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MULTIMEDIA UNIVERSITY FACULTY OF ENGINEERING LAB SHEET ELECTROMAGNETIC THEORY EMG2016 MW2 – IMPEDANCE MEASUREMENT AND MATCHING EM Theory Faculty of Engineering, Multimedia University 2 EXPERIMENT MW2: IMPEDANCE MEASUREMENT AND MATCHING OBJECTIVES: a) To measure the normalized impedance of an unknown load. b) To perform impedance matching using a slide-screw tuner and Smith Chart. APPARATUS: Klystron Source Klystron Power Supply Isolator Slotted-line probe detector SWR measurement amplifier/meter Slide-Screw Tuner Attenuator Short-circuit Plate x 2 BNC coax cable x 1 Spanner INTRODUCTION: The ratio between the electric and the magnetic fields at a particular point along a waveguide is defined as the impedance at that point. It may be denoted as Z = E / H = R + jX. If there is no reflected wave, this ratio is the same at all points along the line. The standing wave ratio (SWR) will be unity. In this case, the load absorbs all the incident energy and is said to be matched to the characteristic impedance Zo of the waveguide. If a reflected wave is present, causing a standing wave, then the impedance will vary periodically with distance along the transmission path. It is therefore necessary to specify the plane to which the impedance is defined when measuring an unknown impedance. It can be shown that the relationship between SWR, reflection coefficient , and the impedance Z at any point on the line be given by Z - Zo = Z + Zo 1 + SWR = 1 = Z / Zo 2 EM Theory Faculty of Engineering, Multimedia University 3 Smith Chart (see Appendix A) is usually used to analyze the values of R and X at any distance along the transmission line. On Smith Chart, impedance values are normalized with respect to the characteristic impedance Zo. Complete circles in the chart are curves of constant resistance R/Zo. Incomplete circles which are at right angles to the complete circles are curves of constant reactance jX/Zo. Thus, every point in the chart specifies a normalized impedance Z/Zo=(R+jX)/Zo. The impedances at various points along the waveguide lie on a circle with its centre at the centre of the Smith Chart. This circle is often called the circle of constant mismatch (or the SWR circle). When the load is equal to Zo, there is no mismatch and the radius of the SWR circle will be zero. The impedances at various distances from a point (where the impedance is known) can be established by moving around the SWR circle through the appropriate angles. The point where the SWR circle crosses the horizontal axis on the right-side of Smith Chart (i.e. R/Zo + j0) corresponds to a point of maximum electric field in the standing wave pattern. It also gives the VSWR, since at this point the normalized resistance value is equal to the VSWR (i.e. R/Zo = VSWR). The point at the opposite end of the horizontal diameter (on the left-side of Smith Chart) corresponds to a point of minimum electric field and has impedance Z = (1/VSWR) + j0. To measure an unknown impedance, the SWR (=So) of the device connected to a slotted-line waveguide and the position of one minimal point xo is determined (see Fig-1). A circle corresponds to R+j0 where R=So is drawn on the Smith Chart. After that, the unknown device is substituted by a short circuit plate. Two successive minimum points, x1 and x2, are noted. Twice the distance between them is the guide wavelength g. One of the minimum points is used as reference. Let d = (xo - x1) / g. The impedance at the input terminal of the unknown device can be found on the constant mismatch circle at a distance d from the point of minimum electric field towards load if d 0; otherwise towards generator. It should be noted that the impedance along the line is equal to the load impedance at any integral number of half-wavelengths from the load. Plane of load Emax2 minimum with load, Emin2 g / 2 xo d x2 x1 Fig 1 : Illustration to Impedance Measurement. 3 EM Theory Faculty of Engineering, Multimedia University 4 When the load doesn’t match with the transmission line impedance, the reflected energy is usually lost as heat and, in some cases, may destroy the source amplifier. It may also cause a wide variation in performance when the condition is disturbed by, for example, temperature change or signal frequency drift. Therefore, it is usually desirable that the load accepts all the RF energy or additional impedance matching network can be incorporated to the line in order to minimize the amount of energy reflected to the generator. In the case of waveguide, a slide-screw tuner which consists of a slotted waveguide section and a movable metal rod penetrating through the slot can be used for this purpose. A variable capacitive susceptance is introduced in parallel to the transmission line by varying the tuner’s protrusion depth. A convenient feature of Smith Chart is that, if the normalized impedance is represented by one point Z, then the normalized admittance (reciprocal of impedance) is found by simply moving to the opposite end of the diameter through Z on the constant mismatch circle. The admittance Y = G + jB changes along the waveguide according to the values represented by the circle. A point Y1 can be found where the conductance G is equal to the characteristic admittance Yo. If the susceptance at this point has a negative value (ie. -jB), a slide-screw tuner can be used to add a susceptance +jB in parallel with Y so that the combined susceptance will be zero and the resulting admittance Y’ will simply become Yo. There may be a standing wave in the waveguide section between the tuner and the load but, as far as the source generator is concerned, no part of the incident wave is reflected. 4 EM Theory Faculty of Engineering, Multimedia University 5 PREPARATION Conduct background study about the experiment, e.g. read the lab sheet. Bring log book for recording observations and results. Bring scientific calculator. Bring Smith Charts. Bring a pair of compasses. PROCEDURE: CAUTION 1: The RF power levels in the following experiments are not harmful, but a human eye may be damaged by low level of radiation. DO NOT LOOK INTO THE WAVEGUIDE at any time when the equipment is on. CAUTION 2: Klystron tube gets extremely HOT when it is operated and must not be handled by hand. A. Initial Setup (30 minutes) The experimental setup (see Fig. 2) is similar to the source-transmission line-load setup used in MW1. The difference being a slide-screw tuner is inserted in between the transmission line and the load. The slide-screw tuner allows a metal rod to protrude into the waveguide introducing a shunt capacitance at the point of protrusion. The shunt capacitance introduced is proportional to the depth of protrusion. It is used to perform impedance matching in this experiment. As in MW1, the SWR meter used in the setup is a power meter with SWR scales on it and it has a built-in variable gain amplifier. Power increases from the left to the right side of the scales. A primary objective of this initial setup is to tune the components for maximum signal strength at the SWR meter. This includes tuning the Klystron source’s repeller voltage for maximum output power, the tuning gear and the source’s modulation frequency and amplitude for maximum reception at the SWR meter. 1. Set up the equipment as shown in Fig 2. (already done by the lab technician but do verify). Caution: Make sure the SWR meter input setting is ‘XTAL LOW’. Klystron Source Klystron Power Supply Isolator Slotted-line Detector Slide-screw Tuner SWR Meter Fig 2: Experiment Setup 5 Attenuator EM Theory Faculty of Engineering, Multimedia University 6 2. Set the slotted-line probe’s depth to 0.5 mm. (preset by the lab technician) 3. Set the attenuator to >2.8mm (> 20 dB return loss). 4. Make sure that the SWR meter is in the normal deflection mode (set by the smaller dial at and on top of the range-gain knob). 5. Make sure that the tuning screw of the slide-screw tuner is totally out of the waveguide (micrometer setting < 0). 6. Switch on the Klystron power supply (with internal modulation active) and the SWR meter. 7. Adjust the SWR meter’s gain until a significant deflection appears on the meter. 8. Adjust the repeller voltage knob for maximum reception at the SWR meter*. 9. Adjust the tuning gear of the slotted-line probe for maximum reception at the SWR meter*. 10. Adjust the modulation frequency and amplitude for maximum reception at the SWR meter*. 11. At this stage, the SWR meter should give good deflection at gain settings of 30 to 40 dB. If necessary, increase the slotted-line probe’s depth to achieve the stated condition. Make sure that a full deflection can be obtained by adjusting the vernier gain knob. * As one is tuning towards the maximum, the SWR meter will indicate that power is increasing. As one’s tuning reaches the maximum and then moves away from the maximum, the SWR meter will indicate that power reaches a maximum and then decreases. Adjust the SWR meter’s gain if necessary to have a decent deflection on the meter and to avoid overdriving the meter. Note: Do not disturb the repeller voltage, slotted-line probe’s depth, and tuning gear beyond this point. Else, you might have to repeat the above. For slotted-line measurements below, make your measurements at the central part of the waveguide; avoid the two ends of the waveguide. All measurement readings have to be in the correct precision. Please make it a habit. Make your own tables of observations. Make it a habit too. Evaluation A: (cognitive – knowledge, level 1) [10 marks] i. Please make sure you know all components of the setup and their functions. You may consult the lab instructor if necessary. ii. Request for evaluation when you are ready. 6 EM Theory Faculty of Engineering, Multimedia University 7 B. Determine the Normalised Load Impedance (50 minutes) 12. Replace the load (attenuator and short-circuit) by a short circuit plate. You need spanners; borrow them from the lab technician. Do not turn off the Klystron Power Supply. Do not look into the waveguide. Do not lose the screws. 13. Move the slotted-line probe along the waveguide to locate two successive points of minimum power. Record the positions of these two points, x1 and x2. Determine the waveguide wavelength g . 14. Restore the load. Do not turn off the Klystron Power Supply. Do not look into the waveguide. Make sure the joints are tight, e.g. cannot be displaced by hand. 15. Set the attenuator to 1.1 mm (about 6 dB return loss). 16. Move the detector probe along the waveguide to locate the point of maximum power. Henceforth, for convenience, it will be referred to as the maximum point (or minimum point for minimum power). 17. Adjust the gain of the SWR meter so that its reading is 0 dB on the bottom scale (i.e. full scale deflection). Do not overdrive the SWR meter. 18. Move the probe to locate a minimum point (any minimum point). Record its position, x0 . Read and record the SWR from the SWR meter**. ** There are 5 scales on the SWR meter. From the top, the first two are meant for the expand mode (not used). Third and fourth are linear scales. The third scale is used when the maximum and minimum are observed using the same range-gain. The fourth scale is used when the minimum is observed using a range-gain 10dB higher than that of the maximum. The fifth scale is a log scale (dB). Difference in range-gain between the maximum and minimum should be added to the reading on the log scale to obtain the SWR in dB. 19. – (it means skip this line) 20. Calculate d = (x0 – x1) / g . 21. On the Smith Chart, locate the resistance grid having a value equal to the recorded SWR. Locate the intersection between this resistance grid and the horizontal line in the middle of the Smith Chart. See Appendix A. 22. Using a pair of compasses, draw a circle that goes around the center of the Smith Chart and passes through the intersection point of step 21. It is the circle of constant mismatch, also known as the SWR circle. See Appendix A. 23. On the Smith Chart, locate the short circuit point zsc = 0 + j0. Starting from the short circuit point, move around the ‘toward load’ scale to locate the distance d if d > 0 (hereafter known as point E); use the ‘toward generator’ scale for d < 0. See Appendix A. 24. Draw a straight line that passes through point E and the centre of the Smith Chart, and crosses all the circles. There are two intersections between this line and the SWR circle. The normalized load impedance zL is given by the intersection nearest to point E. The farther intersection gives the normalized load admittance yL. With the aid of the resistance/conductance grids and reactance/susceptance grids, read zL and yL. See Appendix A and B. 7 EM Theory Faculty of Engineering, Multimedia University 8 Evaluation B: (psychomotor – complex overt response, level 5) [30 marks] i. Tabulate your measurements and draw on the Smith chart. ii. Be ready to demonstrate how the measurements were done. iii. Request for evaluation when you are ready. C. Impedance Matching Using Smith Chart (20 minutes) 25. The line drawn in step 24 also makes two intersections with the ‘toward generator’ scale. Record the distance d1 on the ‘toward generator’ scale (irrespective of the sign of d) for the farther intersection. See Appendix B. 26. Determine the point y1 where the SWR circle intersects the unity constant resistance circle. There are two intersections; use the one with negative susceptance. Draw a line from the center of the Smith Chart, through y1, to the outer most circle. The line will intersect the ‘toward generator’ scale. Record the distance d2 on the ‘toward generator’ scale at the intersection point. See Appendix A and B. 27. Calculate d = (d2 - d1)g d is the distance from the load terminal towards generator where the input conductance G will be equal to the characteristic admittance Yo. Evaluation C: (cognitive – application, level 3) [20 marks] i. Draw on the Smith chart. ii. Request for evaluation when you are ready. D. Verify and Fine Tune Impedance Matching Conditions (60 minutes) 28. The slide-screw tuner (hereafter referred to as tuner) acts as a variable shunt capacitor. For impedance matching, it should be placed d from the load terminal. Note that d is measured from the load towards generator. d computed from step 27 may not give a practical position to insert a tuning screw. In that case, add an integral number of half-wavelengths (ng/2) to d in order to determine a practical position to insert a tuning screw. Record the distance Do = d + ng/2 from the load, where the tuning screw is to be inserted. 29. Position the tuner at distance Do from the load terminal. The distance between the load terminal and the beginning of the vernier scale on the tuner is 50 mm. 30. Measure the SWR before impedance matching (see step 16. to 18. ). Henceforth, it will be referred to as the initial SWR. 31. Increase the tuner (not slotted-line probe!) protrusion depth slowly until there is a noticeable change in the meter reading. Re-measure the SWR at this point. 32. If the new SWR is less than the initial SWR, proceed to step 33. Otherwise, there were errors in impedance matching calculations and Do is not correct. Move the tuner to the left or right (choose a direction with ample movement space) by 1 mm. Remeasure the SWR. Repeat the 1 mm movement and re-measure the SWR of course, until the SWR is noticeably less than the initial SWR. 33. At this point, you should have a new SWR less than the initial SWR. 8 EM Theory Faculty of Engineering, Multimedia University 9 34. Increase the tuner protrusion depth slowly until there is a noticeable change in the meter reading. Re-measure the SWR at this point. 35. Repeat step 34. until the new SWR is more than the previous one. You have just missed the optimum protrusion depth giving minimum SWR. 36. Fine tune the protrusion depth to locate the point of minimum SWR. 37. If the new SWR is less than 1.1, proceed to step 39. Otherwise, further fine tuning is required. With the protrusion depth intact, move the tuner to the left or right by 1 mm Use a smaller movement value (this requires heuristic judgments) if you are close to SWR 1.1. Re-measure the SWR. If the new SWR is more than the previous one, very likely the movement direction is wrong, try moving in the opposite direction and remeasure the SWR. Repeat the process until you have the optimum tuner position giving minimum SWR. 38. Repeat steps 36. and 37. until you have the SWR less than 1.1.*** 39. Record the final SWR = S1 achieved, the position D1 of the tuner, and the protrusion depth p. *** Note that, for simplicity, the above tuning procedure assumes that independent tuning of tuner position and protrusion depth will converge to the optimum point. From previous experience, it is generally true, but not always true. In the case that it is not true, one has to find the optimum depth for each tuner position in order to locate the optimum tuner position. Evaluation D: (psychomotor – adaptation, level 6) [40 marks] i. Tabulate your results. ii. Be ready to demonstrate the impedance matched state. iii. Request for evaluation when you are ready. 9 EM Theory Faculty of Engineering, Multimedia University 10 APPENDIX A toward generator scale (23) reactance/susceptance grids (24) SWR circle (22) unity constant resistance/conductance circle centre 0 + j0 (23) SWR (21) resistance/conductance grids (21,24) Intersections with the unity circle toward load scale (23) http://www.sss-mag.com/pdf/smithchart.pdf 10 EM Theory Faculty of Engineering, Multimedia University 11 APPENDIX B SWR circle (22) d1 (25) yL (24) d zL (24) E (23) y1 (26) d2 – d1 (27) d2 (26) http://www.sss-mag.com/pdf/smithchart.pdf 11 EM Theory Faculty of Engineering, Multimedia University http://www.sss-mag.com/pdf/smithchart.pdf 12 12 EM Theory Faculty of Engineering, Multimedia University http://www.sss-mag.com/pdf/smithchart.pdf 13 13