FEEDBCK MPLIFIERS Feedback n mplers FEEDBCK IS THE PROCESS OF FEEDING FRCTION OF OUTPUT ENERGY (VOLTGE OR CURRENT) BCK TO THE INPUT CIRCUIT. THE CIRCUIT EMPLOYED FOR THIS PURPOSE IS CLLED FEEDBCK NETWORK. Need or eedback: n open loop ampler wth hgh gan generally suers rom poor stablty n gan, small bandwdth, excesse dstorton and nose. Moreoer, the nput mpedance (Z ) o ampler should be hgh enough to aod the loadng eect wth the output secton o source (or precedng stage n multstage amplers) and the output mpedance (Z o ) should be low so that maxmum power can be delered at the output. To mproe one or more o the aboe characterstcs, eedback s employed n amplers. The amplers, whch use the eedback, are called eedback amplers. Basc ampler (ampler wthout eedback): Fgure shows the block dagram o a basc ampler. s the nput sgnal and 0 s the output sgnal. I s the oltage gan o the ampler, the output 0 s related to the nput by the equaton = 0. 0 = or s 0 Voltage gan s called the open loop gan and ths type o system s called open loop or non-eedback system. In ths system, the output sgnal gets dstorted, there s no mechansm to correct ths and hence the dstorton wll contnue to exst n the output sgnal. Prncple o eedback amplers: Fgure shows the block dagram o a eed back ampler. It conssts o two parts. They are, ampler crcut (called as basc ampler or ampler wthout eedback) and eedback network. The eedback network (or network) transers a racton 0 o the output oltage back to the nput secton. Ths changes the net nput oltage to the nternal ampler (ampler wthout eedback or basc ampler)..e., = s ±. Such a system s called as closed loop system or eedback system. Page o 4
s Basc ampler o R L o = S ± Feedback ampler = o Feedback network o Block dagram o a eedback ampler: [Basc ampler s also called as nternal ampler or ampler wthout eedback or the open loop ampler ]. Fgure shows the block dagram o a eedback ampler, where s s the source oltage or the nput oltage to the eedback ampler, o s the output oltage and s the nput oltage o nternal ampler whose gan s gen by, =, s called the eedback rato or eedback actor or reerse transmsson actor. The product s called loop gan = 0 s the eedback oltage. Voltage gan o the eedback o ampler s gen by, =. Due to the eedback, the net nput to the s nternal ampler changes to s ± 0. Dependng upon whether the eedback sgnal ncreases or decreases the net nput or the nternal ampler, there are two types o eedback n amplers. They are poste eedback and negate eedback. POSITIVE FEEDBCK: I the eedback sgnal (oltage or current) s appled n such a way that t s n phase wth the nput sgnal (.e., source sgnal) and thus ncreases the net nput to the nternal ampler, the eedback s sad to be poste. Here, the net nput to the nternal ampler s gen by = s. Poste eedback s also called as regenerate eedback or drect eedback. [The poste eed back ncreases the gan o an ampler smultaneously ntroducng sgnal dstorton and nstablty n gan. Due to ths reason, ths type o eedback s not generally used n amplers. But, poste eedback s employed n electronc oscllators]. o Page 2 o 4
Feedback n mplers NEGTIVE FEEDBCK: I the eedback sgnal (oltage or current) s appled n such a way that t s out o phase wth the nput sgnal (.e. source sgnal) and thus decreases the net nput to the nternal ampler, the eedback s sad to be negate. Here, the net nput to the nternal ampler s gen by = s -. Negate eedback s also called as degenerate eedback or reerse eedback. Negate eedback reduces the gan o an ampler. Howeer, t mproes the perormance o the ampler n many other aspects. dantages o negate eedback:. It ncreases the stablty o ampler gan. 2. It reduces the dstorton and nose. 3. It ncreases the nput mpedance. 4. It decreases the output mpedance. 5. It ncreases the bandwdth. Four ways o applyng negate eedback The negate eedback may be ether oltage or current. Ths can be ether n seres or n parallel. Thus, there are our basc ways o prodng the eedback sgnal; namely, a) Voltage-seres eedback b) Voltage-shunt eedback c) Current-seres eedback d) Current-shunt eedback. Voltage-seres eedback ampler: s Basc ampler o = S = o Feedback network It s also called as shunt dered seres ed eedback or oltage-oltage eedback ampler. Here, a racton o the output oltage s selected through eedback network and s appled n seres wth the nput source sgnal s (.e., = o ). Ths type o eedback ncreases the nput mpedance and decreases the output mpedance. The transer gan o ths ampler s Voltage amplcaton actor or Voltage gan as gen by the equatons = and o s = o wth and wthout eedback respectely. Thereore, ths s an example o true oltage ampler. In ths type o eedback, and hae no dmensons. Page 3 o 4
Voltage shunt eedback: S Basc ampler o = S - = 0 It s also called as shunt dered shunt-ed eedback connecton or Voltage- Current eedback. Here, the Feedback sgnal ( ) proportonal to the output oltage s deeloped by passng through the eedback net-work and s appled n parallel wth the nput source sgnal. Ths type o eedback decreases both the nput and output mpedances. The transer gan o ths ampler gen by the equatons o = wth and wthout eedback respectely and hae the dmensons o resstance. Ths type o ampler s a Trans-resstance mpler. The eedback actor o = υ o s = has the dmensons o conductance. Thereore, the loop gan has no dmensons. Current seres eedback: It s also called as seres dered, seres-ed eedback ampler or current-oltage eedback. Here, the eedback sgnal proportonal to the output current o s deeloped by the eedback network and then appled n seres wth the source sgnal. Ths type o eedback connecton ncreases both the nput and output mpedances. The transer gan o ths ampler gen by the o o equatons = and s hae the dmensons o conductance. Ths type o ampler s a Trans-conductance mpler. The eedback actor = has the o dmensons o resstance. Thereore, the loop gan has no dmensons. = wth and wthout eedback respectely and Basc ampler s - o = o =S- and Page 4 o 4 o
Feedback n mplers Current shunt eedback: It s also called as seres-dered shunt-ed eedback or current-current eedback. Here, the eedback sgnal proportonal to the output current s deeloped by the eedback network and appled n parallel wth the source sgnal. Hence, the nput mpedance decreases and the output mpedance ncreases. The transer gan o ths ampler s Current amplcaton actor or Current gan as gen by the equatons o = o s and = wth and wthout eedback respectely. Thereore, ths s an example o current ampler. In ths type o eedback, and hae no dmensons. Seres eedback Basc connectons tend to S ampler o ncrease the nput mpedance whle the shunt eedback connectons tend to o = S - decrease the nput mpedance. Voltage eedback tends to = 0 decrease the output mpedance, whle current eedback tends to ncrease the output mpedance. For most multstage amplers, hgh nput mpedance and low output mpedance are desrable. VOLTGE SERIES FEEDBCK MPLIFIER EXHIBITS BOTH THESE CHRCTERISTICS ND HENCE IS GENERLLY EMPLOYED. Expresson or the Voltage gan o oltage seres Negate eedback mpler S Basc mpler O V = o Feedback network V= s- Negate eedback ampler Page 5 o 4
Fgure shows the block dagram o a oltage seres eedback ampler where, s s the source oltage (nput oltage to the eedback ampler), o s the output oltage. s the eedback oltage and s gen by = o ---- (), where, s the eedback rato or reerse transmsson actor. s the nput oltage to the nternal ampler and s gen by, = s ------ (2) Gan o the nternal ampler (ampler wthout eedback) s gen by, 0 = ---- (3) Output oltage o the eedback ampler s gen by, 0 = = ( s ) [rom equaton (2)].e. o = ( s o ) [rom equaton ()].e. o = ( s o ) = s o.e. o o = s.e. o ( )= s or In the aboe equaton (4), the term eedback and s represented as.e., o s o s = = ------ (4) s the oerall gan o the ampler wth ------- (5) The actor (-) s called the loop gan or return rato. The oltage gan wth eed back s some tmes called as closed loop gan. The gan wthout eedback s called as open loop gan. The term /() s called Senstty actor and the term () s called desenstty. Equaton (5) shows that the gan o the negate eedback ampler s less than the gan o ampler wthout eedback. {Note: The oltage gan o a poste eedback ampler s gen by = } Page 6 o 4
Equaton 5 can be studed under the ollowng cases. Feedback n mplers. I ( )>, then < and the eedback s negate. 2. I ( ) <,.e., the loop gan s negate, > and the eedback s poste. 3. I ( ) = 0,.e, = -, o = =. s Ths means that the ampler s capable o gng maxmum output een when the nput s zero. Ths mples that the ampler behaes lke an oscllator. Ths s the specal case o a poste eedback ampler employed n oscllators.. Stablsaton o gan due to negate eedback :- [The gan o an ampler may change due to change n power supply oltage, temperature or change n the parameters o the acte dece (lke the current gan o the transstor). By applyng the negate eed back to such an ampler, stablty o the oltage gan can be mproed]. Consder a eedback ampler o gan. Let the gan wthout eedback be represented as. We know that the gan o negate eedback ampler s, = ----------------- (). Case : I the open loop gan o the ampler s ery hgh, then >>. In equaton (), neglectng compared to the loop gan, the term () becomes. = =.e, -------------- (a) Equaton (a) shows that the gan o a negate eedback ampler s ndependent o the nternal gan. depends only on whch s arly constant by usng hgh precson resstors lke Metal Flm Resstors ( s due to resste network.e, = R /(R R 2 ) ). Q Thereore, the gan s stablsed. Ths s possble >>. Een ths condton s not ully met, gan o negate eedback ampler s stable to some extent as shown n the next case. Case 2: I the loop gan s not ery hgh when compared to : Derentatng equaton () wth respect to, we get, d = d d d Page 7 o 4
( ) d ( ).e. = = d ( ) 2 ( ) 2 d d = 2 ( ) or Ddng the aboe equaton by equaton (), we get, d d ( ) = = 2 ( ) ( ) d = d In equaton (2), d change n gan wthout eedback. d change n gan wth eedback. gan wthout eedback. gan wth eedback. --------- (2) Snce ()> or negate eedback, the term <. Thereore, d < d. Gan s comparately stable wth negate eedback. 2. Reducton n Dstorton and Nose :- Negate eedback decreases the dstorton and nose n the output sgnal. When the nput sgnal to a transstor ampler s large, sgnal dstorton occurs due to the non lnearty o the transer characterstcs o the transstor. Ths results n dstorton n the shape o the sgnal. Due to the proper amount o negate eedback, strength o the nput sgnal to the nternal ampler decreases. s D Hence the dece s preented rom gong nto saturaton and cut o ponts o ts characterstcs. The eedback sgnal n negate eedback tends to decrease the strength o both the nput sgnal and the nose sgnal [because, along wth the eedback o the racton o actual output sgnal, negate eedback o the nose sgnal also takes place]. Thereore, the nose output decreases. Page 8 o 4 d D 0
Feedback n mplers Thus, the dstorton and nose are reduced n the output sgnal. In the output sgnal, D s the dstorton wthout eedback, D s the dstorton wth negate back and N s the nose wthout eedback, N s the nose ater negate eedback, we can wrte D = D and N = N Snce <, D < D and N < N. 3. Improement n requency response: Let BW be the bandwdth o the ampler wth eedback and BW be the Bandwdth wthout eedback and let be the eedback rato,, the oltage gan o the ampler wthout eedback and, the oltage gan o the ampler wth eedback. 0.707 Wthout eedback wth eedback 0.707 l BW 2 I 2 BW Frequency response cures o an ampler wth and wthout eedback. Snce the product o oltage gan and bandwdth s a constant (wth and wthout eedback) or an ampler, t can be wrtten that G BW = Constant -- () To satsy the aboe equaton or the ampler wth and wthout eedback, t can be wrtten as, BW = BW. where, the arables are dened as aboe. (.e., the oltage gan decreases rom to due to negate eedback, the Bandwdth ncreases rom BW to BW so that the gan band wdth product remans constant). Substtutng the relaton = n the aboe equaton, we get Page 9 o 4
BW = BW..e., ---- (2) BW = BW ( ) s per the aboe equaton, negate eedback ncreases the bandwdth by a actor equal to (). Further, the cuto requences are also aected by the negate eedback as shown below. I and are the lower cuto requences wthout and wth eedback respectely, t can be shown that, = -- (3).e., the lower cuto requency decreases rom to. Smlarly, 2 and 2 are the upper cuto requences wthout and wth / = ( 2 2 ) eedback respectely, t can be shown that, ---- (4),.e., the upper cuto requency ncreases rom 2 to wth negate eedback s gen by BW = l l 2 / 2. Thereore, bandwdth 4. Increase n the nput mpedance: Basc s Z Z mpler = o = s - Feedback network 0 Negate eedback ampler Voltage seres negate eedback ampler Consder a oltage seres eedback ampler. The nput mpedance Z o the nternal ampler (ampler wthout eedback) s gen by, Z = --------- () Where s the nput oltage to the nternal ampler and s the nput current. Wth negate eedback, the nput mpedance s gen by, Page 0 o 4
Feedback n mplers Z s = ------- (2) Output oltage o an ampler s gen by, 0 = -- (3) We know that or negate eedback ampler, the net nput to the nternal ampler s = S.e S =.e S = 0, Substtutng equaton(3), aboe equaton becomes, S =.e. S = (),Substtutng n equaton (2) we get ( ) Z = -------- (4). From equaton () and (4), Z = Z () Snce, ()> or negate eedback, Z > Z by a actor o (). 5. Decrease n the output mpedance: = 0 Z Oo Z O Basc ampler = Feedback network o Negate eedback ampler To nd the output mpedance (Z o ) o a oltage seres negate eedback ampler, the nput sgnal s made zero and a hypothetcal generator o oltage V O s connected across the output termnals. Snce the source sgnal s zero, the eedback sgnal alone s the net nput to the nternal ampler as shown n the gure..e, =. -------- () Ths sgnal gets ampled n the basc ampler and appears at the output secton as. From the basc theory o the eedback, = o ------ (2). Page o 4
Where, and are the Gan wthout eedback and eedback rato respectely. Let Z o be the output mpedance o the ampler wthout eedback and o be the output current wth eedback. ssumng the nput mpedance o the network to be ery hgh, the racton o output current passng through the nput secton o the network can be neglected. Thereore, or the output loop, we can wrte the ollowng equaton. o = o Z o. Usng equaton (), o = o Z o (- ). Usng equaton 2, we can wrte o = o Z o - o.e. o Z o = o o = o (). Z o O.e. = o where, ( ) o o =Z o the output mpedance wth eedback. Z o Z = O ( ) ------- (3). For negate eedback, the term () >. Z O < Z O. Thus, the output mpedance s reduced by a actor (). Crcut examples o derent types o negate eedback:. Voltage Seres eedback: Crcut o Common collector ampler shown Vcc here s an example o oltage seres negate eedback ampler. The eedback oltage s R same as the emtter oltage E whch s C B nothng but the output C E oltage..e., E = o. pplyng KVL to the s R 2 nput secton o the crcut BE we get the relaton or the o o eecte nput oltage n terms o the nput sgnal oltage and the eedback oltage as Page 2 o 4
Feedback n mplers υ S = υ υ o, hence the net nput oltage ( = BE ) to the emtter-base juncton (nternal ampler) s gen by BE = s - o. In ths crcut eedback sgnal depends only on the output oltage and ths s ed n seres wth the orgnal sgnal, hence the name. In ths crcut eedback racton s gen by = υ /υ o = υ o /υ o = =00% Snce the whole o the output oltage s ed back to the nput, the negate eedback here s 00%. 2. Current Seres eedback: V CC The crcut shown s a Common Emtter ampler wthout emtter bypass capactor. Snce the emtter resstor s uncoered all the a.c emtter current wll low through the emtter resstor and there wll be a.c oltage drop across the resstor. Ths oltage s eedback to the nput wth opposte phase(ce mode). The eedback oltage s proportonal to the output current E ( c ) and s n seres wth the orgnal sgnal hence the name current seres negate eedback. The eedback oltage s gen by = E = E R E. C B s R R 2 BE R C R E E C C R L o The eedback oltage gets subtracted rom the nput source sgnal and hence the net nput oltage ( = BE ) to the emtter-base juncton (nternal ampler) s gen by BE = s - E R E. The eedback racton n ths crcut s gen by = E / o 3. Voltage Shunt eedback: Crcut employng the oltage shunt negate eeedback s shown n the g. Feedback s through the Resstor R B connected between the collector and the base. The eedback sgnal s the current. It s proportonal to the output oltage o. The eedback actor s gen by = o. Ths crcut exhbts low nput and output mpedances. s C B R I V C R C C C O Page 3 o 4
4. Current Shunt eedback: The crcut shown s an example or current shunt eedback. The eedback current proportonal to the output current 0 (emtter current E ) s selected through the eedback network and s appled n parallel wth the nput current source. Vcc R R C C C C B s R 2 R E E C E R L o E Feedback network Page 4 o 4