Digitally Programmable Grounded Impedance Multiplier

Transcription

1 Itratioal Joural of Egirig sarch ad Dvlopmt -ISS: X, p-iss: X, Volum 11, Issu 0 (Fbruary 015), PP.4-8 Digitally Programmabl Groudd Impdac Multiplir. Afzal Dpartmt of Elctroics ad Commuicatio Egirig, Jamia Millia Islamia, w Dlhi-11005, Idia. Abstract:- A ovl digitally programmabl gralizd impdac multiplir is prstd. It uss scod gratio currt covyor ad a digital cotrol modul. Th w multiplir ca provid digital cotrol to groudd impdac fuctios such as, rsistor, capacitor, iductor without quatizig th sigal. Th tchiqu usd is simpl, vrsatil as wll as compatibl for micromiiaturizatio i cotmporary IC tchologis. Th simulatio rsults o digitally programmabl gralizd impdac multiplir vrify th thory. Kywords:- Currt covyor, multiplir. I. ITODUCTIO I rct yars th scod gratio currt covyors (CCIIs) hav provd to b fuctioally flxibl ad vrsatil buildig block. It possss highr sigal badwidth, gratr liarity ad larg dyamic rag [1-]. As a rsult it is gaiig wid accptac as a buildig block for dsigig voltag/currt mod aalog sigal procssig circuits [3-6]. I th mixd sigal systms th o chip cotrol of th systms paramtr ca b providd through digital mas with high rsolutio capability ad th rcofigurability[4-7]. Howvr, ot much cott is availabl i th tchical litratur o th subjct. I this papr a ovl digitally programmabl groudd multiplir (DPGIM) usig scod gratio currt covyor is prstd. To dmostrat th vrsatility of th DPGIM, digitally cotrolld groudd rsistor(), capacitor(c) ad iductor ar ralizd. Th circuit cosists of a CCII, a digital cotrol modul (DCM), which is ralizd usig - laddr ad a -bit switchig array, alog with impdac udr cotrol. Th ralizd DPGIM is simulatd for positiv ad gativ rsistors usig PSPICE. II. DIGITAL COTOL MODULE Th ralizatio of th digital cotrol modul (DCM) usd i th DPGIM is show i Figur 1(a), which uss - laddr ad aalog switchig array [6]. Its routi aalysis yilds th output voltag V as Fig. 1(a): Digital Cotrol Modul-Th DCM. 1 V A0 A1 4A A 1 (1) whr, A 0, A 1,, A -1 ar th bit valus of th -bit digital cotrol word (). Equatio (1) ca also b xprssd as whr, K 1 = /. V () K1V 1 Th quivalt of th Figur 1(a) is giv i Figur 1(b) ad ow owards shall b xprssd as th K 1 - Block. If two stags of th K 1 - Block with sam cotrol word ar cascadd through a voltag buffr as show i Figur 1(c), 4

2 Digitally Programmabl Groudd Impdac Multiplir K1 V Th trasfr gai ca b xprssd as Fig 1(b): Th K 1 Block. V K (3) whr, K = K 1 K 1 = (/ ). Hcforththis doubl stagblock shall b rfrrd as th K Block. Its quivalt is also show i Figur1(c). It is obvious from quatio () ad (3) that th trasfr gai of th K 1 ad K moduls ca b cotrolld through digital cotrol word (). Fig. 1(c): Th K Block Th j th digital switch usd i th DCM is show i Figur 1(d), whr, j rags from 0 to -1. Fig. 1(d): Th j th Digital Switch. III. CICUIT EALIZATIO Th proposd DPGIM usig a CCII ad a DCM is giv i Figur. Th routi aalysis yilds its impdac fuctio as V Z i KZ (4a) I Fig. : DPGIM for positiv impdac paramtrs 5

3 Digitally Programmabl Groudd Impdac Multiplir whr, K (= / )is th trasfr gai of th DCM ad is a -bit cotrol word. Thus, th ralizd impdac of quatio (4) rducs to Zi Z (4b) It is to b otd that for gativ CCII th ralizd impdac Z i is positiv whil for positiv CCII, agativ Z i is ralizd. From quatio (4b) it is clar that th impdac s at th iput port of th Figur ca asily b cotrolld by digital word, i tur th trmiatig impdac Z is cotrolld. Th trmiatig impdac Z may b slctd ithr rsistor(), capacitor (C) or iductor (L) or ay combiatio of ths compots. Thus th circuit ralizs digitally cotrolld positiv as wll as gativ impdac multiplir Cas 1: Digitally Programmabl I Figur, if Z is cosidrd as rsistor i.., Z =, quatio (4) rducs to Z i = (5a) For K = K 1 ad for K = K (5b) (5c) It is ca b s from quatio (5) that th ralizd ffctiv rsistac is programmabl through digital cotrol word. For, K=K 1, is dirctly rlatd to th digital cotrol word, whil for K=K, It is dirctly rlatd to. Cas : Digitally Programmabl C If Z i Figur is assumd as capacitor i.. Z = 1/sC, quatio (4) rducs to Z i 1 (6a) sc For K = K 1 C C (6b) whil for K = K C C (6c) Thus it is obvious from quatio (6) that through digital cotrol word (), th ralizd ffctiv capacitac(c ) ca b cotrolld ivrsly through or. Cas 3: Digitally Programmabl L I Figur if Z is cosidrd as a iductor i.. Z = sl, quatio (4) rducs to Z i = s L (7a) Agai for K = K 1 L L (7b) ad for K = K 6

4 (KOhm) I (ma) Digitally Programmabl Groudd Impdac Multiplir L L (7c) Thus by cotrollig th digital cotrol word th ralizd ffctiv iductac L is also programmabl ithr through or. IV. SIMULATIO ESULTS Th practical validity of th proposd digitally programmabl groudd impdac multiplir is simulatd usig PSPICE for. Th SPICE modl of CCII availabl i th tchical litratur was usd []. Th digital cotrol modul of Figur (1) was implmtd for 4-bit with W/L ratio of uity. Th voltag - currt plot obtaid from PSPICE simulatio for th DGPIM of Figur with =100KOhm for various is show i Figur 3(a). = 8 = =3 =3 4 =6 =6 =15 =15 0 V (mv) Fig. 3(a): V-I plot for digitally programmabl positiv ad gativ rsistors for \ diffrt digital cotrol word ralizd from th DPIM (simulatd) (Thoritical) Fig. 3(b): Variatio of with for positiv ad gativ rsistor. 7

5 Digitally Programmabl Groudd Impdac Multiplir Also, by varyig th digital cotrol word () th rsistac is cotrolld ad th rsults obtaid ar show i Figur 3b. Th Figur 3 clarly xhibits th rsposs i clos coformity with th dsig. V. COCLUSIO A digitally programmabl impdac multiplir usig CCII is prstd. This impdac multiplir ralizsdigitally cotrolld positiv as wll as gativ groudd rsistor, capacitor, ad iductor. Th tchiqu usd is simpl vrsatil as wll as compatibl i cotmporary IC tchologis. It is to b otd that th digitally programmabl circuit paramtrs i all th ralizatios ar rcofigurabl. Th rsolutio of th digital cotrol ca b improvd by usig largr umbr of bits i th digital cotrol modul. Th ralizd circuit was dsigd ad simulatd for usig PSPICE. Th rsults thus obtaid vrify th thory. EFEECES [1]. B. Wilso, (199). Tutorial rviw: Trds i currt covyors ad currt mod amplifir dsig. It. J. Elctroics, 73(3), []. J. A. Svobodo, (1994). Trasfr fuctio sythss usig currt covyors. Itratioal Joural of Elctroics, 76, [3]. I. A. Kha ad Mahshwari, (000). Simpl first ordr all pass sctio sigl CCII. Itratioal Joural of Elctroics, Vol. 87, o. 3, pp [4]. H. Alzahr, (006). CMOS digitally programmabl iductac, ICM 06, Saudi Arabia. [5]. S. M. Al-Shahrai, ad M. Al-Gahtai, (006). A w poly-phas currt-mod filtr usig digitally programmabl currt-cotrolld currt-covyor, ICM - 06, Saudi Arabia. [6]. I. A. Kha, M.. Kha ad. Afzal, (006). Digitally programmabl multifuctioal currt mod filtr usig CCIIs. Joural of Activ ad Passiv Dvics. Vol. 1, pp [7]. V. Lakshmiarayaa, (1997). Frqucy programmabl aalogu basd pass filtr. Elctroics world, pp