ECE 2133 Electronc Crcuts Dept. of Electrcal and Computer Engneerng Internatonal Islamc Unversty Malaysa
Chapter 12 Feedback and Stablty
Introducton to Feedback
Introducton to Feedback 1-4 Harold Black, an electroncs engneer from Western Electrc Company, nvented the feedback amplfer n 1928 whle searchng for methods to stablze the gan of amplfers for use n telephone repeaters. In a feedback system, a sgnal that s proportonal to the output s fed back to the nput and combned wth the nput sgnal to produce a desred system response. Feedback can be ether negatve or postve. In negatve feedback, a porton of the output sgnal s subtracted from the nput sgnal. Tends to mantan a constant value of amplfer voltage gan aganst varatons n transstor parameters, supply voltages, and temperature. In postve feedback, a porton of the output sgnal s added to the nput sgnal. Used n the desgn of oscllators and other applcatons.
Advantages of Negatve Feedback Gan senstvty 1-5 aratons n the crcut transfer (gan) as a result of changes n transstor parameters are reduced by feedback Bandwdth extenson The bandwdth of a crcut that ncorporates negatve feedback s larger than that of the basc amplfer Nose senstvty Increase the sgnal-to-nose raton f nose s generated wthn the feedback loop educton of nonlnear dstorton At large sgnal levels, dstorton may appear n the transstor output sgnal due to ts nonlnear characterstcs. Negatve feedback reduces ths dstorton Control of mpedance levels The nput and output mpedances can be ncreased or decreased wth the proper type of negatve feedback crcut
Dsadvantages of Negatve Feedback 1-6 Crcut Gan Stablty The overall amplfer gan, wth negatve feedback, s reduced compared to the basc amplfer used n the crcut The feedback crcut may become unstable (oscllate) at hgh frequences
Basc Concepts of Feedback
Basc Feedback Crcut 1-8 S current or voltage. A open loop gan of a basc amplfer S fb feedback sgnal by samplng the output sgnal S ɛ error sgnal by subtractng the feedback sgnal from the nput source sgnal Error sgnal s the nput to the basc amplfer and amplfed to produce the output sgnal
Assumptons 1-9 The nput sgnal s transmtted through the amplfer only, none through the feedback network The output sgnal s transmtted back through the feedback network only, none through the amplfer There are no loadng effects n the deal feedback system The feedback network does not load down the output of the basc amplfer The basc amplfer and feedback network do not produce a loadng effect on the nput sgnal source
Ideal Closed-Loop Sgnal Gan 1-10 A amplfcaton factor feedback transfer functon A f closed-loop transfer functon T loop gan S * can be ether voltage or currents or a combnaton of both T s (+) for negatve feedback but can be a complex number also
Ideal Closed-Loop Sgnal Gan 1-11 If the loop gan s large so that A >> 1, the overall gan of the feedback s a functon of the feedback network only For a large loop gan
Gan Senstvty 1-12 Consder the feedback transfer functon s a constant The percent change n the closed-loop gan A f s less than the correspondng percent change n the open-loop gan A by the factor (1+ A)
Ideal Feedback Topologes
Prevew 1-14 There are four feedback topologes, based on the parameter to be amplfed (voltage or current) and the output parameter (voltage or current). Seres-Shunt (voltage amplfer). Shunt-Seres (current amplfer) Seres-Seres (transconductance amplfer) Shunt-Shunt (transresstance amplfer)
Prevew 1-15
Seres-Shunt Confguraton 1-16 The crcut s a voltage-controlled voltage source and s an deal voltage amplfer. The feedback crcut samples the output voltage and provdes a feedback voltage n seres wth the source voltage. An ncrease n the output voltage produces an ncrease n the feedback voltage, whch n turn decreases the error voltage due to the negatve feedback. The smaller error voltage s amplfed producng a smaller output voltage. Whch means that the output sgnal tends to be stablzed.
Seres-Shunt Confguraton 1-17 The output of the feedback network s an open crcut fb feedback voltage, v (= fb / o ) voltage feedback transfer functon Source resstance S s neglgble A vf closed-loop voltage transfer functon The magntude of A vf s less than that of A v, the advantage s that A vf becomes ndependent of the ndvdual transstor parameters
Seres-Shunt Confguraton 1-18 A seres nput connecton results n an ncreased nput resstance compared to that of the basc voltage amplfer. Ths elmnates loadng effects on the nput sgnal source due to the amplfer
Seres-Shunt Confguraton 1-19 A shunt output connecton results n a decreased output resstance compared to that of the basc voltage amplfer. Ths elmnates loadng effects on the output sgnal when an output load s connected
Seres-Shunt Confguraton 1-20
Shunt-Seres Confguraton 1-21 The crcut s a current-controlled current source and s an deal current amplfer. The feedback crcut samples the output current and provdes a feedback sgnal n shunt wth the sgnal current. An ncrease n the output current produces an ncrease n the feedback current, whch n turn decreases the error current due to the negatve feedback. The smaller error current s amplfed producng a smaller output current. Whch means that the output sgnal tends to be stablzed.
Shunt-Seres Confguraton 1-22 The output of the feedback network s a short crcut I fb feedback current, (= I fb /I o ) feedback current transfer functon Source resstance S s large A f closed-loop current transfer functon The magntude of A f s less than that of A, the advantage s that A f becomes ndependent of the ndvdual transstor parameters
Shunt-Seres Confguraton 1-23 A shunt nput connecton decreases the nput resstance compared to that of the basc amplfer. Ths elmnates loadng effects on the nput sgnal current source due to the amplfer
Shunt-Seres Confguraton 1-24 A seres output connecton ncreases the output resstance compared to that of the basc voltage amplfer. Ths elmnates loadng effects on the output sgnal when an output load s connected
Shunt-Seres Confguraton 1-25
Seres-Seres Confguraton 1-26 The feedback crcut samples a porton of the output current and converts t to a voltage. Ths feedback crcut s a voltage-to-current amplfer.
Seres-Seres Confguraton 1-27 The output of the feedback network s a short crcut fb feedback voltage, z (= fb /I o ) resstance feedback transfer functon Neglectng the affect of Source resstance S A gf closed-loop current-to-voltage transfer functon or transconductance gan
1-28 Seres-Seres Confguraton Input resstance ncreases compared to that of the basc amplfer. g z f g z g z g z g z o z fb A I A I A A A I 1 1 1 1 ) (
1-29 Seres-Seres Confguraton The output resstance ncreases compared to that of the basc amplfer. o g z x x of o g z x o x z g x o g x x A I A I I A I A I 1 1
Seres-Seres Confguraton 1-30
Shunt-Shunt Confguraton 1-31 The feedback crcut samples a porton of the output voltage and converts t to a current. Ths feedback crcut s a current-to-voltage amplfer.
Shunt-Shunt Confguraton 1-32 The output of the feedback network s an open crcut I fb feedback current, g (= I fb / o ) conductance feedback transfer functon Source resstance S s very large A zf closed-loop voltage-to-current transfer functon or transresstance gan
1-33 Shunt-Shunt Confguraton Input resstance decreases compared to that of the basc amplfer. z g f z g z g z g o g fb A I A I I A I I I A I I I I I 1 1 1
1-34 Shunt-Shunt Confguraton The output resstance decreases compared to that of the basc amplfer. z g o x x of o z g x o x g z x o z x x A I A A I A I 1 1
Shunt-Shunt Confguraton 1-35
Feedback Networks
1-37 oltage Amplfers 1 2 2 1 2 2 2 1 1 1 1 v v A v v v v v v v v v o v o o o fb fb A v s very large v s feedback transfer functon.
oltage Amplfers 1-38 A v s the open-loop voltage gan of the basc amplfer. For o 0 s very large
oltage Amplfers 1-39. A v s postve and v s also postve, thus the loop gan s postve for negatve feedback T v A v I, A o v, fb =
Current Amplfers 1-40 A s open-loop current gan and very large f S >> f, then I I and I s neglgble, Assumng 1 s at vrtual ground
Current Amplfers 1-41 A s very large Assumng 1 s at vrtual ground
Current Amplfers 1-42. Solvng for I fb and substtute to and rearrangng to fnd the closed-loop current gan
Transconductance Amplfers 1-43 A g s open-loop transconductance gan and very large A g s very large Neglectng base current
Transconductance Amplfers 1-44 Assume I c I e ad s very large
Transresstance Amplfers 1-45 A z s open-loop transresstance gan and very large A z s very large Assumng 1 s at vrtual ground I fb = I
Transresstance Amplfers 1-46 o = -A z I, I = I I fb, and o = -A z (I I fb ) Assumng 1 s at vrtual ground