chedule Date Day Class N. Title Chapters HW Due date 29 Oct Wed 17 Operatinal mplifiers 8.1 8.2 Lab Due date Exam 30 Oct Thu 31 Oct ri ecitatin HW 7 1 N at 2 N un 3 N Mn 18 Operatinal mplifiers 8.3 8.4 4 N Tue 5 N Wed 19 Binary Numbers 13.1 13.2 LB 6 ECEN 301 Discussin #17 Operatinal mplifiers 1
Increase Helaman 12:2 2 Yea, and we may see at the ery time when he dth prsper his peple, yea, in the increase f their fields, their flcks and their herds, and in gld, and in siler, and in all manner f precius things f eery kind and art; sparing their lies, and deliering them ut f the hands f their enemies; sftening the hearts f their enemies that they shuld nt declare wars against them; yea, and in fine, ding all things fr the welfare and happiness f his peple; yea, then is the time that they d harden their hearts, and d frget the Lrd their Gd, and d trample under their feet the Hly One yea, and this because f their ease, and their exceedingly great prsperity. ECEN 301 Discussin #17 Operatinal mplifiers 2
Lecture 17 Operatinal mplifiers ECEN 301 Discussin #17 Operatinal mplifiers 3
Ideal mplifiers mplifier: a deice fr increasing the pwer f a signal. Pwer increase is called gain () 0:21 CD (t) Gain L L urce mplifier Lad urce mplifier Lad L ( t) ( t) ECEN 301 Discussin #17 Operatinal mplifiers 4
Ideal mplifiers implified mplifier Mdel: The surce sees and equialent lad ( in ) The lad sees and equialent surce ( in ) (t) Gain L L (t) in in in ut L L urce mplifier Lad NB: Théenin equialent NB: equialent resistance ECEN 301 Discussin #17 Operatinal mplifiers 5
Ideal mplifiers The gain is dependent n the surce and lad (i.e. is different fr different surces and lads) (t) in in in ut L L in L in in ut in L L L in in ut L L NB: expressin fr L depends n the surce ( ) and the lad ( L ) ECEN 301 Discussin #17 Operatinal mplifiers 6
Ideal mplifiers The gain can be made t be almst independent f the surce ( ) and the lad ( L ) Let in Let ut 0 (t) in in in ut L L if in in : in in if ut L 0 in in ut L L L NB: it is desirable fr an amplifier t hae: a ery large input impedance a ery small utput impedance ECEN 301 Discussin #17 Operatinal mplifiers 7
Op-mps Operatinal mplifier: riginally designed (late 1960 s) t perfrm mathematical peratins (analg cmputer) dditin ubtractin Integratin differentiatin Psitie pwer supply (usually 15V) V Inerting Input Nninerting Input Output NB: the pwer supplies (V and V ) are ften mitted in drawings they are implicit V Negatie pwer supply (usually 15V) ECEN 301 Discussin #17 Operatinal mplifiers 8
Op-mps Open-Lp Mde Open-Lp Mdel: an ideal p-amp acts like a difference amplifier (a deice that amplifies the difference between tw input ltages) in i 2 i in i 2 in ut OL in NB: p-amps hae near-infinite input resistance ( in ) and ery small utput resistance ( ut ) OL OL in ( ) OL pen-lp ltage gain ECEN 301 Discussin #17 Operatinal mplifiers 9
Op-mps Open-Lp Mde Open-Lp Mdel: an ideal p-amp acts like a difference amplifier (a deice that amplifies the difference between tw input ltages) in i Ideally = i 2 = 0 (since in ) i 2 i 2 0 ECEN 301 Discussin #17 Operatinal mplifiers 10
Op-mps Open-Lp Mde Open-Lp Mdel: an ideal p-amp acts like a difference amplifier (a deice that amplifies the difference between tw input ltages) i 2 0 What? N input current?? In reality there is a small current ECEN 301 Discussin #17 Operatinal mplifiers 11
Op-mps Clsed-Lp Mde The Inerting mplifier: the signal t be amplified is cnnected t the inerting terminal i (t) i i 2 ECEN 301 Discussin #17 Operatinal mplifiers 12
Op-mps Clsed-Lp Mde The Inerting mplifier: the signal t be amplified is cnnected t the inerting terminal (t) Nde a i i eedback current: current frm the utput is fed back int the input f the p-amp i KCL at Nde i i i 0 i i 0 1 i 1 a : i ECEN 301 Discussin #17 Operatinal mplifiers 13
Op-mps Clsed-Lp Mde The Inerting mplifier: the signal t be amplified is cnnected t the inerting terminal (t) i i rm Open - Lp Mdel OL OL OL ( (0 OL ) ) : ECEN 301 Discussin #17 Operatinal mplifiers 14
Op-mps Clsed-Lp Mde The Inerting mplifier: the signal t be amplified is cnnected t the inerting terminal (t) i i / OL i i 1 / OL / OL OL OL 1 / 1 OL ECEN 301 Discussin #17 Operatinal mplifiers 15
Op-mps Clsed-Lp Mde The Inerting mplifier: the signal t be amplified is cnnected t the inerting terminal (t) i NB: if OL is ery large these terms 0 i 1 / Clsed CL - Lp OL 1 Gain / : 1 OL ECEN 301 Discussin #17 Operatinal mplifiers 16
Op-mps Clsed-Lp Mde The Inerting mplifier: the signal t be amplified is cnnected t the inerting terminal rm Open - Lp Mdel : i ut OL (t) i NB: as OL 0 s OL ECEN 301 Discussin #17 Operatinal mplifiers 17
Op-mps Clsed-Lp Mde The Inerting mplifier: the signal t be amplified is cnnected t the inerting terminal i NB: tw imprtant results fr an ideal p-amp with negatie feedback (t) i i 2 i i 0 1 2 ECEN 301 Discussin #17 Operatinal mplifiers 18
Op-mps Clsed-Lp Mde Example1: determine OL and = 1kΩ, = 10kΩ, s (t) = cs(ωt), =0.015, ω = 50 rads/s i (t) i ECEN 301 Discussin #17 Operatinal mplifiers 19
Op-mps Clsed-Lp Mde Example1: determine OL and = 1kΩ, = 10kΩ, s (t) = cs(ωt), =0.015, ω = 50 rads/s (t) i i CL 4 10 0.015 cs( 3 10 0.15 cs( t) t) CL 10 ECEN 301 Discussin #17 Operatinal mplifiers 20
Vltage (V) Op-mps Clsed-Lp Mde Example1: determine OL and = 1kΩ, = 10kΩ, s (t) = cs(ωt), =0.015, ω = 50 rads/s (t) i i 0.15 0.10 0.05 0.00-0.05-0.10-0.15 0.0 0.2 0.4 0.6 0.8 1.0 time (s) s(t) (t) ECEN 301 Discussin #17 Operatinal mplifiers 21
Op-mps Clsed-Lp Mde Example2: What is the min/max gain, and gain uncertainty if 5% tlerance resistrs are used? = 1kΩ, = 10kΩ, s (t) = cs(ωt), =0.015, ω = 50 rads/s (t) i i CL min CL nm min max 9500 1050 9.05 10 CL max NB: nminal gain max min 10500 950 11.05 ECEN 301 Discussin #17 Operatinal mplifiers 22
Op-mps Clsed-Lp Mde Example2: What is the min/max gain, and gain uncertainty if 5% tlerance resistrs are used? = 1kΩ, = 10kΩ, s (t) = cs(ωt), Max % Errr : =0.015, ω = 50 rads/s CL nm CL min (t) i i Min 100 100 9.5% 10 % Errr 100 100 10 10.5% CL nm 9.05 10 : CL nm CL nm 11.05 10 CL max ECEN 301 Discussin #17 Operatinal mplifiers 23
Op-mps Clsed-Lp Mde The umming mplifier: surces are summed tgether independently f lad and surce impedances 1 (t) 1 2 i 2 (t) i 2 N N (t) i N ECEN 301 Discussin #17 Operatinal mplifiers 24
Op-mps Clsed-Lp Mde The umming mplifier: surces are summed tgether independently f lad and surce impedances 1 (t) Nde a 1 2 i i 1 i KCL at Nde a : 2 i N i 2 (t) i 2 NB: = = 0 N N (t) i N i n n n n 1, 2,, N i ECEN 301 Discussin #17 Operatinal mplifiers 25
Op-mps Clsed-Lp Mde The umming mplifier: surces are summed tgether independently f lad and surce impedances Nde a 1 (t) 2 (t) 1 2 i 2 N i n N 1 sn sn N n 1 sn sn N (t) i N ECEN 301 Discussin #17 Operatinal mplifiers 26
Op-mps Clsed-Lp Mde The Nninerting mplifier: the signal t be amplified is cnnected t the nninerting terminal i i (t) ECEN 301 Discussin #17 Operatinal mplifiers 27
Op-mps Clsed-Lp Mde The Nninerting mplifier: the signal t be amplified is cnnected t the nninerting terminal Nde a i i i 0 (t) i KCL at Nde a : i i i 0 i 1 i ECEN 301 Discussin #17 Operatinal mplifiers 28
Op-mps Clsed-Lp Mde The Nninerting mplifier: the signal t be amplified is cnnected t the nninerting terminal (t) Nde a i i ince 0: (i.e. n current thrugh i i 1 n ltage drp) ECEN 301 Discussin #17 Operatinal mplifiers 29
Op-mps Clsed-Lp Mde The Nninerting mplifier: the signal t be amplified is cnnected t the nninerting terminal (t) Nde a i i Clsed CL - Lp 1 Gain : NB: always psitie and greater than r equal t 1 ECEN 301 Discussin #17 Operatinal mplifiers 30
Op-mps Clsed-Lp Mde Vltage llwer: the ltage n the utput f the p-amp is equal t the surce ltage (t) ECEN 301 Discussin #17 Operatinal mplifiers 31
Op-mps Clsed-Lp Mde Vltage llwer: the ltage n the utput f the p-amp is equal t the surce ltage NB: an ideal p-amp with negatie feedback has the prperty (t) s ECEN 301 Discussin #17 Operatinal mplifiers 32
Op-mps Clsed-Lp Mde Vltage llwer: the ltage n the utput f the p-amp is equal t the surce ltage i b Circuit 1 a Circuit 1 b Circuit 2 If a b i b is the lad current Lading: changing the behaiur f ne circuit by cnnecting anther circuit t it ECEN 301 Discussin #17 Operatinal mplifiers 33
Op-mps Clsed-Lp Mde Vltage llwer: the ltage n the utput f the p-amp is equal t the surce ltage Circuit 1 Circuit 2 Vltage fllwer can be used t preent lading (i b = 0) Lading: changing the behaiur f ne circuit by cnnecting anther circuit t it ECEN 301 Discussin #17 Operatinal mplifiers 34