SIGNIFICANCE OF SMITH CHART IN ANTENNA TECHNOLOGY

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1 SIGNIFICANCE OF SMITH CHART IN ANTENNA TECHNOLOGY P. Poornima¹, Santosh Kumar Jha² 1 Associat Profssor, 2 Profssor, ECE Dpt., Sphoorthy Enginring Collg Tlangana, Hyraba (Inia) ABSTRACT This papr prsnts Smith Chart as a graph bas mtho of simplifying th complx math n to scrib th charactristics of microwav componnts. Smith Chart can look imposing; it's nothing mor than a spcial typ of 2-D graph, much as polar an smilog log-log scals constitut spcial typs of 2-D graphs. W hav shown th utility of Smith Chart with th hlp of iffrnt graphs an figurs. Kywors: Smith Chart spctral simulation antnna paramtrs, Charactristics impanc, Quartr wav antnna. I. INTRODUCTION Th Smith Chart[1][2] is a graphical ai or monogram sign for lctrical an lctronics nginrs spcializing in raio frquncy to assist in solving problms with transmission lins an matching circuits[3]. It is an altrnativ to using tabular information. Th Smith Chart can b us to rprsnt many paramtrs incluing impancs, amittancs, rflction cofficints, S n scattring paramtrs, nois figur circls, constant gain contours an rgions for unconitional stability[4][5]. Th Smith Chart is plott on th complx rflction cofficint plan in two imnsions an is scal in normaliz impanc (th most common), normaliz amittanc or both, using iffrnt colors to istinguish btwn thm. Ths ar oftn known as th Z, Y an YZ Smith Charts rspctivly. Normaliz scaling allows th Smith Chart to b us for problms involving any charactristics impanc or systm impanc, although by far th most commonly us is 50 ohms. With rlativly simpl graphical construction it is straightforwar to convrt btwn normaliz impanc (or normaliz amittanc) an th corrsponing complx voltag rflction cofficint. Th purpos of this papr is to giv th basic ia of Smith Chart an to show its importanc in antnna tchnology. II. MATHEMATICAL BASIS Transmission lin as shown Z Z j 0 j y i Z Z0 (1) 132 P a g

2 Sinc 1, th valu of must li on or within th unity circl with a raius of 1. Th rflction cofficint at any othr location along a lin is shown in blow. 2a j2 2a j( 2 ) (2) which is also on or within th unity circl. Figur 1 shows circls for a constant rflction cofficint an constant lctrical-lngth raials. Th normaliz impanc along a lin is givn by z Z 1 Z0 1 (3) With no loss in gnrality, it is assum that 0 0 0; thn 1 Z R jx z r jx 1 Z Z an Substitution of Eq. [5] into Eq. [4] yils an 1 r (1 ) 2 i i r i r i (4) z 1 j z 1 2 x (7) (1 ) Equations (6) an (7) can b rarrang as r r i (5) 2 1 r r 1r 1r (8) an r 1 i x x (9) 133 P a g

3 Fig. 1. Constant circls an lctrical-lngth raials. Equation (8) rprsnts a family of circls in which ach circl has a constant rsistanc ( r ). Th raius of any circl is 1/(1+r), an th cntr of any circl is r/(1+r) along th ral axis in th unity circl, whr r varis from zro to infinity. All constant rsistanc circls ar plott in Fig. 2 accoring to Eq. (8). Equation (9) also scribs a family of circls, but ach of ths circls spcifis a constant ractanc ( x ). Th raius of any circl is (1/x), an th cntr of any circl is at 1 r 1 x ( ) i whr x Fig. 2. Constant rsistanc (r) circls Thr ar rlativ istanc scals in wavlngth along th circumfrnc of th Smith chart. Also, thr is a phas scal spcifying th angl of th rflction cofficint. Whn a normaliz impanc z is locat on th chart, th normaliz impanc of any othr location along th lin can b foun by us of Eq. (3). 134 P a g

4 z 1 1 (10) 2 ) j( (11) Th Smith chart may also b us for normaliz amittanc. This is vint sinc 1 Y G jb Z0 an Thn th normaliz amittanc is 1 Y0 G jb Z (12) Y Z 1 Y Z z 0 y g jb 0 A Smith chart or slott lin can b us to masur a staning-wav pattrn irctly an thn th magnitus of th rflction cofficint, rflct powr, transmitt powr, an th loa impanc can b calculat from it. Th following points ar consir about th Smith chart. (i) At xtrm lft on th chart r = 0, x = 0 i.. Z L = 0 + j0, rprsnts a short circuit on th transmission lin. At xtrm right on th chart r =, x = i.. Z L = + j, rprsnts an opn circuit on th lin. (ii) A complt rvolution (360 ) aroun th Smith chart rprsnts a istanc of ƛ / 2 on th lin. Clockwis movmnt on th chart is consir as moving towar th gnrator (or away from th loa), inicat in figur. Similarly, countr clockwis (anticlockwis) movmnt on th chart corrspons to moving towar th loa (or away from th gnrator), inicat in figur. (iii) Th outrmost scal is us to trmin th istanc on th lin from th gnrator n in trms of wavlngths an th nxt scal trmins th istanc from th loa n in trms of wavlngths. (iv) Th cntr on th Smith chart is inicat by a igit 1.Th lft si from th cntr lin givs th valu of V min, I max, Z min, 1/SWR an th right si from th cntr lin givs th valu of V max, I min, Z max, SWR. (v) Th circl aroun th horizontal lin which passs through th cntr inicats th rsistiv part whras th circl away from th cntr inicats ractiv part. Th uppr circl away from th cntr lin inicats inuctiv part whras th lowr circl away from th cntr lin inicats capacitiv part. (vi) Th Smith chart is also us as amittanc chart (as Y = 1/ Z ). (13) 135 P a g

Th quartr wav antnna (λ/4 lngth) must raiat with rspct to a groun plan. Th groun plan can b ithr th PC boar itslf, or th mtal cas of th outlt.

5 Fig. 3. Smith Chart III. USE OF SMITH CHART IN ANTENNA TECHNOLOGY: Smith Chart can b us as 1. Quartr Wav Antnna 2. Singl Stub Impanc Matching 3. Doubl Stub Impanc Matching In this papr only Quartr wav antnna is consir. Quartr Wav Antnna Th quartr wav antnna is th simplst mol of antnna: it only rquirs a rigi wir an a groun plan. Th quartr wav antnna (λ/4 lngth) must raiat with rspct to a groun plan. Th groun plan can b ithr th PC boar itslf, or th mtal cas of th outlt. In both cass mak sur th wir is vrtical to gt th highst impanc. Anyhow, th impanc valu will rmain unr 50 Ω. If th antnna is tilt paralll to th groun, th impanc valu will cras significantly. Fig. 4. Tilt Antnna Th λ/4 lngth is purly thortical. Dpning on th natur of th wir an th gomtry of th groun plan, consir th lngth as (k = λ/4 ) with k compris btwn 0.93 an Wir siz shoul b at last 0.34 mm 2 (AWG 22). 136 P a g

6 In cas th antnna is to b st outsi th cas, th raiating lngth to b consir is only th part outsi th cas. Howvr, th connction from insi th cas to th PC boar must b on with an aapt coaxial cabl. Thus th Smith Chart plays an important rol in Antnna Tchnology. IV. CONCLUSION Smith Chart kps th chart rlvant for toay's instrumntation an sign automation applications. It is nothing mor than a spcial typ of 2-D graph. Th coxistnc of complx-impanc an complx rflction cofficint information on has singl graph allows us to asily trmin how valus of on affct th othr. Typically w might want to know that complx rflction cofficint woul rsult from conncting particular roa impanc to a systm having givn charactristic impanc. REFERENCES [1.] Smith, P.H.(1939). Transmission Lin Calculator, Elctronics, Vol. 12(No. 1): 29-31, January [2.] Smith, P.H.; "An Improv Transmission Lin Calculator", Elctronics, Vol. 17, (No. 1):130, January [3.] Ramo, Whinnry an Van Duzr (1965). "Fils an Wavs in Communications Elctronics"; John Wily an Sons; pp [4.] Pozar, Davi M. (2005); "Microwav Enginring", Thir Eition (Intl. E.); John Wily an Sons, Inc.; pp ISBN [5.] Gonzalz, Guillrmo (1997); "Microwav Transistor Amplifirs Analysis an Dsign", Scon Eition; Prntic Hall NJ; pp , ISBN [6.] C.A. Balanis, Antnna Thory Analysis an Dsign, thir ition, Wily, Nw Jrsy, [7.] J.D. Kraus, Ronal J. Marhfka, Antnna for all applications Tata Mc-Grawhill 137 P a g

Y 0. Standing Wave Interference between the incident & reflected waves Standing wave. A string with one end fixed on a wall

Y 0. Standing Wave Interference between the incident & reflected waves Standing wave. A string with one end fixed on a wall Staning Wav Intrfrnc btwn th incint & rflct wavs Staning wav A string with on n fix on a wall Incint: y, t) Y cos( t ) 1( Y 1 ( ) Y (St th incint wav s phas to b, i.., Y + ral & positiv.) Rflct: y, t)