phase difference is the employment of Lissajous curves. Lissajous curves are actually the x-y plots of our two waves with same frequency that we wish to measure phase difference between them. In the figure shown above there is a diagram in which a list of lissajous curves to determine phase shift variations of two signals with same frequency.

Moreover, Lissajous curves seem more advantageous because they are also employed for identification of frequency variations of the signals compared.

- To determine bandwidth of an oscilloscope, upper (high) and lower (low) cut-off frequencies must be observed or calculated. These frequencies are observed when the magnitude of the signal decreases its 70.7% value. This decrease corresponds to -3dB in logarithmic plots. After high and low cut-off frequencies are determined bandwidth can be calculated as follows:

As we know from practice, fup >> flow and this gives us the approximation below to find bandwidth.

- It is possible to determine input capacitance value of an oscilloscope using bandwidth, as long as R is known.

- Another way to calculate input capacitance value of an oscilloscope is to employ square wave signal instead of sinusoidal signal. By this way, display of square wave in AC coupling provides the response of an RC network. From this response, rise time (or fall time) to 90% of the amplitude gives time constant. It should be noted that the charge and discharge responses of an

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RC network is an exponential function. By using the following formula, together with the known value of R, and observed waveform from oscilloscope, C can be calculated.

PROCEDURE & RESULTS a) A 1kHz, 250mVp-p sinusoidal signal is generated with function generator. Adjusted oscilloscope settings are: Volt/div = 50mV/div, time/div = 200us. Sketch of the waveform:

Fig.1

b) To have two signals with phase difference between them, we used an RC network, in other words we exploited the phase shifting feature of capacitors. We experienced two circuits; first with 4.7kΩ - 10 nF and second with 4.7kΩ - 30 nF. To obtain 30nF capacitor we connected three 10nF capacitors in parallel. For our first try with 4.7kΩ resistor and 10nF capacitor, we observed the phase shift both by observing two signals on the same display and by using lissajous curves - namely x-y plot. We sketched what we observed as below.

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Fig.2 Fig.3

From Fig.2 there is approximately 45us phase difference between two signals. This corresponds to 16.2°. Also from Fig.3; B/A ratio is approximately equals to 0.28 radians. Converting radians to degrees gives us 16.051° as a result. For second, with 4.7kΩ resistor and 30nF capacitor, we observed the phase shift both by observing two signals on the same display and by using lissajous curves - namely x-y plot. We sketched what we observed as below.

Fig.4 Fig.5

From Fig.4 there is approximately 120us phase difference between two signals. This corresponds to 43.2°. Also from Fig.5; B/A ratio is approximately equals to 0.7 radians. Converting radians to degrees gives us 40.13° as a result.

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c) Yes, the oscilloscope that we used in the experiment has a storage mode. By using this mode, we observed two different frequency signals on the same display. First one is the sinusoidal waveform of 1kHz, 250mVp-p that we used in part(a). We saved this signal and decreased the frequency to obtain a second signal. Thus, as the second signal we used 250 Hz, 250mVp-p signal. Using our saved waveform and our new waveform, we observed and sketched them together on the same display. Adjusted oscilloscope settings are: Volt/div = 50mV/div, time/div = 500us.

Fig.6

d) External triggering mode of the oscilloscope is used for synchronizing the voltage that we aim to observe - with another or external pulse source. *** e) Maximum amplitude of the 1kHz sinusoidal wave that we generated is 20Vp-p. f) The ‘duty-cycle’ control of function generator is used for creating pulse width modulation (PWM) signals. PWM signals determines how long the pulse will be ‘on’ state - in other words, by ‘duty-cycle’ control we can generate square wavs with different positive and negative (or zero) durations. g) We measured our 1kHz, 20Vp-p sinusoidal waveform with multimeter and we read 7.071V in rms. We changed sinusoidal to square wave - measured again with the multimeter and we read 10V in rms. According to the root mean square definition, a square wave’s rms value equals its peak value and a sinusoidal wave’s rms value equals the multiplication of its peak value by 1/sqrt(2). Thus, our measurements with multimeter are in conformity with the analytical calculations. h) We can depend on the function generator’s frequency settings if the function generator does not have any calibration troubles. In general, function generators produce regular and simple repeating waveforms. Thus we use these waveforms produced by the function generator as reference signals when observing complex signals.

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i) Our function generator has an offset adjustment selection. This mode allows adding positive or negative DC components into the signal. j) To find the iner resistance of the oscilloscope, we used 5V-dc from DC power supply and connected it directly to the oscilloscope with an ampermeter between them. We measured approximately 5.04 uA and by calculation we found the internal resistance of the oscilloscope about 992kΩ = 1MΩ. k) Oscilloscope’s bandwidth is the frequency at which a sinusoidal input signal is attenuated to 70% of the signal’s true amplitude, namely the –3 dB point, a term that equals on a logarithmic scale. To determine the bandwidth of our oscilloscope, we increased frequency of the waveform and after MHz range amplitude began to decrease. Amplitude of the voltage signal that we applied only decreased to its 85% value at the maximum frequency level (~2300 kHz) of the function generator as shown in Fig.7. This level does not provide the required -3dB value decrease, therefore we were not able to determine upper cut-off frequency of the oscilloscope.

Fig.7 As a second step, we decreased the frequency of the applied voltage signal to 5 Hz. In this frequency we observed 3dB of 30% decrease of the amplitude. We recorded this observation as indicated on Fig.8. As a result, we could determine 5 Hz as the lower cut-off frequency of the oscilloscope. fup = more than 2300 kHz flow= 5 Hz bandwidth = fup - flow ~= fup Consequently, we do not have required information to calculate the bandwidth of the oscilloscope.

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Fig.8

l) We repeated the above process with same frequencies, but this time we used square-wave instead of sine-wave. For maximum frequency (~2300 kHz) of the function generator could deliver, we recorded the waveform in Fig.9. For 5 Hz frequency - that we determined as the lower cut-off frequency - we recorded the waveform in Fig.10.

Fig.9

As mentioned in the k’th step, we could not observe the upper cut-off frequency. However, when square wave is applied in AC coupling - at the lower cut-off frequency (5 Hz) - obtained waveform is a RC network response. This provides us to calculate input capacitance of the oscilloscope in the following step.

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Fig.10 m) In order to cancel out DC component or bias/offset of the signals input of AC coupling includes a capacitor to display signals in AC mode. As it can be seen from Fig.10, at the lower cut-off frequency value determined in k’th step, square-wave began to behave like series RC network response. In this last step we employed this result to determine input capacitance of the oscilloscope. By using the formula below; input resistance (992kΩ) of the oscilloscope is calculated in previous steps and rise time (tr) from Fig.10 is approximately 50ms - we calculated the capacitor value as = 22.94 nF

In the equation above, rise time (tr) corresponds to the linear rising period of the exponential curve and this linear rising period is approximately between 10% and 90% of its amplitude. So, the equation above means the rise time takes 2.197xRC period where RC is time constant. Another way to calculate capacitance using time constant is to accept the period for full charge or discharge takes 5xRC duration as a rule of thumb. Therefore, if we accept the fully discharge period as 120ms; RC (time constant) equals to 24 ms. Thus, C = 24.19 nF. To sum up, 22.94nF and 24.19nF values of capacitor closely approximate with each other.

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DISCUSSIONS In this experiment, we practiced main displaying options, particular features, and important limitations of oscilloscope and function generator. We displayed two signals on x-y plot to observe phase difference of two signals. To observe signals with different frequencies, we used storage mode of the oscilloscope. Also, we examined different triggering modes of the oscilloscope. We calculated the inner resistance of the oscilloscope as well as AC coupling input capacitance. To find capacitance value of AC coupling we tried to determine bandwidth of the oscilloscope, but we could not due to thr frequency limit of the function generator. We employed square-wave testing and with the use of RC network analysis found the AC coupling input capacitance value. From the function generator side; we observed and recorded maximum voltage and frequency outputs. Furthermore, we practiced and observed ‘duty-cycle’ or PWM providing feature of the signal generator as well as its offset manipulation feature. REFERENCES 1. Boylestad & Nashelsky, Electronic Device and Circuit Theory, 2006 2. TL071 datasheet 3. Wikipedia, “Bandwidth”, “Lissajous curve”, “Rise time” 4. NI, Labview Basics 1 – Introduction, Course Manual 5. NI, Labview Basics 2 – Development, Course Manual