Non Linear Op Amp ircuis. omparaors wih 0 and non zero reference volage. omparaors wih hyseresis. The Schmid Trigger. Window comparaors. The inegraor. Waveform conversion. Sine o ecangular. ecangular o riangular. Triangular o recangular. Waveform generaion. elaxaion oscillaors. Generaing riangular waves. Triangular generaors. Acive diode circuis. Acive peak deecor. Acive clipper. Acive clamper. The Differeniaor.
A comparaor is a circui ha compares he inpu signal wih a reference volage and provides an oupu signal (HIGH sae) if he inpu signal is greaer han he reference volage. The simples comparaor is a differenial amplifier wih no feedback. V A V υ ou The circui shown produces a posiive oupu if he inpu signal is posiive, and a negaive one if he inpu signal is negaive. However i sauraes unless he inpu signal is beween Vcc/A and Vcc/A. For some opamp Is A could reach very high values like 100,000 and for Vcc = 10 V he inpu signal should be beween 0.1mV and 0.1mV pracically 0 for some applicaion. We can herefore say ha for pracical applicaions he circui goes high for a posiive signal and low (10V) for a negaive inpu signal. omparaors usually are being used o drive digial circuis or swiches, since heir oupu can be seen as a digial signal obained from an analog inpu.
omparaor inerface wih MOS. V υ ou V
Invering omparaor wih proecion claming circui. If he inpu goes higher han 0.7 or lower han 0.7V one of he diodes conducs and he inpu o he comparaor chip is limied beween ±0.7V. V υ ou V
omparaor wih an adjusable reference volage. By varying he poeniomeer posiion we can vary he reference volage above which he comparaor is high and below of which he comparaor is low. V A υ ou V V 0
A comparaor wih zero reference volage can be viewed as a circui ha will conver an inpu sinusoidial signal ino an oupu square one. During he ime he inpu signal is posiive (half he period of he inpu signal) he oupu is high (Vcc) and during he oher half when he inpu is negaive he oupu signal is low (Vcc). Moreover we can bind he oupu signal by using ordinary and Zener diodes in special configuraions. V υ ou V Z 0.7V 0.7V υ ou V Z 0.7V
omparaors wih hyseresis. A comparaor is very easy o be riggered by noise, ha is why comparaors wih hyserisis have been invened. They are called Schmid riggers. A Schmid rigger is a comparaor wih posiive feedback. The oupu signal in he circui below can ake wo only values ±V sa. A porion of he oupu signal B= 1 /( 1 2 ) is fed o he posiive inpu of he comparaor. Imagine ha he oupu signal is posiive. This means ha he inpu signal is negaive and in order for he comparaor o change sae he inpu mus become posiive and greaer han BV sa (upper rip poin, UTP). Imagine ha he oupu signal is negaive. This means ha he inpu signal is posiive and in order for he comparaor o change sae he inpu mus become negaive and less han BV sa (lower rip poin, LTP). This behavior is called hyseresis. υ in V υ ou υ ou V sa V LTP = BV sa UTP = BV sa 2 1 V sa
Non invering Schmid rigger. The posiive inpu of he inverer is a Vx=( 2 V in 1 V ou )/( 1 2 ). Suppose ha for some inpu posiive volage he oupu become high a Vsa. The posiive inpu of he inverer is a Vx = ( 2 V in 1 Vsa)/( 1 2 ). In order for he oupu o change sae Vx < 0 ha is V in < V sa ( 1 / 2 ). Suppose now ha for some inpu negaive volage he oupu became low a Vsa. The posiive inpu of he inverer is a Vx=( 2 V in 1 V sa )/( 1 2 ). In order for he oupu o change sae Vx > 0 ha is V in > V sa ( 1 / 2 ). υ ou 2 V sa υ in 1 V υ ou LTP UTP V sa V LTP = ( 1 / 2 )V sa UTP = ( 1 / 2 )V sa
This is an invering window comparaor where he oupu is low when he inpu is wihin he window defined by he wo reference volages UTP and LTP. υ ou V sa V LTP LTP UTP V υ ou V L UTP V
υ ou V sa 5V LTP LM339 V LTP UTP υ ou UTP V LM339 This is an invering window comparaor where he oupu is high when he inpu is wihin he window defined by he wo reference volages UTP and LTP.
The op amp circui below inegraes he inpu signal. For a consan inpu signal he oupu is: V ou = (V in /). If he offse volage of he op amp is Voff, he circui is evenually going o saurae. In order o avoid his problem a large resisor >10 or (an FET swich) is conneced parallel o he capacior. υ dq d i I = = q( ) = υ ( ) 1 0 i d υ i υ o = q υ o 1 ( ) = υ ( ) d 0 i υ o
The presence of he F will limi he oupu volage a an asympoic value a lile larger han V OS. I F F V OS I 1 I υ o V OS
The Schmid rigger will conver an inpu sinusoidial wave ino a square wave wih he same period. V Z 0.7V υ in V V υ ou LTP = BV sa υ ou V sa UTP = BV sa 2 1 V sa
A recangular wave inpu o he inegraor will produce a riangular wave as an oupu. The peak o peak riangular oupu volage is υ ou( pp) = 2 V 0 f υ i υ o
A riangular wave inpu o comparaor wih hreshold volage V hr will produce an oupu square wave wih ampliude he sauraion volage of he comparaor and period depending on he hreshold volage V hr. υ i 1 V V hr υ o 2
The circui below is a relaxaion oscillaor ha will produce a recangular oupu wave wihou an inpu signal. I is A Schmid rigger wih boh posiive and negaive feedback. Le us assume ha he oupu is a posiive sauraion. The capacior will sar charging iself and he negaive inpu will sar becoming posiive. When i reaches he UTP he sae of he Schmid rigger will change and he capacior will sar discharging iself and obaining negaive charge. When he negaive inpu volage reaches he LTP he Schmid rigger will change sae once more and he circle will sar repeaing iself. The period of oscillaion can be calculaed as: V T = 1 2 ln 1 B B υ o V 2 1 By feeding hese recangular pulses ino an inegraor we can have sponaneous generaion of a riangular waveform.
We will now ry o find he period of oscillaions of he relaxaion oscillaor. The volage oupu from he capacior is fed ino he negaive inpu of he Schmid rigger and herefore i direcly affecs he rigger s oupu. V () depends on he oher hand on he rigger s oupu V i since he capacior is charged from he oupu volage V i via he resisor. V () is given by he differenial equaion: V () V i V q( ) V i = ( ) q = V = q(0) e dq d (0) e d d qe e 0 e e 0 / V i = e e V d i / / V d When he Schmid rigger goes from High o Low (V sa V sa ) V () sars from an iniial value BV sa (he cause of he rigger change) o V sa he inpu volage o he circui ha charges he capacior. The above equaion from V () gives: V ( ) / V sae / = BVsae e d V = V sa Vsa ( ) 1 0 ( B) e i T /
When he Schmid rigger goes from High o Low (V sa V sa ) V () sars from an iniial value BV sa (he cause of he rigger change) o V sa he inpu volage o he circui ha charges he capacior. V () is given by: V () V i BV V ( ) = V V 1 sa sa ( B) e However when V reaches he value BV sa he Schmid rigger changes saes. The oupu becomes high V sa and a new cycle of charging he capacior sars. The ime i will ake for V o become BV sa is: sa = V sa V sa 1 ( B) e = ln 1 1 1 B 1 B When V = BV sa hen V i = V sa and he capacior sars charging. V () is given by: V ( ) / V sae / = BVsae e d V = Vsa Vsa ( ) 1 0 ( B) e When V reaches he value BV sa he Schmid rigger changes saes again. The oupu becomes low V sa and he capacior sars discharging again. The cycle sars all over. The ime i will ake for V o become BV sa is: BV sa = V sa V sa 1 B 1 B 2 ( B) e = ln 1 2
The cycle of charging and discharging repeas iself periodically wih period T. V () T = 1 2 = 1 2 ln 1 B B BV sa BV sa V ou () T 1 B = 2 ln 1 B V sa V sa
Sponaneous generaion of riangular pulses. V V V υ o V 1 2
This is anoher ype of riangular wave generaor wih frequency: f = 2 4 1 3 2 1 V V υ o V 3 V
Acive Diode ircuis. Half wave recifier.when he inpu is negaive he diode cus off and he oupu volage is 0. When he inpu is posiive and he diode conducs he oupu from he op amp is Vin0.7 V and he oupu from he diode is Vin. The superdiode does no suffer from he Knee volage of 0.7 V. V υ ou V
Acive Diode ircuis. Acive peak deecor. This acive peak deecor does no suffer from he diode s knee volage of 0.7 V. V υ ou V
Acive Diode ircuis. Acive posiive clipper. This acive posiive clipper does no suffer from he diode s knee volage of 0.7 V. υ ou V ref V ref V V V
Acive Diode ircuis. Acive posiive clamper. This acive posiive clamper does no suffer from he diode s knee volage of 0.7 V. υ ou V p 2V p V p V V
The circui below is a differeniaor. I produces spices when fed wih a recangular waveform. The oupu signal is he derivaive of he inpu. υ ou
Acive Differeniaor wih Op Amp. υ i υ o υ = i υ υ O o q = i υ dυ ( ) i ( ) = ( ) o d = dq d