ECE331_lab2_Melinda_Van

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ECE 331 LAB 2: TIME DOMAIN REFLECTOMETRY Name: Melinda Van Lab Partners: Yebin Woo Garrett Smith Lab TA: Justin Bell Date: Oct 31, 2016

3.1 Relative Dielectric Constant Objectives: Time Domain Reflectometry is utilized to determine the relative dielectric constant ࠵? " of a short length of cable. Set up: One end of a SMA-SMA cable was connected to the one of the channels in of the 80E04 Sampling Module, and the other was left floating. Theory: The signal generated from the TDR was sent to the input port of the cable which was the end connected to the 80E04 and then it was delivered to the load at the output end of the cable which was left open in this experiment. As the signal travelled to the load and reflected back to the source, the TDR was able to capture the events happening inside the cable and display the voltage waveform which showed the time delay ( ∆࠵?) between the incident and the reflected edge. The time delay collected from the voltage waveform and the length of the cable ( ࠵? ) were then used to determine the propagation velocity ( ࠵? ( ) that was further used to compute the relative dielectric constant. Equations: ∆࠵? = 2࠵? ࠵? ( ⟹ ࠵? ( = 2࠵? ∆࠵? ࠵? ( = ࠵? ࠵? " = 2࠵? ∆࠵? ⟹ ࠵? " = ࠵?∆࠵? 2࠵? . Collected data: ∆࠵? = 8.32࠵?࠵? and ࠵? = 90࠵?࠵? ⟹ ࠵? " = (8×:; < =/?)×(@.8.A?) .×(;.B;=) . = 1.9

Images: Discussion: The calculated relative dielectric was in the accepted range 1.5-2. 3.2 Identifying Transmission Discontinuities Objectives: The nature of different transmission line discontinuities was identified by using TDR. Set up: The setup was the same as in Experiment 3.1, yet the open end this time was connected to each of the output ports, A – G, of the TDR Measurement Board. Theory: The waveform displayed on the TDR was composed of the incident and reflection wave of the signal. Since reflections were due to trace width, direction changes and components, faults, or shorts and opens, a nature of a discontinuity could be identified by observing the voltage and Figure 1:TDR waveform of the SMA cable with an open end, and the two vertical red lines indicated the time delay of the signal.

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measuring the voltage reflection coefficient ( Γ) directly on the TDR screen in order to calculate the load impedance. Equations: Γ = ࠵? F − ࠵? H ࠵? F + ࠵? H (࠵? H = 50Ω) Collected Data: Table 1: Collected data from port A to port G of the TDR measurement board Voltage Coefficient ( Γ) Load impedance ( ࠵? F ) ( Ω ) Types of discontinuity Port A .973 3654 Open Port B -.973 .684 Short Port C -.351 24.0 Unmatched Resistor Port D 0 50 Match Port E .324 97.9 Unmatched Resistor Port F -.973 .684 Inductor Port G .189 73.3 Capacitor Images: Figure 2: Voltage waveform of port A ( ࠵? represents voltage reflection coefficient on TDR)

Figure 3: Voltage waveform of port B. Figure 4: Voltage waveform of port C. Figure 5: Voltage waveform of port D. Figure 6: Voltage waveform of port E Figure 7: Voltage waveform of port F Figure 8: Voltage waveform of port G

Discussion: Since the cable and the TDR measurement board did not have high quality and might be broken down inside, the voltage coefficient was not perfect as predicted for the short and open port which were -1 and 1 respectively. However, the values could be considered to be in an expectable range and so were the load impedance. In spite of some noise present in between the transmission line, for the next 4 ports, port C to port E, the load impedance values were very close to the values shown in the board. The impedance of port C and D were exactly the same as the actual values whereas it was only .3 Ω off to the actual resistance at port D. In case of port G, the circuit inside the board was broken, so the waveform did not look like the predicted one. 3.3 Mystery Box Objectives: The purpose of this experiment is to determine and locate the discontinuity on a transmission line by observing the waveform on TDR only. Set up: The end of SMA cable was kept connecting to the Sampling Module while the other was connected to the port of the mystery box. Theory: The same theory mentioned in preceding experiments was also applied in this experiment. Equation: ࠵? ( = M N O and ∆࠵? = .P Q R

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Collected data: Table 2: Load impedance collected from various position. Impedance ( Ω ) Area 1 (Z 1 ) 59.7 Area 2 (Z 2 ) 27.4 Area 3 (Z 3 ) 28.9 Area 4 (Z 4 ) 50.7 Table 3: The time delay between two areas and the corresponding location of the impedance. Time delay (ps) Corresponding location (mm) Area 1 to Area 2 266 19.0 Area 2 to Area 3 140 10.0 Area 3 to Area 4 460 32.9 Images: Area 1 Area 2 Area 3 Area 4 Figure 9: The waveform observed from the Mystery box and the areas of the load impedance in interest.

Equivalent Simplified Transmission Line of the Mystery Box: Questions: 1. What is the propagation velocity of the SMA-SMA cable used in experiment 3.1? The propagation velocity of the cable is 2.13×10 @ m/s. 2. What are some possible causes of inaccuracy for the method used to calculate the value of the dielectric constant in experiment 3.1? There might be noise present inside the TDR that can affect the time delay shown on the waveform. The temperature in the lab room can decrease or increase the dielectric constant, and there is also an error in the meter used to measure the length of the cable. 3. Can you determine the characteristic impedance of each of the transmission lines on the TDR Demo Board? If so, what are they? The characteristic impedance of each transmission lines on the TDR Demo Board can be determined by manipulating the equation shown in Experiment 3.2 to solve for Z L using the voltage reflection coefficient collected from the TDR. Figure 10: Simplified transmission line circuit of the mystery box.

Γ = ࠵? F − ࠵? H ࠵? F + ࠵? H ⟹ ࠵? F = ࠵? H 1 − Γ 1 + Γ For instance, at port A, Γ = .973 , so ࠵? F = 50 :T.BU8 :V.BU8 = 3654Ω . 4. Where does the 2 come from in equation 8? The signal travels back and forth along the transmission line, so the length was multiplied by 2. 5. What determines the characteristic impedance of a transmission line? The characteristic impedance is determined by the square root of the ratio between the inductance per unit length and the capacitance per unit length. 6. What types of transmission line discontinuities are there and what does their corresponding waveform look like? The types of transmission line discontinuities are shorts and opens, inductive and capacitive discontinuities. For short circuits, since the entire pulse is reflected back with the opposite value which cancels out the incident pulse, the waveform has a small pulse at first and then stays at zero for the remaining time as shown in Figure 3. For open circuits, the entire voltage is also reflected back to the source with the same polarity, therefore, twice of the incident voltage appears across the output terminal as shown in Figure 2. For the inductive discontinuity, the waveform initially has an upward spike but then gradually decreases and eventually looks like the short circuit which can be seen in Figure 7. The waveform of the capacitive discontinuity, on the other hand, has a downward spike and gradually increases and eventually appears the same as an open circuit (since the last port was broken, the waveform of the capacitive discontinuity could not be obtained). 7. What are possible causes of faults along the transmission line? Possible causes of faults are open and short circuits, and mismatched load impedance. 8. What affects a TDRs resolution, accuracy, and measurement range?

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The pulse width of the step input can affect the TDR’s resolution. Notably, a narrow pulse offers a better resolution. However, if the frequency of a component used is high, the signal can be attenuated along the transmission lines impacting on the accuracy of the TDR. At different material of the medium, the sensor inside the TDR might not be able to adjust accordingly and the measurement range is likely to be inaccurate.