Chapter 6. Operational Amplifier. inputs can be defined as the average of the sum of the two signals.
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1 6 Operatonal mpler Chapter 6 Operatonal mpler CC Symbol: nput nput Output EE () Non-nvertng termnal, () nvertng termnal nput mpedance : Few mega (ery hgh), Output mpedance : Less than (ery low) Derental and Common Mode Operaton: One o the more mportant eatures o a derental crcut connecton as provded n an op-amp s the crcut ablty to greatly amply sgnals that are opposte at the two nputs whle only slghtly amplyng sgnals that are common to both nputs. n op-amp provdes an output component that s due to the amplcaton o the derence sgnals appled to the plus and mnus nput and a component due to the sgnals common to both nputs. Snce amplcaton o the opposte nput sgnals s much greater than that o common nput sgnals the crcut provdes a common-mode rejecton as descrbed by a numercal value called COMMON MODE EJECTON TO (CM). Derental nput: When separate nputs are appled to the op-amp, the resultng derence sgnal s the derence between the two nputs. d Common nput: When both nput sgnals appled to an op-amp s common, sgnal element due to the two nputs can be dened as the average o the sum o the two sgnals. C. Output oltage: Snce any sgnal appled to op-amp n general have both n phase and out o phase components the resultng output can be expressed as dd c c. Where d = derence voltage, C = common mode voltage, d = derence mode gan o the ampler, c = Common mode gan o the ampler. CM {Common Mode ejecton ato}: CM d c The value o CM can also be expressed n log term as d CM(n db ) log ( db) c
2 Operatonal mpler Equvalent Crcut: Whle an nput to the mnus () nput results n on opposte polarty output. The ac equvalent crcut o the op-amp s shown n gure. s shown the nput sgnal appled between nput termnals sees as nput mpedance typcally very hgh. The output voltage s shown to be the ampler gan tmes the nput sgnal taken through output mpedance, whch s typcally very low. n deal op-amp crcut, as shown n gure would have nnte nput mpedance zero output mpedance and nnte voltage gan. 7 d d op-amp d d d d nvertng mpler: The most wdely used constant gan ampler crcut s the nvertng ampler. op-amp. We can wrte () sgn represent 8º phase. Non-nvertng mpler: The connecton o gures shows an op-amp that works as a non-nvertng ampler or constant gan multpler. t should be noted that the nvertng ampler connecton s more wdely used because t has better requency stablty. n p By vrtual ground law: n = p = oltage Follower or Unty Follower: The unty ollower crcut as shown n gure provdes a gan o unty () wth number polarty or phase reversal. From the equvalent crcut, t s clear that and that the output s the same polarty and magntude as the nput. The crcut operates lke an emtter or source ollower crcut except that the gan s exactly unty. op-amp
3 8 Summng mpler: Three nput summng ampler. Operatonal mpler Derentator : derentator crcut s shown n gure whle not as useul as the crcut orms covered above the derentator does provde a useul operaton, the resultng ar the crcut beng d ( t) ( t) C dt (t) C op-amp (t) where the scale actor s C. C ntegrator: op-amp (t) ( t) ( t) dt C Oset Currents and oltages {d.c. characterstc o op-amp}: B B () nput bas current : B B () nput oset current: s = B B (3) nput oset voltage : s = Note: Due to msmatchng between and output voltage may be postve or negatve so we apply oset voltage ( os ). Slew ate: nother parameter relectng the op-amp s ablty to handlng varyng sgnal s slew rate, dened as slew rate = maxmum rate at whch ampler output can change n volts per mcro second. S / s t wth t n s.
4 Operatonal mpler SOLED POBLEMS. Calculate the slew rate o gven crcut. 9 K 3 (., = 3 ) 4K Soln. For a gan o magntude K = CL, = 4(.).48 S.5v / s K.48 CL F 4K 4. The output voltage provdes. K 6. rad/sec oltage Buer: voltage buer crcut provdes a means o solaton on nput sgnal rom a load by usng a stage havng unty gan wth no phase or polarty nverson. Controlled Sources: Op-amp can be used to orm varous types o controlled sources. n nput voltage can be used to control on output voltage or current or an nput current can be used to control on output voltage or current. There type o connectons are sutable ar use n varous nstrument system (crcut). t has our types: () oltage Controlled oltage Source () oltage Controlled Current Source (3) Current Controlled Current Source (4) Current Controlled oltage Source () oltage Controlled oltage Source: n deal orm o a voltage source whose output s controlled by on nput voltage J s shown n gure. The output voltage s seen to be ndependent on the nput voltage. Ths type o crcut can be bult usng an op-amp as shown n gure. () nvertng op-amp: n p K By vrtual ground condton n = p = Now KCL at pont,
5 3 () Non-nvertng op-amp: Operatonal mpler By vrtual ground condton p = n = Now KCL at pont n K p O o () oltage Controlled Current Source: n deal orm o crcut provdng an output current controlled by an nput voltage s that o gure. The output current s dependent on the nput voltage. Practcal Crcut: (3) Current Controlled oltage Source: n deal orm o a voltage source controlled by a nput current s shown n gure. The output voltage s dependent on the nput current. Practcal Crcut: L L (4) Current Controlled Current Source: n deal orm o a crcut provdng on output current dependent on an nput current s shown n gure. n ths type o crcut on output current s provded dependent on the nput current. Practcal Crcut: L K Low Pass Flter: st order, low pass lter usng resstor and capactor as n gure shown has a practcal slope o db per decade as shown n gure (rather them the deal response o gure). The voltage gan below the cuto requency s constant at v G, at a cut o requency o OH C
6 Operatonal mpler 3 ~ G ( ) ( ) ( ) Output voltage / OH db/decade Second Order Flter: Connectng two sectons o lter as n gven gure result n a second order low pass lter wth cut o at 4 db decade closer to the deal characterstc. 4 / op-amp C C db/decade 4 db/decade Hgh-Pass ctve Flter: Frst and second order hgh-pass actve lter can be bult as shown n gure. The ampler cut o requency s OL s the same cut o requency as n gure. C wth a second order lter = and C = C result 4 4 C op-amp C C op-amp / db/decade OL OH 4dB/decade Band Pass Flter: Fgure shows a band pass lter usng two stages. The st a hgh pass lter and the second a low pass lter. The combned operaton beng the desred band pass response. 4 4 C op-amp op-amp C Hgh Pass Secton Low Pass Secton
7 3 Operatonal mpler (md) db/decade db/decade OL OH nstrument mpler: L Calculaton o output voltage: ( )... ()... ()... (3) ( )( ) ( ). n ctve lter shown n gure. The DC gan and 3dB out o requency are nearly. C v = 5.9K, = 59K, C = nf (a) 4dB, 3.4KHz (b) 4dB, KHz (c) db, 68KHz (d) db, KHz Soln: D( s) / ( CS ) ( C S) ( S )
8 Operatonal mpler 33 db log {log } t 3dB requency ( S ) ; ( S ) ( C) Snce, DC gan On puttng the value o, C and comparng L.H.S. and.h.s. = KHz 3. n the gven op-amp nd, the value o output voltage. Gven = d.c. and = 4 d.c., OL = 5, CC = 5. nvertng termnal Non-nvertng termnal Soln: Let OL s open loop voltage gan. n ths care = ( ) OL = (4.) =.4 [ sat output wll vary between sat and sat ] =, = 4 = (4 ) 5 6 = =. For deal Op-amp (Open Loop): nput and output voltage characterstc o open loop Op-amp. sat sat t s clear that open loop op-amp s able to amply sgnals o very small ampltude. So, practcally, open loop Op-amp s not used. For deal Op-mp (Open loop): () =, () OL =, () =, (v) Slew rate = (v) CM = (v) Band wdth = P n deal Op-amp = OL ( ) OL p n ( ) p n OL p n
9 34 Operatonal mpler Concept o rtual Ground: = OL = (deal case) OL n deal case, = = 4. n the gven op-amp crcut. Fnd the output voltage. 4K =. S 4K Current s zero =K Soln. The gven op-amp s nvertng ampler. By the nvertng ampler gan ormula. Gven, = 4K, = 4K, =. = For the gven op-amp crcut. Fnd voltage gan. 45K B K K p n K Soln. pplyng KCL at pont. 4.5 () Now KCL at pont B. 45 (Now by equaton () = 4.5 ) On solvng
10 Operatonal mpler n the gven gure o OP-amp. Fnd the value o resstance. Gven B K K K p n Soln. By vrtual ground condton KCL at pont K K p n.... () K Now KCL at pont B... () K K (Gven)... () By equaton (), () and (), = 45K 7. n the gven crcut o op-amp. Fnd and L. K K = 5K L Soln. Ths s nvertng ampler = For current L ( ) 5K L L.4m For current, 5 ( ) K =.m = L =.4..5 m
11 36 8. Based on Non-nvertng ampler. Operatonal mpler K 5K p n = L 5K. From the above gven op-amp. Fnd L and? Soln. By GP, n = p =. KCL at pont, 5 5 L = m = 5 5 = m, = 5 So, the current drecton o and wll be reverse. 9. n the gven gure o op-amp. Fnd the value o and L? =.m, = L = (.) = (.)m 4K K p n 5 L 5K Soln. Ths s non-nvertng ampler. p = n = 5 by GP. Now, KCL at pont, 5 5 D D 5 K 4K, L 5 5 m L 5 5m, 5K 5 5 5m 4K 4 oltage Follower: Means a unty gan non-nvertng op-amp. Open crcut = (a), (b), (c), any value o (d) = For whch value o and t makes voltage ollower. oltage Follower: n out ery hgh ery low Ths resstance range s used or mpedance matchng or used as buer.
12 Operatonal mpler Derence mpler: 37 n p n the above gven op-amp gure. Fnd the value o output voltage n term o and. Soln. By the GP condton p = n =. For the upper loop, For the lower loop,... ()... (). ( ) Now puttng the value o equaton () n equaton ()... () ( ) or deal subtractor crcut CM s Super Poston, Prncple: Let be at ground, then. ( ). ; ( ) Now, when be at ground, then,. ; Total ( )
13 38. n the gven op-amp crcut. Fnd the output voltage? Operatonal mpler 33K 4 K = K 3 n p = 33K 4 Soln. = 3(4 ), = 6 volt 4 Hence,, then 3 ( ) or ( ) 4 3. n the gven op-amp crcut. Fnd the value o. K 4 K K p 9K Soln. Frstly, consderng rst nvertng loop, Now, consderng non-nvertng loop P = = dder: (39.6 ( )) 9.6olt n 3 p 3 Soln: By GP n = p = 3 KCL at pont 3( 3 ) 3 So, the above op-amp s workng as a nvertng adder. For the gven op-amp crcut. Fnd the value o output voltage. 3 B =
14 Operatonal mpler 39 3 Soln. KCL at pont B or ( ) ( ). ( 3 ) 3 So, ths s non-nvertng adder.. n the gven op-amp gure. Fnd the output voltage. ( ) 5K K 5K K K n B p Soln. By GP condton (rtual Ground Poston) ( p = n ) Let p = p =. Now, KCL at pont B, 4 5 p p 3 p olt 3 Now, KCL at pont, n n n 3 n n n, Now puttng the value o n, n p K 3. Soln. 8 5 K K 4K n p. n the above gven op-amp crcut, nd output voltage. p = n = (By GP) KCL at postve termnal, olt KCL at postve termnal, olt K 3
15 4 Operatonal mpler 4. For the gven op-amp crcuts. Fnd. K K 3 = = Soln. For the op-amp... (), ths s non-nvertng ampler. Op-amp () s workng lke buer, = Op-amp (3) s workng lke nvertng ampler, 5. n the gven op-amp crcut nd output voltage. 3K K B K 4K.4m Soln. Because = =.4 m 3K.4 m; B.4.4,.4 ; K
16 Operatonal mpler 6. n the gven op-amp crcut nd and. 4 8K.m n p L K = L Soln: By GP n = p = Now, KCL at pont. =.8olt, 8 7. n the gven op-amp gure. Fnd the output voltage. L.8.4 m, =.4. =.5m L = = 5 K 5K K 5K B K = 3 Soln. By GP, B = =, Now, KCL at pont, 5 5 3olt ( 3) 4 Now, KCL at second OP-ampler ; 5 5 T olt 8. n the gven Op-amp crcut. Fnd? 3K = = K K n p K Soln. p.5, By GP condton, n = p = Now, KCL at pont,.5olt 5 3
17 4 9. n the gven Op-amp crcut. Fnd output voltage. 8K 5K ~ = K 68K 75K 33K B Operatonal mpler Soln. We wll st calculate, ; Smlarly on solvng, B , 4, B olt olt, =.49 olt. Calculate the output voltage or the crcut wth nput = 4m, = m. 47K K B 47K Soln. = B =, Now applyng KCL n nvertng loop 47 47, 4 (4 47) (48 94) m.83olt 6 6. Calculate the output current n the gven crcut. = m K B F K Soln. Potental at and B ponts are equal by GP..e. = B = Now applyng KCL n nvertng loop K Now, k
18 Operatonal mpler. n the gven Op-amp crcut. Fnd and? 3K 43 4k m B = L 6K Soln. pplyng KCL at pont B, 4K 3K (5 olt) 3K L.5m mp, 6 5 5m, L 7.5m 3K 3. n the gven crcut nd voltage gan K. K n p 3K K Soln. n the non-nvertng loop applyng KCL let p = n = n the 4,. 3 4 n the nvertng loop applyng KCL, 4. n the gven crcut. Fnd 4 8 4? K 6K 4K Soln. 6 4 ; 6
19 44 5. n the gven crcut nd? Operatonal mpler 3K 6 B K 3K n p Soln. n = p = {GP}, Now, KCL at pont, 6 B B 4 3 Now, KCL at pont B, B 3 B B 6. n the crcut calculate the output voltage? 4, K 6K D D K = Soln. () = 3, then? () = 3, then? () When = 3, dode D wll on, Now KCL n D loop 3 6 9olt () When = 3, dode D wll on, Now, KCL n D loop olt 7. n the gven crcut calculate S. S B 4K K K Now, KCL at pont. 5( ) ( ) 4
20 Operatonal mpler Now, KCL at pont ( S ) S 8. n the gven crcut nd value o L S 7 7 S S n p L L Soln. By GP, n = p =. Frstly, KCL n non-nvertng termnal L... () Smlarly, KCL n nvertng termnal... () Now, puttng value o () n equaton () L, L L DC Characterstc o Op-amp: () nput bas current (For DC analyss) () nput oset current () nput oset voltage B () nput bas current = B B. Let B B, ; To compensate eect o nput bas current comp s used. comp B B () nput oset current;, OS output, due to nput oset current. OS B B () nput oset voltage; OS, output to nput oset; OS.
21 46 K Operatonal mpler 9. K Calculate L, Gven OS = m, B = 3n, OS = p. Fnd (a) Calculate maxmum output voltage due to OS and B. (b) Calculate comperate. (c) Calculate output voltage comp s connected. Soln. () we are consderng nput bas current then OS =, as we have already assumed. () comp s connected, then nput bas current wll not consdered, only OS wll be consdered. comp s connects then or zero nput = zero output. B B (a).. OS B (b) comp K =..3n 3m 3m (c). OS OS = m K p = m.m.m 3. nput oset voltage = 4m, nput oset current = 5n, nput bas current = 3n. 5K 5K 5K Soln.. OS OS = = 479mvolt. Calculaton o CM = 5.4m 5K 5n 5 = 4 75 CM d d = derental mode gan, C = Common mode gan C d d C C, d C, d C d C, C d
22 Operatonal mpler 3. n the gven crcut. Fnd the value o CM? 47 Soln. ( ), ( ), d d For C,. C CM 3. n the op-amp crcut, CM = 4dB and d = 5dB. Fnd C. Soln. Here, CM = Common Mode ejecton ato d = Derence Mode gan, C = Common Mode gan CM and d are gven n db. Frst o all we wll change t n normal value. 4dB = log CM CM = 4 5dB = log d () d =.5 = 36. CM = C = 3.6 d C = C d CM 36.7 Slew ate: = sn t = = = 33. What s the maxmum value o nput voltage gven to an voltage ollower so, that there s no dstorton (Slew rate s gven). Soln: sn t, Slew ate = m. cos t, S.. = m 34. For the crcut shown below the value o s S. m. m K 6 K 48K n p 6K 5K (a) 4 3 (b) 3 (c) 3 (d) 4 3
23 48 Operatonal mpler 66 Soln. p = , p For the crcut shown below the nput resstance s = 4 () 3 3 s n p 4K K s K z (a) 38K (b) 7K (c) 5K (d) 47K Soln. Snce op-amp s deal, n p, k s 4k s, s k s k, s s s s s k s k( s ) k k 7K s s s n s 36. The voltage transer characterstc o an operaton ampler s shown n gure. What are the values o gan and oset voltage or ths op-amp (m) n (a), m (b) 75, m (c), m (d) 75, m Soln. ( n OS ), OS Oset oltage, oltage Gan d ( 5) 75 d ( ) m, When =, n = OS n Oset voltage s OS n / m 37. n nvertng operatonal ampler shown n gure has an open gan o and closed loop gan o 4, gan error s n (a).4% (b).5% (c).5% (d) % Soln. Gan error s gven as g, = (Open loop gan) 4 (Closed loop gan), g ( 4).5%
24 Operatonal mpler n the ollowng non-nvertng ampler. The op-amp has an open loop gan o 86dB, gan error s 5K K n (a).5% (b).3% (c).93% (d).675% Soln. Gan error or non-nvertng ampler s gven by g where open loop gan log 86(gven),, = 5 K, = K So, gan error s 5 g 6.75, 4 or g.675% 39. Op-mp o a gven gure has open loop gan o 45. What s closed loop gan o an op-amp. K= =K n Soln. For non-nvertng Derentator: CL OL c N C n p comp = d = C dt d d By GP, p = n =, Now, KCL at pont N, C C ( N ) C dt dt, ths s ar capactor current. For eedback resstor. d d C dt C dt We may now wrte the magntude o gan o the derentator as, or where a J C C a C
25 5 4. n the gven derentator, = sn( t). Draw wave orm o. Operatonal mpler =.5K C.F d Soln. C, dt..5.cos ( t). 6 3 t t 3 cos( ).9 cos( ) 5m sec 5m sec.9 Practcal Derentator:.9 Z Z C C comp = = ( >> ) ( s) Z S C Ths s nvertng op-amp: Z ( S ( )( SC ) For C C, we get ( s) ( S ) S C S C ( S ) ( SC ) j b Where, b C
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