c Γ a) λ 0.6 m, e W = = = = R in R in 0 r 1 in g in in 2 in in g in g in

Transcription

1 - Consider a coaxial cable with characteristic impedance Z 75. Ω and solid plastic sulator with ε r 4. and α.94 N/m as shown the figure. Consider f 5 MHz. a) Fd the wavelength, the load and the put reflection coefficient and the put impedance. b) Fd the phasor voltage and current and average power at the put of the cable le. c) Fd the average power delivered to the load. c 5 75 e e Z Z Ω αl jβl a) λ.6 m,. 5.3 R R f ε r Z V b) V V 4.8 V I ma Re V I 7.96 W c) g g Z Z Z Z g g γl e.633 V Z G γl e W.633 Z Z

2 3- Aşağıdaki iletim hattı devresde V V, f GHz, Z 3Ω, Z 5Ω,. ise. Z,, g Z, VWR,,,, değerleri bulun c, ref, 3- Given V V at GHz, Z 3Ω, Z 5Ω,. as shown the g followg figure. Calculate Z, g, Z, VWR,,,,. c, ref, g jβl f GHz λ 3 cm, Z Z 75 Ω, e. Z Z Ω, VWR.5 V ( V Z I ) V ( Z Z ) a a c, G c, Z Z Z ( Z Z ) G 4.73 W, W n c, ref, ref, c, i W

3 4- Given V V at GHz, Z 3Ω, Z 5Ω,.. An ideal 3 db g g attenuator ( Z 5Ω ) is serted at port between the source and the le to give Z 36.3Ω as shown the figure. Calculate,,,,,. ref, trans, Z Z ( ),, V Z Z G,.59, VWR.378, a, Z Z Z ( Z Z ),, G, 3 4 a 4.36 W 6.7 dbm,.7 W?? dbm c, ref, c,, 3 ( ) 4.9 W?? dbm trans, c,,., VWR.5, 3?? dbm?.?? mw, c, c, ( )?? mw?? dbm c,

4 - For the followg circuit below , 5. 35,. 4, and.6 4 a 5 ohm system. Fd the time-average power delivered to the load Z. Z jz tanβl Z Z Z 5 j5ω Z Z j5ω Z jz tanβl Z jβλ/8 jβλ/8 V 7 j V( z λ 8) V ( e e ) V (.3 j.848) V Z 5 V j ce b we need to determe a( V ) with match at port. a a V V ( z ) V e V a V b a 5 9 jβ av b Z 6.5 W. Method Vp g Vg c a 8Z g 8Z 4.5 a, b a 6.5 W

5 - A lossy section of transmission le of length m is operated at MHz and has When the le is termated with a matched load and fed by a matched generator, a watts 3 ( ). a) Fd the attenuation constant and phase velocity of the transmission le. b) Fd b and the power absorbed by the load. αl jβl αl a) e e.6 e α ( l) ln.6.58 Np m βl π4 ωv π4 V 8f.6 b) ( b a ) b (.6 45 )( 3 ) 6 5 ( watts) a bb (6) 8 W p p 5- A lossy section of transmission le of length m is operated at f MHz. When the le is termated with a matched load and fed by a matched generator, a 6 (watts) and b 9 3 (watts). d) Fd the attenuation constant. e) Fd the phase velocity. 8 m s αl jβl αl d) e e.9 e α ln.9.5 Np m l π ω πf 8 e) βl Vp lf. m s 6 V V p p a) Fd the put power to the transmission le. b) Fd the power absorbed by the load. c) Fd.

6 G A - Aşağıda verilen devre iç T, ve değerleri bulun. V V, Z 5Ω, Z 5Ω,.5,.85 45,.85 45,., Z 5Ω. - The s-parameters of a two-port network a 5 ohm system is given by.5,.85 45,.85 45,.. a) Determe whether the network is reciprocal or lossless. b) If port is termated with a matched load, what will be the return loss at port? c) If a short circuit is placed on port, what will be the return loss at port? d) Fd T, and if V V, Z 5Ω, and Z 5Ω. G A a) [ ] is not symmetric, the network is reciprocal..745 not lossless. b).5 R log 6.5 db c).45 R log 6.9 db V G 3 d) GT db, AV. W, AVG T 7.5 W 8Z

7 3- An amplifier circuit below is connected to a source with V V and Z 5Ω, and its output is connected to a load of Z Ω. (a) Fd G, GA, GT, andg TU (b) Fd A and. The s-parameters of the two port 5 ohm are given by.6 7,.3 8,.6 7,.7 5. Z Z Z Z V V, Z 5 Ω, Z Ω,.33,.33, Z Z Z Z , G G out AVN A AV out 3.8. db GT AV out AV db.8.3 db GTU GT.4. db G V Z Z Z. W ( ) VG Z AVG T.6 W Z Z

8 4- Consider the network shown below. a) Give the s-parameters of 3 db attenuator. b) Compute GA, GT, G when Z Z 5Ω. c) Compute GA, GT, G when Z 5 Ω, Z 5Ω. d) Compute GA, GT, G when Z 5 Ω, Z 5Ω..77 [ ],, G, G, G out.77 A T out a),, G G G.5 3 db out A T b).33,,, out 6 G.5 3 db, G db, G db A T c).33,,, out 6 G db, G db, G.5 3 db A T

9 5- A two port network is driven at both ports such that the port voltages and currents have the followg values when Zo 5 ohm. Use the scatterg parameters concept to determe the put impedance and the cident & reflected voltages at each port. V, V 4 9, I.4 9, I.8 V V Z 5 jω, Z 5jΩ,, I I V V V, I ( V V ) Z, () V V V Z I V V () Add () and () V Z I V V ( V Z I ) jv ub () and () V Z I V V ( V Z I ) jv similarly V ( V Z I ) jv V ( V Z I ) jv.8 35

10 3- Aşağıdaki devre iç a), avs, c, b) G, T G, AG değerleri hesaplayın. 3- For the followg amplifier circuit fd a), avs, c b) G, T G, AG..3 7, ,., j.58 Z Z 63.5 j.4ω V ( V Z I ) V ( Z Z ) a.733 j.45 b c, G Z Z Z ( ZG Z) V ( V Z I ) V ( Z Z ) a. 45 j.46 ref, G Z Z Z ( ZG Z) b a b a a a.38 j.87 a b a a orab b.73 j.4 c, ref, c, a.747 W, b.33 W, ( ) VG Z a b c, Z Z ( ) ( ).74 W VG Z b a.984 W Z Z G G avn avs A VG Z.55 W Z Z ( ) out VG Z.78 W Z Z dB avn avs out db avs out GT.56. db

11 - Aşağıdaki devrede transistorun 5 ohm sistemdeki s-parametreleri verilmiştir. Buna göre port deki Return oss u. a) θ 45 ve Z 5Ω. b) θ 45 ve Z açık devre c) θ 9 ve Z kısa devre iken bulun..5,.5 45,.5 45, The scatterg matrix for a -port network (assumg 5 ohm system impedance) is given by.5,.5 45,.5 45,.5 9. Fd the return loss at port if port is connected to a 5 ohm transmission le when: a) θ 45 and Z 5Ω. b) θ 45 and Z is an open circuit. c) θ 9 and Z is a short circuit. a) Z 5 Ω R log log 6. db b) j, R log db c),.4 j. R log log db - Calculate the put impedance, cident and reflected power at put and power delivered to the load. The s-parameters of the transistor as measured a 5 ohm system are given by.5 35,.5 3,. 3,.8. V V (peak), Z 5Ω. g.5 35 Z Z??. j??? Ω a ( V Z I ) V ( Z Z ) V G G.5 Z Z ( ZG Z) Z c r c c a.5 W,.65 W,.565 W, VG Z Vg Z (, ).565 W Z Z Z Z ( )

12 - Calculate the put impedance, cident and reflected power at put and power delivered to the load. The s-parameters of the transistor as a 5 ohm system are given by.5 35,.5 3,. 3,.8. V V (peak). g (5) Ω.5, or.5, λ 4 8 rotation Z Z.8 j.ω Vc, ( V ZI) VG ( Z Z) a.5 Z Z Z ( Z Z ) b V ( V Z I ) V ( Z Z ) b a b a a a.3383 j.953 a b a a orab b.353 j.78 a.5 W, b G ref, G Z Z Z ( ZG Z) c, ref, c, ( ) ( ) a.5 W, VG Z a b c,( ).998 W Z Z VG Z b a.888 W Z Z G G avn VG Z W Z Z ( ) out VG Z avs Z Z A. 5 W db avn avs out db avs out GT db

13 - A two-port network is measured a 5 ohm system and the followg scatterg matrix is obtaed: , 5. 35,. 4, and.6 4. a) If port is termated with a matched load, what will be the return loss at port? b) If a short circuit is placed on port, what will be the resultg return loss at port? c) Calculate the power delivered to the load if V V (peak), Z Z 5Ω. g a), R log log 6.99 db b),.58 j.875 R log db ( ) VG Z VG c), 6.5 W Z Z 8Z

14 - A two-port network is measured a 5 ohm system and the followg scatterg matrix is obtaed:.5,.85 45,.85 45,.. a) Determe whether the network is reciprocal or lossless. ce [] is not symmetric, the network is reciprocal. ce.745 the network is not lossless. b) If port two is termated with a matched load, what will be the return loss at port?.5 R log log db c) If a short-circuit is placed on port, what will be the resultg return loss at port? V V V V V V V V V V V V V V V V V V.45 R log log db. d) Calculate the power delivered to the load if V V (peak), Z Z 5Ω. g,.5 Z Z 67.65Ω a ( V ZI) VG( Z Z) VG.5 Z Z ( Z Z ) Z a.5 W,.865 W,.565 W VG Z Z Z G c c r c ( ) VG.865 W 8Z

15 - Consider the two port device obtaded by cascadg a section of transmission le with a 8 resistor as shown below with l 5cm, f 3GHz, V 3 m s, R Ω, Z 5 Ω. p a) Fd the ABCD matrix of this two port network. AB cosβl j5sβl 5 CD j 5 s βl cosβl b) Fd the scatterg matrix of this network (referenced to 5 ohm) by usg tables. λ cm, l λ, Thus we really need only to fd the s - matrix of a series load. 5 ( ) [( )( ) ], 5 ( ) 4 ( ) ( 5) ( ) 4 (sce device is passive) - Bir iletim hattının bir direnç ile kaskat bağlanmasından elde edilen iki port devre aşağıda verilmektedir. Bu iki port devren 5 ohm sistemde ve parametreleri hesaplayın l λ 4, R Ω, Z 5 Ω.) ( - Consider the two port device obtaded by cascadg a section of a transmission le with a resistor as shown below. Fd and of this network (referenced to 5 ohm). l λ 4, R Ω, Z 5 Ω. Termate port with 5 ohm, Z V z V e V e V e e (5) jβz jβz jβz jβz ( ) [ ], (5 5) (5 5) 5 7 λ c, ref, c, c,, V( 4) V j 7 V V V ( ) V V j 7( ) V () V 7 3V 3Vref, Vref, V 4 7 ( V V ) j( ) 4j 3 ref, c, Vc, (by reciprocity)

16 - Bir iletim hattının bir direnç ile kaskat bağlanmasından elde edilen iki port devre aşağıda verilmektedir. Bu iki port devren 5 ohm sistemde ve parametreleri hesaplayın - Determe all four scatterg parameters for the circuit shown assumg a characteristic (system) impedance of Zo. Usg your scatterg matrix, show that the circuit is lossy. Termate port with jβz jβz jβz jβz V() V 7 3V, Z ( Z ) Z Z Z 3Z Z Z 3, V( z) V e V e V [ e e ], (3Z Z ) (3Z Z ) 5 7 V( λ 4) V j 7 Z ( a b ) Z a ( ) a jv [7 Z ( )] Termate port with 3 Zb b 4 V [7 Z ] b a j( ) 4j 3 a (by reciprocity) Z 9Z 9Z 4 Z 5 Z, Z, Z 4 4 9Z 4 Z 3 3 j4 3 First column ( 3) (4 3).8 so, circuit is lossy. j Compute ans and for the followg circuit. Use a reference impedance of Z., Termate port Zo, so Z, Z hence jβz jβz V( z) V [ e e ], hence V( z) V e β V( λ 4) V j Z ( a b ) Z a ( ) a V V() V V Zb b hence Z (by reciprocity) Termate port Zo, Z, Z 5, so Z Z Z Z 3 b j z Z jv ( ) j j ( ) 3 a a Z 5 Z. Z 5 Z 3 3 j 3 j 3 3

17 4- The and parameters of cascaded two port networks with dividual scatterg A B matrices [ ] and [ ] are given below. Use this result to compute and for the followg circuit with respect to a reference impedance of Z. A B A B A B A A A B A B Calculation of and of a transmission le with a characteristic impedance of Z and length of λ 4 is given below. The reference impedance is Z. Z ( Z ) Z Z Z 3 Z 4 Z Z 5 Z Z jβz jβz, V( z) V [ e e ] V( λ 4) V j 3, Z Z 3 jv 5jV V( λ 4) Z( a b) Za( ) a 3 Z ( ) 3 Z V() V 4 3 V Z b b 4 V [3 Z ] b a j4 5 (by reciprocity) a The s-parameters of a series resistance of Z is given by When we use the formula we get 3 j4 3 j

18 - Compute all four -parameters for the followg circuit. Be sure to reference the - parameters to the proper system impedances shown (Z o for ort and Z o for ort ). (Z Z Z) Z Z Z Z Z s, s (Z Z Z) Z Z Z 3 Z Z 3 4 Z V V Z ( a b) Za( s) Za, V b Z 3 Z Z V b 3 Z 3 b b V Z a a a s s The network below is known to have. 8 ; 8 ;. 9. is not known, however, ZIN 4 Ω, Z 5Ω. a) Determe (at x). Z Z λ jβ IN jπ jπ 8 IN e INe e ZIN Z b) Fd a and b at x. λ V gen λ jπ 4 8 Z 8 a ( ).7 a () a ( ) e.7 45 b () a ().7 35 c) Calculate avs, and. avs a.5 mw, avs ref a b.47 mw b a but, soa, b a a.4 9 mw

19 3- In the below circuit, Z j3 ohms, I -j ma, Z d -j ohms, I 7j9 ma, Z d -jl5 ohms, V 4j5 V, Z j6 ohms. All currents and voltage are effective values. a) Determe the operatg power ga of each stage. b) Determe the operatg power ga of the entire amplifier. Gp Gp Gp 35.8 db c) Determe the transducer power ga of the entire amplifier. GT GT Gp 8.4 db, G T 3.5W dB 4.33 mw avs

20 - 5 ohm sistemde bir transistorun s-parametreleri şöyledir:.4 5, ref. 5,. 85,.8. a) Z? b)? c)? - Two port s-parameters of a transistor a 5 ohm system are given by.4 5,. 5,. 85,.8. a) Calculate the put impedance, power delivered to the load, and reflected power at put.,.4 5 Z Z j38.87ω c r c W, 8 mw 3- For the amplifier circuit below the transistor has.6 45, 3.4 8,.7 75, a) Determe Z,, Z,,, Z,, Z at GHz. out out Z 4.5 j4.5ω.8 j.88.9 Z 6 j5ω.4 j Z Z j78.77ω, Z Z 76 j35ω out out out out

21 - For the network below E, V 5 5, b. 45 V. All voltages are rms quantities. a) Fd the value of a. Give your result polar form. a V ( V Z I ) E E Z Z 5 5 c, ( 5 ).77 b) Fd the value of,, and the operatg power ga if a.5 3 V rms. G b. 45 V (5 5 ).4 5, a Z on port- E V db a b - A two-port network below has. j.4 and.8 j.4 a 5 ohm system. a) Determe the put reflection coefficient. 75 5,.33 j rad , b) Determe the transmission coefficient b a. b V V V T but, T. j.4. a V V V

22 - A two-port network a 5 Ω system is shown below. The total voltages and currents at the ports are given by V, I. 3, V 9, I.4 9 with Z Z 5 ohm. Calculate the cident and reflected voltage waves at both ports and and. - Aşağıda Z Z 5 Ω, V, I. 3, V 9, I.4 9, ise devren ve değerleri ne olmalıdır? V ( V Z I ) , V ( V Z I ) c ref V ( V Z I ), V ( V Z I ) 9 c ref ( V V ) , ( V V ) ref c ref c c V c V, 5- A two port network below has V, I. 3, V 9, I.5. Fd the cident and reflected voltages at both ports. Assume 5 ohm system impedance. 5- Aşağıdaki devre iç V, I. 3, V 9, ve I.5. Buna göre her iki porta giren ve yansıyan voltajları hesaplayın. 5 ohm sistem empedansı varsayın. V ( V Z I ) 7.65 j.5v I.43 j.5a V ( V Z I ).835 j.5v I.57 j.5a V ( V Z I ).875 j9.48v I.37 j.85a V ( V Z I ).875 j.75v I.37 j.55a

23 -Asağidaki devre iç operatg ve transducer power galeri hesaplayın. -Determe the operatg, available and transducer power gas db of the below circuit for Z 45 j3 Ω, Z j Ω, Z 7 j5 Ω, Zout 5 jω and V. 45 V, a.7 35 V, b.7 V. Z Z Z Z V a out 45 j3 Ω, j Ω, 7 j5 Ω, 5 jω. 45 V,.7 35 V, b.7 V

24 - The two-port network belowis an ideal lossless matchg network that matches the source Rs to the load Z at the design frequency. It is made up of lossless ductors and capacitors. a) In terms of the variables shown the figure, what are the put impedances seen lookg to ports and of the matchg network? Z Z R, Z Z R jx s b) If we were to determe the impedances of our two-port matchg network, are your answers (a) equal to Z and Z? Why or why not? Z ( V I ), Z ( V I) portisoc neither port is open circuited the circuit. No! portisoc c) If Vs 8 V and Rs 8 ohm, what is the power available from the source? avs Vs Rs 8 W c) If Rs 8 ohm, R ohm, X ohm and assumg maximum possible power transfer from the network, what is the magnitude of the forward voltage ga of the network? ossless MN Z Rs 8 avs transferred to the load. avs V V W V V. R 4 Ω so V VR ( R R ) V 4V. G V V 4 5. s s s s s e) For a standard measurement setup with Zo 5 ohm, is the value calculated (c) equal to? Why or why not? No! We must termate 5 ohm, and then measure GV if we want. f) If we could fd a network analyzer with Zo ohm, what values would it measured for and if we hoked it up to the two-port matchg network? 8 Z 8 With a ohm R, lookg to port Z 8 ohm Z 8 Now the load is properly termated to make the Gv calculated (d) be equal to. 5 v

25 3- The scatterg parameters of a microwave amplifier are found at 8MHz as follows ( Z 5 Ω ):.45 5,.,.5,.4 5. The source and load impedances are and 3 ohm, respectively. Determe the transducer power ga, operatg power ga, and available power ga. Z Z 5 Z Z ,.5 Z Z 5 Z Z , out out GT G G A db out db db 4- What are the formulas for the powers terms of -parameters? V Z bg G, G avs ( Z Z) b b ( ) bg bg avn out out, ( )

26 - Asağıdaki devren -parametreleri verilmiştir. Buna göre port deki yükte harcanan gücü ve port den yansıyan gücü bulun. ( Z 5 Ω ):,., 3, The scatterg parameters of the below network is given below. Determe the power delivered to the load at port,, and power reflected from port. ( Z 5 Ω ):,., 3,.6 8 V a V V b a a, ( a b, a ) b gen gen gen Z Z Z b a a b b a V V gen gen,.38, Z Z 4 ref b 5.65 W, b a b ( ) or out ( ) 4 ref a out , V G Z Z Z out 5.65 W gen V 4Z 8.75µ W ( ) 8.75µ W

27 - Given the below two-port network determe the operatg, available, and transducer power gas if they exist. If a particular power ga does not exist, expla why it does not exist. Why can the circuit have power gas greater than unity? All currents and voltage are effective values. (45)(3) R , G does not exist scer < p I, I.86 A, I I.35 A, I R mw R mw, G log 4.8 db avs T 4() avs (45)( 37) R > G does not exist sce d A V T avn V..5 V, 9.4 mw G log 6.45 db T avn A ( 37) 45 4R d avs

28 3- - Determe the s-parameters of the followg T-network (the network without source and load impedance) based on ohm system impedance. Then determe the transducer power ga and the power delivered to the load All currents and voltage are rms values. (5 ) Z 5 5 Z R ( R Z ) 64 ( ) R Z R ( R ( R Z )) V Z V G G.84 W,.47 W Z Z 4Z G G G T A db out db db out

29 - In the below circuit, I 6 3 ma, V.6 65 V, I 3 ma. Determe the operatg, available, and transducer power gas. If one or more power gas cannot be found, state what additional formation is needed to calculate the ga. All currents and voltage are effective values.

30 - At some reference plane on a transmission le it is observed that a.5 35 and Determe the followg at this reference plane. a) Determe the total voltage at this reference plane. b) Determe the total current at this reference plane. c) Determe the net power delivered at this reference plane. - Given the followg circuit, fd the scatterg matrix for R 8.56 Ω, R 4.8 Ω, and Z 5 Ω. What is the function of this circuit? - Aşağıda verilen devren elemanları R 8.56 Ω, R 4.8 Ω, ve Z 5 Ω olsun. Buna gore yansıma matrisi [ ] yi hesaplayın. Bu devre ne işe yarar? R R Z R Z V Z Z V Z V Z (port is matched) Z 8.56(4.8 (8.56 5)) 5 Ω. o. From symmetry. V (port is matched). ce, we know that V, and V V V V Then.77. V log 3dB. This is a matched 3 db attenuator.

31 A B 4- Consider cascaded two port networks with dividual scatterg matrices [ ] and [ ]. Fd and of the cascade of these two networks. A B olution: V V A x y B V V The ouput port is matched to fd ( V ) A A A A B B V V y...(), x V y...(), y x...(3), V x...(4) A A B (3) to () gives x V x. Rearrangg, x( A B ) A V. (5). A B V A B A V () to (5) gives ( ) B V. Then we have. A B V A A B To fd, (3) to () gives V V x.(6). A B A A B A A V V A (5) to (6) gives V V. Then we have A B. A B V 3- db kazancı olan iki kuvvetlendirici kayıpsız bir iletim hattı ile şekildeki gibi bağlanmıştır. A B 3.6< A B A B,.77< a) l iken sistem toplam kazancını hesaplayınız. b) l λ 4 iken sistem toplam kazancını hesaplayınız. A B 3- Compute the cascade ga of the two db amplifiers ( 3.6 < ) shown A B A B below with.77 when; l A Z, β B a) directly connected ( θ ) A B A B ( ) ( ) (3.6) ( (.77) ) 6dB b) connected through a lossless cable with a length of l λ 4 ( θ 9 ) and Z 5 Ω. db ( A B A B ) ( ) (3.6) ( (.77)(.77)) B A λ 4 transmission le transforms.77 < B to.77 < 8.77 <

32 5- Determe the s-parameters with respect to a system impedance Z for the followg circuit terms of Z,C, g m and frequency ω. Is this network reciprocal? ort. V Z Z Z jωcz jωc V Z V Z jωc Z jωcz V V, V V V, I gmv, V ZgmV Z V V j CZ V V V V V V ω jωcz jωcz Zg m V Z g V jωcz, m ort. V g V, therefore port sees an open circuit m and ). Note: We have unidirectional transmission the network must NOT be lossless.. The network is clearly not reciprocal ([ ] [ ] t

33 - Usg the defitions of the -parametes, determe and for the below network. Assume that the same value of Z o is present on both ports. - Z o referans empedansına göre aşağıdaki devren ve parametreleri hesaplayın. There are no dependent sources or components connectg port- with port- Z R Z R, so R Z. To fd I R E s Z AZ E s ( )( ) V R Z R Z V AZ E ( R Z )( R Z ) s Z on both ports 7- Aşağıdaki 3-port eşit güç bölücü iç sadece i hesaplayiz. olution:

34 8- Compute the -parameters (as a function of the length and propagation constant) for a transmission le of characteristic impedance Zo and length l}. Compute the -parameters for a system impedance of Zo. Z Z Z jz x tan βl x Z jz tan β l x

35 9- Calculate the four -parameters for the network below. The system impedance is 5 ohm. - The -parameters for a two-port network is.3 j.7, j.6, j.6,.3 j.7. What are the equivalent Z-parameters if the characteristic impedance is 5 ohm? Z.4 j5.4, Z j44.78, Z j44.78, Z 5.4 j For a lossless -port network: (a) if the network is reciprocal, show - and (b) if the network is non-reciprocal, show that it is impossible to have unidirectional transmission (e.g. and / ). Network is lossless and reciprocal so [ * ] [ T ] [U] and T >, but so

36 3- A four-port network has the scatterg matrix shown below (a) What is the return loss ( db) at port when all the ports are matched? (b) What is the sertion loss ( db) and phase between ports and 4, when all other ports are matched? When all other ports are matched, the sertion loss from port to port 4 is, (e) What is the reflection coefficient seen at port if a short circuit is placed at the termal plane of port 3, and all other ports are matched? For a short circuit at port 3, and matched loads at other ports, we have

37 4- (a) A lossy section of transmission le has the followg -arameters at 3. GHz: What is its shortest possible length if the wavelength on that le is.6 times the wavelength free space? (b) What would be the -parameters of a le three times as long? ce and are zero, there is no reflection at the junctions between the sections. The phases of the transmission parameters will be added and their magnitudes will be multiplied: (c) Calculate the normalized put impedance of the le section (b) if it is termated a short-circuit. There are several methods for computg this put impedance. We will first calculate the put reflection coefficient of the le section usg the formula: This result can also be found usg the mith Chart.

38 7- A certa three-port network has the followg -parameters. [ ] a) Briefly describe the function of this network. In the above matrix, the only non-zero -parameters are, 3, 3 (all ). Therefore ower to port port ower to port 3 port ower to port port 3 a) Is the network (i) matched? (ii) reciprocal? (iii) lossless? Justify your answers. (i) ii matched at all ports (ii) [ ] [ ] t Not reciprocal (iii) [] t [] * [U]? ossless if 4- Fd the s-parameters of the followg network.

39 8- Consider the followg three port network. The characteristic impedance of each transmission le section is 5 ohm. a) Determe and C for the circuit to be matched at port at a frequency of.4 GHz. Z Z jz ω C ωc Z j ω ωc For matched put Z Z j ω ωc ω C Z C Z Z Z C Z C Z C Z ω Z ω, C ω ωz, 3.3 nh, C.3 pf. b) Comment on the operation of this circuit vs. Frequency. What function does the circuit perform? High frequencies pass to port but are blocked by the ductor. ow frequencies are passed to port 3 but are blocked by the capacitor. The circuit is a DIEXER.

40 9- Fd the scatterg matrix (-parameters) for the followg two port network, relative to a system impedance of Z 5 ohm. 9- Aşağıdaki iki port devren -parametreleri 5 ohm sisteme göre hesaplayın. Z Z 5Ω 5Ω 5Ω Z Z 5Ω 5Ω 5Ω Consider a three-port network described by a scatterg matrix. If port three is shorted, derive the equivalent two-port representation of the system. Note: Do this calculation directly and not by convertg the Z matrix.

41 - Fd the parameters of the followg T junction: The system impedance is 5 ohm. Z Z Z [ ( 5) ] 5Ω Z Z 3 V( z) V e V e V e V e jβz jβz jβz jβz V() V ( ) V ( 3) V V (3 ) V port V V ( 5) 3 Va V V ( 5) 5 5 V Va 5

42 6- Determe the s-parameters of the below network. Assume that the same value of Z o is present on both ports. a) Determe s V IR AV IR A( BIZ ) I( R ABZ), Z R ABZ Z Z R Z( AB) Z Z R Z ( AB) b) Determe s V V BZ BI Z, Es IZ I( R ABZ) I( R Z( AB)) E R Z ( AB) s c) Determe s V E, V Z AV Z R s AV, I, V Es BIZ R Z ABZ, E s V R Z AZ R Z ( AB) d) Determe s Z out V I ( R Z ) AV, I R Z, V BI A ( R Z ) Zout Z, Z Z, Zout AB out R Z( AB) R Z ( AB)

43 - A three port network has the followg scatterg matrix. a) Is this device lossless? Justify your answer. No. it does not satisfy T I b) Is this device reciprocal? Justify your answer. Yes, sce T c) Is this device active or passive? Expla your answer. Active sce a volt signal sent port is returned with an amplification factor of. d) Are any ports on this device isolated from one another? If so, which ones? Expla. Yes, ports and 3 are completely isolated from port. A signal sent either of these ports has no effect on port. e) What is the reflection coefficient seen lookg to port when port and port 3 are termated matched loads? When ports and 3 are matched, the reflection at port is due only to. Therefore f) What is the reflection coefficient seen lookg to port when port is termated a matched load and port 3 is termated a short circuit?

44 - Fd the [Z] parameters for the followg two-port network. Convert the [Z] parameters to [] parameters for the -port network a 5 ohm system. The [Z] parameters for the transistor alone are Z 5 - j6, Z, Z 5 j9, Z 5 - j6. ce parallel connection of -ports need [Y] parameters of each, then add to get [Ytotal] then [Ytotal] - to get [Ztotal] Y R j.98, [ Y ] [ Z ] TR TR.9 j j.98.3 j j j.98 [ Y ] [ Y ] [ Y ] Total TR R 9.7 j j [ Z ] [ ] Total YTotal.6 j j feedback 5 no feedback 5 feedback reduces ga Z Ω, [ Z ] [ Z ] TOT Z Ω, [ Z ] [ Z ] transistor, V V db, V V db

45 6- Fd Z and Y matrix for the circuit below.

46 4- Compute the Y matrix of the equivalent circuit of a FET amplifier shown below.,