Lecture 29. Operational Amplifier frequency Response. Reading: Jaeger 12.1 and Notes
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1 Lecture 9 perational mplifier frequency epone eadg: Jaeger. and Note ECE Dr. lan Doolittle
2 Ideal p mp Ued to Control Frequency epone - Low Pa Filter Preiouly: Now put a capacitor parallel with : - C If j C C C C ECE Dr. lan Doolittle
3 Ideal p mp Ued to Control Frequency epone Low Pa Filter - C C t DC (0) the ga rema the ame a before (- / ). t high frequency C >> the ga die off with creag frequency C C π f ω C t high frequencie more negatie feedback reduce the oerall ga H H ECE Dr. lan Doolittle
4 D Ideal p mp Ued to Control Frequency epone D 0 Log D Low Pa Filter 0 Log i the ga expreed d -3d drop at f H ( ha dropped half!) Slope 0 d / Decade f H t DC (0) the ga rema the ame a before (-/) t high frequency C >> the ga die off with creag frequency Log(f) f H π C Implement a Low Pa Filter : Lower frequencie are allowed to pa the filter with attenuation. High frequencie are trongly attenuated (do not pa). ECE Dr. lan Doolittle
5 Ideal p mp Ued to Control Frequency epone - High Pa Filter C - t DC (0) the ga i zero. C C C t high frequency C >> the ga return to it full alue (- / ) ECE Dr. lan Doolittle
6 Ideal p mp Ued to Control Frequency epone High Pa Filter D D 0 Log -3d drop at f H t DC (0) the ga i zero. t high frequency C >> the ga return to it full alue (- / ) Slope 0 d / f L Decade Log(f) C C Implement a High Pa Filter : Higher frequencie are allowed to pa the filter with attenuation. Low frequencie are trongly attenuated (do not pa). f L ECE Dr. lan Doolittle π C
7 Ideal p mp Ued to Control Frequency epone and Pa Filter (combation of high and low pa filter) - ou t C C C C C C Low Pa C C High Pa C C ECE Dr. lan Doolittle
8 Ideal p mp Ued to Control Frequency epone and Pa Filter (combation of high and low pa filter) D C C C Slope 0 d / Decade -3d drop at f H D 0 Log f L << f H f L f H f L π C π C f H Log(f) ECE Dr. lan Doolittle
9 Ideal p mp Ued to Control Frequency epone and Pa Filter (combation of high and low pa filter) D C C C Slope 0 d / Decade D 0 Log More than a -3d drop at f L and f H f L < f H and f L f H f L f H Log(f) ECE Dr. lan Doolittle
10 General Frequency epone of a Circuit Pole and Zero Generally a circuit tranfer function (frequency dependent ga expreion) can be written a the ratio of polynomial: ( τ )( τ )( τ )... z z z ( τ )( τ )( τ )... p p 3 p ( τ ) ( τ ) ( τ ) ( τ ) ( τ ) ( τ )... Complex oot of the numerator polynomial are called zero while complex root of the denomator polynomial are called pole Each zero caue the tranfer function to break to higher ga (lope creae by 0 d/decade) Each pole caue the tranfer function to break to lower ga (lope decreae by 0 d/decade) z p z p 3z 3 p... 0Log 0 d/decade τ 40 d/decade z 0 d/decade τ p τ 0 d/decade p τ -0 d/decade 3 p τ 0 d/decade 3z Typically τc ECE Dr. lan Doolittle
11 eal p mp Frequency epone To thi pot we hae aumed the open loop ga pen Loop of the op amp i contant at all frequencie. eal p amp hae a frequency dependant open loop ga. where j penloop T T pen loop ga at DC pen loop bandwidth Unity - ga frequency ( frequency where ) penloop ECE Dr. lan Doolittle
12 eal p mp Frequency epone penloop penloop ( ( j ) j ) t Low Frequencie: penloop T t High Frequencie: penloop For mot frequencie of teret ω>>ω the product of the ga and frequency i a contant ω T T f Ga andwidth Pr oduct ( GW ) T π ECE Dr. lan Doolittle
13 eal p mp Frequency epone For the"74" p mp ~ d T ~ ~ ( π ) 5 Hz ( π ) MHz GW For the"p 07" p mp ~ d T ~ ~ ( π ) 0.05 Hz ( π ) 0.6 MHz GW If the open loop bandwidth i o mall how can the op amp be ueful? The anwer to thi i found by coniderg the cloed loop ga. ECE Dr. lan Doolittle
14 ECE Dr. lan Doolittle eal p mp Frequency epone Preiouly we found that the cloed loop ga for the Nonertg configuration wa (for fite open loop ga): where penloop penloop CloedLoop Ug the frequency dependent open loop ga: H DC CloedLoop H CloedLoop CloedLoop penloop penloop CloedLoop andwith Loop Cloed Frequency Cutoff Upper Low Pa
15 eal p mp Frequency epone The cloed Loop mplifier ha a lower ga than the pen Loop mplifier pen LoopGa Cloed LoopGa Cloed Loop andwidth T H ( ) CloedLoop CloedLoop Cloed Loop DC Ga penloop DC The cloed Loop mplifier ha a higher bandwidth than the pen Loop mplifier ECE Dr. lan Doolittle
16 eal p mp Frequency epone Cloed Loop Ga et by feedback network below ω H Cloed Loop Ga et pen Loop Ga aboe ω H ( Ga x andwidth ) ( Ga x andwidth ) pen Loop Cloed Loop Example: 74 p mp i ued a a low pa filter with f L 0kHz. What i the maximum oltage ga poible for thi circuit? From before we can write: ( x 5) ( Ga x ) ( Ga ) 00 Maximum Cloed Loop pen Loop Cloed Loop ECE Dr. lan Doolittle
17 eal p mp Frequency epone For the Inertg Configuration: - - y up erpoition but o penloop penloop CloedLoop penloop penloop ECE Dr. lan Doolittle
18 ECE Dr. lan Doolittle Inertg the frequency dependent open loop ga: eal p mp Frequency epone CloedLoop CloedLoop CloedLoop penloop penloop CloedLoop
19 ECE Dr. lan Doolittle eal p mp Frequency epone DC CloedLoop CloedLoop DC CloedLoop T Cloed Loop andwidth penloop penloop CloedLoop Cloed Loop DC Ga The frequency behaior i the ame a for the the Non-Inertg cae!
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