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# Hi ECET 3410

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This 6 page Class Notes was uploaded by Mrs. Maud Gutkowski on Tuesday October 20, 2015. The Class Notes belongs to ECET 3410 at Southern Polytechnic State University taught by Staff in Fall. Since its upload, it has received 15 views. For similar materials see /class/225439/ecet-3410-southern-polytechnic-state-university in ELECTRICAL AND COMPUTER ENGINEERING at Southern Polytechnic State University.

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Date Created: 10/20/15

ECET 3410 Hi h S stems Cha ters Four 4 Exam Problems Instructions This exam is closed book except for one 85 x11 sheet of handwritten notes as specified for exam 1 Coaxial Cables AWG Nom Nom Nom Nom Nom Attenuation Standard RG Mate al Insulation Shields Jacket OD Imp Vel Of Cap per 100 Spool inch Ohms Prop pF ft MHZ dB Lengths 20 Poly Black 0 100 30 100 14U copper ethylene 1 Vinyl 420 95 66 160 33 4613 500 20 Poly Black 0 100 35 100 14AU copper ethylene 1 Vinyl 420 92 66 160 33 33 500 18 calm poly Black 0 100 50 100500 16AU copper ethylene 1 Vinyl 195 50 78 A 30 8 33 35 1000 18 calm poly Black 0 100 40 100500 18U copper ethylene 1 Vinyl 280 75 78 A 24 33 3 1000 Problem 1 A 50 meter long lossy coaxial transmission line Z0 50 O y 0005 j002513 meter is connected to a 25j50 Q load and is supplied by an 828 kHZ rfsource Determine the input impedance ofthe line using a Smith Chart Note 7 if you are not able to determine the length of the line in wavelengths you may use the value 77 but points will be deducted from your score 25450 Z0 Ohms Z f 7265j165 i9 50 meters Problem 2 A 6 meter long lossy coaxial transmission line has the following characteristics Zo 75 O y 0037 jl365 Npm and radm respectively The line is connected to a 225j75 Q load and is supplied by an 43 MHZ rfsource Determine the input impedance of the line using a Smith Chart In Z0 225j75 Ohms Zn if 375j1275777 2 6 meters Problem 3 A 365 meter long lossy transmission line has the following characteristics Zo 759 y 00189 jl904 Npm and radm respectively The line is connected to a 150 Q load and is supplied by a 600 MHZ rfsource Determine the actual input impedance of the line You must use and completely LABEL the Smith Chart for your solution In Zo 150 Ohms 365 meters Problem 4 Multiple Choice Choose the best response to complete each statement If a Smith Chart to determine the input impedance of a transmissionline terminated with a known load OU N VVV 3 the solution will require a rotation around the Smith Chart in the clockwise direction the input impedance will be closer to the chart s center than the load impedance for a lossy line the plotted impedances must be normalized if the impedance value of the chart s origin center point is not equal to the line s characteristic impedance all ofthe above a c are correct none of the above ad are correct Given a transmissionline with known input impedance solving for the load impedance connected to the receivingend of the line requires a rotation on a Smith Chart a In the clockwise direction b In the counterclockwise direction c In a direction that is dependant on the initial input impedance value d That will reverse direction with every 12 wavelength traveled A lossless shortcircuited stub of length L a Can appear as an opencircuit at its input depending on the length L b Can appear as any desired inductance value at its input depending on the length L c Can appear as any desired capacitance value at its input depending on the length L d All of the above choices ac are correct e None of the above choices ad are correct Given a lossy transmission line a normalized loadimpedance s plotted position on a Smith Chart a Will be in the top half of the chart for a capacitive load b Would change is the line was actually lossless c Will be further from the origin than the position of the line s normalized input impedance d All of the above choices ac are correct e None of the above choices ad are correct Compared to s 1Awavelength tuner a singlestub tuner a Always utilizes standard transmissionline impedance values such as in table 13 of the teXt b Can be used to match a complex loadimpedance to a purely resistive source impedance c Will result in a better match for a purely real load to a purely real source impedance d All of the above choices ac are correct e None of the above choices ad are correct Problem 5 For each of the following specify whether or not each of the responses is true or false by writing i True i True either TRUE or FALSE in the blank preceding each response The magnitude of the re ection coe icient due to a load impedance on a transmissionline relates to the distance from the normalized load impedance to the center of the Smith Chart The circle that provides the outerboundary of the Smith Chart de nes a set of impedance points all of which have real values of zero purely imaginary impedances iFalsei The set of normalized load impedances formed by drawing a circle centered about the origin of a i True Smith Chart will all result in the same reflection coef cient on the transmissionline The set of normalized load impedances formed by drawing a circle centered about the origin of a Smith Chart will all result in the same VSWR on the transmissionline iFalsei The point with the largest impedance magnitude within a set of impedances de ned by a circle centered about the Smith Chart s origin will be the leftmost point on the circle iFalsei Adding 12 wavelength of line to a transmissionline terminated by a load will effectively cause an additional rotation of 12revolution during the solution of the problem on a Smith Chart Problem 6 For each of the following specify whether or not the statements are true by writing either TRUE or FALSE in CAPITAL LETTERS in the blank preceding each statement The set of normalized impedances de ned by a circle centered at the origin of a Smith Chart will all result in the same re ection coe icient on a given transmission line The set of normalized impedances de ned by a circle centered at the origin of a Smith Chart will all result in the same VSWR on a given transmission line i A rotation in the clockwise direction around a Smith Chart relates to a movement on a transmission line from a known impedance location towards the sending end of the line i 7 To account for losses on a transmission line when using a Smith Chart a change in the distance from the origin along with a rotation around the origin is required when solving for an unknown impedance either load or input impedance The impedances shown on the top half above but not including the horizontal aXis of a Smith Chart will all have an inductive reactance component 7 Given an impedance plotted on a Smith Chart the admittance value of the plotted impedance may be determined by drawing a circle centered at the origin that passes through the impedance point and then nding the point that is 180 from the plotted impedance around the circle ECET 3410 Hi h S stems Cha ters Five and Six 5 Exam Problems Instructions This exam is closed book except for one 85 x11 sheet of handwritten notes as specified for exam 1 Coaxial Cables AWG Nom Nom Nom Nom Nom Attenuation Standard RG Mate al Insulation Shields Jacket OD Imp Vel Of Cap per 100 Spool inch Ohms Prop pF ft MHZ dB Lengths 20 Poly Black 0 100 30 100 14U copper ethylene 1 Vinyl 420 95 66 160 33 4613 500 20 Poly Black 0 100 35 100 14AU copper ethylene 1 Vinyl 420 92 66 160 33 33 500 18 calm poly Black 0 100 50 100500 16AU copper ethylene 1 Vinyl 195 50 78 A 30 8 33 35 1000 18 calm poly Black 0 100 40 100500 18U copper ethylene 1 Vinyl 280 75 78 A 24 33 3 1000 Problem 1 A singlestub tuner consisting of an adjustablelength Z5509 main line connected in parallel with an adjustablelength Z5509 short circuited stub is used to match a load of 100j20 9 to a Z5509 transmission line Determine the lengths um and 1m in centimeters if the lines are air lled and the frequency of operation is 2 GHz Use the Smith Chart on the following page 3 Assume all transmission V lines segments have a characteristic impedance U U D llim 7 1995 cm 100 j20 Ohms lstub 7 72235 7 cm HEIDI V 39 Ihhe Problem 2 When an air lled slottedline is terminated with a shortcircuit voltage minima are measured at positions of 10cm and 25cm on the line When an unknown load is connected to the line the VSWR on the line is 24 and voltage minima are detected at 16cm and 31cm Determine the impedance value of the load in rectangular form the reflection coefficient of the load in polar form and the frequency of operation if the characteristic impedance of the line is 509 You must use and label the Smith Chart for the impedance and re ection coef cient answers Note that there is a second valid solution 2W 777825j4757779 I39R 7 70422397 7 f 77771G777Hz Problem 3 A 1 iwavelength tuner is used to match a load to a 1009 line If the characteristic impedance of the 1 iwavelength tuner is Z0t 509 the tuner line is Polyethylene lled 8 23 and the length of the tuner is 52 centimeters determine the load value and the operational frequency EIEIIZI 100 Ohms Zot 50 Ohms Load EIEIIZI Zload if 25 7 9 y f 77731777k lz 52 cm Problem 4 A singlestub tuner consisting of an adjustablelength Z5509 main line connected in parallel with an adjustablelength Z5509 short circuited stub is used to match a load of 120j120 9 to a Z5509 transmission line Determine the lengths lline and lstub in centimeters if the line is air lled and the frequency of operation is 24 GHz Use the Smith Chart on the following page Assume all transmission e y Short th39 lines segments have a characteristic impedance of 50 Ohms EIEIIZI lline 7 18757 7cm lsmb 7 7104 7 cm 120120 Ohms Note that there is a second valid solution El El III I V 39 lime Problem 5 When a slottedline is terminated with a shortcircuit voltage minima are measured at positions of 10cm and 35cm on the line When an unknown load is connected to the line the VSWR on the line is 2 and voltage minima are detected at 20cm and 45cm Determine the impedance value of the load in rectangular form the reflection coef cient of the load in polar form and the frequency of operation Assume that the characteristic impedance of the line is 50 9 You must use and label the Smith Chart for the impedance and re ection coef cient answers 2m 777775j347779 I R 7 70334397 7 f 777600M7777Hz Problem 6 A singlestub tuner consisting of an adjustablelength Z5509 main line connected in parallel with an adjustablelength Z5509 short circuited stub is used to match a load of 10j5 9 to a Z5509 transmission line Determine the lengths um and 1m in centimeters if the lines are RG l4U and the frequency of operation is 400 MHZ Use the Smith Chart on the following page 5 Short th Assume a transmission 9 lines segments have a characteristic impedance EIEIIZI Solution 1 Solution 2 1 45 0th 1quot 7722277 7417 cm a a D I L I lstub 74077 72077cm lime Problem 7 When an air lled slottedline is terminated with a shortcircuit voltage minima are measured at positions of 262cm and 449cm on the line When an unknown load is connected to the line the VSWR on the line is 3 and a voltage minimum is detected at 30cm on the same scale Determine the impedance value of the load in rectangular form the reflection coefficient of the load in polar form and the frequency of operation if the characteristic impedance of the line is 509 You must use and label the Smith Chart for the impedance and re ection cae icient answers ZLoad77725j317 7 79 FR 7054107 7 f 7777802M777E Problem 8 A 6 cm long piece of RG 16AU coaxial cable is used as a 1Awavelength tuner to match a load to a 6009 source Assuming that the cable may be considered lossless due to the short length determine the load impedance and the frequency of operation for the tuner ZLoad 7 74167 Q f 777975M777HZ Problem 9 A singlestub tuner consisting of a Z5509 main line connected in parallel with a Z5509 short circuited stub is used to match a load of 15j35 Q to another 509 transmission line Determine the lengths In and mm in centimeters if the lines are the air lled lines from the laboratory and the frequency of operation is 400 MHZ You may assume the line is lossless for this problem 76 Short Ckl U U D 50 Ohm Line 15j35 Ohms lline 777777770111 u u D I L I lstub 7 7 770m gt lime Problem 10 When an air lled slottedline is terminated with a shortcircuit voltage minima nulls are measured at positions of 223cm and 41cm on the line When the shortcircuit is replaced by an unknown load the VSWR on the line is 24 and a voltage minimum is detected at 26cm Determine the load impedance in rectangular form and the reflection coef cient of the load in polar form if the characteristic impedance of the line is 509 ZLoad Problem 11 A piece of RG 18U cable will be used as a 1Awavelength tuner to match a load to a 1509 source at a frequency of 200MHz Assuming a perfect match determine the load impedance value and the physical length to which the cable should be cut Problem 12 When a 20watt source is applied to the input of a directional coupler 12 milliwatt of power is measured at the sample port When the same 20watt source is connected directly to the output of the coupler 01 milliwatts of power is emitted from the sample port Determine the coupling factor and the directivity of the directional coupler 20 gt Sample Coupling Factor 7 467 dB m gt gt Out Directivity 777 dB Problem 13 A directional coupler has a coupling factor of 40 dB and a directivity of 60 dB 20 watts of rf power is applied at the input of the coupler The main arm of the coupler is terminated by a short circuit Determine Pm the power coupled into the auXiliary arm of the directional coupler Do NOT round your answer Hint 7 this is not a trivial onestep problem Think I gt Paux Pmain gt Short Circuit Paux 000200000277w

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