Impedance Matching and Tuning
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1 Impedance Maching and Tuning
2 Impedance Maching and Tuning Impedance maching or uning is imporan for he following reasons: Maximum power is delivered Improve he SN of he sysem educe ampliude and phase errors in Figure 5. (p. 3) A lossless nework maching an arbirary load impedance o a ransmission line.
3 Impedance Maching and Tuning Oher Discussion Maching nework usually use lossless componens:, C, ransmission line, ransformer, There are many possible soluions available Use Smih char o find he opimal design Facors in he selecion of a paricular maching nework: Complexiy andwidh Implemenaion Adusabiliy 3
4 Maching wih umped Elemens e Figure 5. (p. 3) -secion maching neworks. (a) Nework for z inside he + x circle. (b) Nework for z ouside he + x circle. 4
5 Maching wih umped Elemens e Analyic Soluions ( = + ) Case: z is inside he x ( ) Case : z ( ) is ouside he x Separaing ino e/im pars: For a maching condiion : For a maching condiion : Separaing ino e/im pars: Soluion : Soluion : 5
6 Maching wih umped Elemens e - - C - - C C C C C 6
7 Maching wih umped Elemens e Smih char soluions Case: z is inside he x circle x circle 7
8 Maching wih umped Elemens e Case : z is ouside he x circle b circle 8
9 Maching wih umped Elemens e Example 5. -Secion Impedance Maching, f 5 MHz Soluion : z y.4. y.4. 5 C b f 9pF.9, b z. x. x f nh.3 9
10 Maching wih umped Elemens e Example 5. -Secion Impedance Maching, f 5 MHz Soluion : z y.4. y.4. 5 z. x. C.6pF f x f b 46. nh, b.7
11 Maching wih umped Elemens e Example 5. -Secion Impedance Maching Figure 5.3b (p. 7) (b) The wo possible -secion maching circuis. (c) eflecion coefficien i magniudes versus frequency for he maching circuis i of (b).
12 Maching wih umped Elemens e umped elemens (l < /): parasiic C/, spurious resonances, fringing fields, loss and perurbaions caused by a ground plane. nh.5 pf 5 pf
13 Maching wih umped Elemens e Esimaing andwidh: single frequency bandwidh Approximae uning may be eer!! Frequncy Conours: Foser' s as and f, of reacance heorem of impedance admiances Impedancesand admiances on he Smih char race clockwise arcs as frequency is increased. 3
14 Maching wih umped Elemens ac g w u ped e e s Consan Q circles: F Q Q F Q 4
15 Maching wih umped Elemens e roadband ow Q maching Q n F Q=.74 5
16 Maching wih umped Elemens e One-secion High Q Maching v. s. 3-secions ow Q Maching 6
17 Single-Sub Sub Tuning in (a) No umped Elemens (b) Easy o fabricae in microsrip or sripline. in Figure 5.4 (p. 9) Single-sub uning circuis. (a) Shun sub. (b) Series sub. 7
18 Single-Sub Sub Tuning (Shun) Example 5. S.C , f Hz S.C. y z..6 y.6.8 SW circle i inersecs b circle: d. for y.47 d.6 for y S.C. l SC S.C. l.45 8
19 Single-Sub Sub Tuning (Shun) Example 5. 9
20 Single-Sub Tuning (Shun) S g e Sub u g (S u ) : d for, an d an where d for, an s s where For an open - circuied sub, l s o s s - circuied sub, For a shor an an l s o is chosen so ha d an an, l s s f for negaive is he resulan If l s for
21 Single-Sub Sub Tuning (Series) es) Example 5.3 z.6 O.C. f SW circle inersecs d d 5, Hz x. for z for z.33 OC O.C. l.33 O.C. l circle: O.C. z
22 Single-Sub Sub Tuning (Series) es) Example 5.3
23 Single-Sub Tuning (Series) S g e Sub u g (Se es) : d for, an d an where d for, an s s where For an open - circuied sub, l o s s - circuied sub, For a shor an an l s o is chosen so ha d an an, l s s f for negaive is he resulan If l 3 for
24 Double-Sub Tuning 4
25 Double-Sub Tuning Figure 5.7 (p. 36) Double-sub uning. (a) Original circui wih he load an arbirary disance from he firs sub. (b) Equivalen-circui wih load a he firs sub. 5
26 Double-Sub Tuning Forbidden region : No inersecion poin wih oaed b circle reduce d for reducing forbidden region d or / : sensiive frequency d as are generally chosen /8 or 3 /8 6
27 Double-Sub Tuning Example , 5 Subs: open-circuied subs, d /8, f Hz : a series resisor and capacior Soluion: z..6 y.3.4 b.34 l.46 b y.4 l y.38 b l b l
28 Double-Sub Tuning.995 pf pf (c) Figure 5.9b (p. 39) (b) The wo double-sub uning soluions. (c) eflecion coefficien magniudes versus frequency for he uning circuis of (b) (b) 8
29 Double-Sub Tuning oub e Sub u g Analyic Soluion s : sub he lef of he Jus o 4 region : Forbidden ransmission line lengh d nd sub : he lef of he us o d sin / and an where d par of real l o an sub : For O.C. 4 l s an sub : For S.C. 9
30 The equarer-wave Transformer Figure 5. (p. 4) A single-secion quarerhi ransformer. a he design wave maching 4 frequency f. 4 sec cos for near in where an l an, a f in in Figure 5. (p. 4) Approximae behavior of he reflecion coefficien magniude for a singlesecion quarer-wave ransformer operaing near is design frequency. 3
31 The Quarer-Wave Transformer equa e Wave a s o e : andwidh m sec or cos m m m hen TEM lines, assume we If m m 4 f f f v v f l p p Fi 5 ( 43) fl i ffii cos 4 4 f f m m m Figure 5. (p. 43) eflecion coefficien magniude versus frequency for a singlesecion quarer-wave maching ransformer wih various load mismaches 3 m wih various load mismaches.
32 The Theory of Small eflecions e eo y o S a e ec o s Single-Secion Transformer e T T e T T n n n n e e T T 3 3 n n e T T x x x 3 for, e e e T T e e e Figure 5.3 (p. 44) Parial reflecions and ransmissions on a single secion maching ransformer 3 3 on a single-secion maching ransformer.
33 The Theory of Small eflecions ec Mulisecion Transformer Figure 5.4 (p. 45) Parial reflecion coefficiens for a mulisecion maching ransformer. n N n e Transformer can be e 4 made N e N symmerical : e e e e e N N N N N n n N n n e cos N cos N n cos N n N N : vary monoonically N /, for N even N e cos N cos N cos N n ( N )/ iven, design,, cos, for N N odd n 33
34 The ode-fano ocrierion Circui ode- Fano limi Figure 5. (p. 6) The ode-fano limis for C and loads mached wih passive and lossless neworks (ω is he cener frequency of he maching bandwidh). (a) Parallel C. (b) Series C. 34
35 The ode-fano ocrierion Circui ode- Fano limi Figure 5. (p. 6) The ode-fano limis for C and loads mached wih passive and lossless neworks (ω is he cener frequency of he maching bandwidh). (c) Parallel. (d) Series. 35
36 The ode-fano ocrierion Figure 5.3 (p. 63) Illusraing he ode-fano crierion. (a) A possible reflecion coefficien response. (b) Nonrealizable and realizable reflecion coefficien responses.. iven C. m m m :, unless number of 3. or C high Q load only a a or finiei frequencies m is harder o mach 36
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