Lecture 9 perational mplifier frequency epone eadg: Jaeger. and Note ECE 3040 - Dr. lan Doolittle
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 3040 - Dr. lan Doolittle
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 3040 - Dr. lan Doolittle
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 3040 - Dr. lan Doolittle
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 3040 - Dr. lan Doolittle
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 3040 - Dr. lan Doolittle π C
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 3040 - Dr. lan Doolittle
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 3040 - Dr. lan Doolittle
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 3040 - Dr. lan Doolittle
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 3040 - Dr. lan Doolittle
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 3040 - Dr. lan Doolittle
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 3040 - Dr. lan Doolittle
eal p mp Frequency epone For the"74" p mp ~ 00000 06 d T ~ ~ ( π ) 5 Hz ( π ) MHz GW For the"p 07" p mp ~ 000000 4 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 3040 - Dr. lan Doolittle
ECE 3040 - 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 where @ Low Pa
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 penloop @ DC The cloed Loop mplifier ha a higher bandwidth than the pen Loop mplifier ECE 3040 - Dr. lan Doolittle
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: ( 00 000 x 5) ( Ga x 0 000 ) ( Ga ) 00 Maximum Cloed Loop pen Loop Cloed Loop ECE 3040 - Dr. lan Doolittle
eal p mp Frequency epone For the Inertg Configuration: - - y up erpoition but o penloop penloop CloedLoop penloop penloop ECE 3040 - Dr. lan Doolittle
ECE 3040 - Dr. lan Doolittle Inertg the frequency dependent open loop ga: eal p mp Frequency epone CloedLoop CloedLoop CloedLoop penloop penloop CloedLoop
ECE 3040 - Dr. lan Doolittle eal p mp Frequency epone DC CloedLoop CloedLoop CloedLoop @ DC CloedLoop T H @ Cloed Loop andwidth penloop penloop CloedLoop Cloed Loop DC Ga The frequency behaior i the ame a for the the Non-Inertg cae!