EE 230 Lecture 12 Spring 2010

# EE 230 Lecture 12 Spring 2010 - EE 230 Lecture 12 Basic...

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EE 230 Lecture 12 Basic Feedback Configurations Generalized Feedback Schemes Integrators Differentiators First-order active filters Second-order active filters

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Input and Output Impedances with Feedback R INF =? R OF =? Exact analysis : 1 12 R β = R+R A V V 1 V 1 Two-Port Nonideal Op Amp R IN R O R 1 R 2 Consider amplifier as a two-port and use open/short analysis method Will find R INF , R OF , A V almost identical to previous calculations Will see a small A VR present but it plays almost no role since R INF is so large (effectively unilateral) VF 1 A β ± 0 0F V R R 1+ β A ± ( ) 1 INF IN V R= R A β + VRF A β ± Review from Last Time
Buffer Amplifier 1 OUT V IN V A V = = Provides a signal to a load that is not affected by a source impedance One of the most widely used Op Amp circuits Special case of basic noninverting amplifier with R 1 = and R 2 =0 1 OUT 2 IN 1 V R VR =+ R IN = R OUT = 0 This provides for decoupling between stages in many circuits Review from Last Time

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Basic Inverting Amplifier OUT 2 IN 1 V R - VR = 2 1 IN OUT R IN =R 1 OUT IN 12 V V += 0 RR R OUT = 0 Input impedance of R 1 is unacceptable in many (but not all) applications This is not a voltage feedback amplifier (it is a feedback amplifier) of the type (note R IN is not high!) Feedback concepts could be used to analyze this circuit but lots of detail required Review from Last Time
Summing Amplifier F 1 1 OUT 2 2 k k OUT 12 k F1 2 k V VV V + + +...+ =0 RR R R FF F OUT 1 2 k k R V = - V - V -. ..- V R • Output is a weighted sum of the input voltages • Any number of inputs can be used • Gains from all inputs can be adjusted together with R F • Gain for input V i can be adjusted independently with R i for 1 I k • All weights are negative • Input impedance on each input is R i Review from Last Time

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Generalized Inverting Amplifier () ( ) F 1 Zs Ts =− s-domain representation Z 1 and Z F can be any s-domain circuits If Z 1 =R, Z F =1/sC, obtain 1 sRC What is this circuit?
Generalized Inverting Amplifier () 1 Ts sRC =− What is this circuit? Consider the differential equation 0 t yK x d τ = ( ) Xs Ys = K s Taking the Laplace Transform, obtain ( ) Ys K Ts= = s Thus, this circuit is an inverting integrator with a unity gain frequency of K = (RC) -1 K is the frequency where |T(j ω )|=1 and is termed the Integrator Unity Gain Frequency

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Inverting Integrator () 1 Ts sRC =− 1 Tj ω j ω RC 1 ω ω RC = 90 ω o ∠= Unity gain frequency is 0 1 ω RC =
Inverting Integrator () 1 Ts sRC =− () () 0 OUT IN IN 1 VV V 0 RC t d ττ + Integrators are widely used ! The integrator function itself is ill-conditioned and integrators are seldom used open-loop If the input has any dc component present, since superposition applies, the output would diverge to ± as time increases The offset voltage (discussed later) will also cause an integrator output to diverge The ideal integrator has a pole at s=0 which is not in the LHP R IN =R R OUT =0

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Inverting Integrator () () 0 OUT IN IN 1 VV V 0 RC t d ττ =− + What is the output of an ideal integrator if the input is an ideal square wave?
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EE 230 Lecture 12 Spring 2010 - EE 230 Lecture 12 Basic...

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