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Physics 116A NotesDavid E. PellettDraft v.0.95• Notes Copyright 2004 David E. Pellett unless stated otherwise.• References:– Text for course:Fundamentals of Electrical Engineering, second edition, by LeonardS. Bobrow, published by Oxford University Press (1996)– Others as noted1Op-Amp Basics: Outline• Operational amplifier and negative feedback– Introduction and historical development: long distance telephone re-peaters, analog computers, commodity electronic components...– Motivation of golden rules: i+= i−= 0, v+= v−.∗ Inverting amplifier with finite gain op amp∗ Same thing using golden rules– Current-to-voltage converter– Summing amplifier– Non-inverting amplifier– i and v across a capacitor– Integrator– Differentiator2Negative Feedback Amplifier Development1927: Repeater amplifiers needed every few miles for long distance telephonetransmission on coaxial cable (“pipe”)• Frequency division multiplexing (See text, Sec. 10.6 for details)– Frequency shifted channels 4kHz wide for multiple conversations– 3 to 4 channels per line max possible in 1927– Harold Black, EE at Western Electric (NYC) wanted 1000 ch or more– Required linear (low distortion) amplifier, stable gain (unavailable)• H. Black sketched negative feedback amplifier idea on newspaper on ferryboat to NYC office, witnessed for patent application• Difficult to build: stability problems–tended to “s ing” (oscillate)• Development and theoretical understanding worked out with– Harry Nyquist, Physics Ph.D., stability criterion– Hendrik W. Bode, Physics Ph.D., phas e shift and gain as function offrequency– Patent awarded in 19373Negative Feedback Amplifier DevelopmentFirst commercial IC Op Amp, mid 1960’s: Fairchild µA709, designed byRobert J. Widlar. Followed by µA741.“The technology of communications advances when new physical phenomenaare discovered and applied.”– Pierce and Noll, Signals: the science of telecommunications4Op Amp: LM741 SchematicLM741 Op Amp circuit diagram:Diagram Copyright 2000 National Semiconductor CorporationThis is pretty complicated, but we can model it (at low frequen-cies) with a voltage-controlled voltage source and two resistors.5Op Amp: Simplified ModelA simple low frequency model uses a controlled source and two resistors:The factor Av≡ vo/vifor the dependent source is called the voltage gain.For LM741, Ri= 2 MΩ, Ro= 75 Ω and Av= 200000 (DC).For LF411, Ri= 1012ΩIdeal case with finite voltage gain: Ri→ ∞, Ro= 0since Ri→ ∞ (i.e., open circuit), i+= i−= 0.(This is one of the two op-amp “golden rules.”)6Negative Feedback: Inverting AmplifierNow use this model to make an inverting amplifier:Note: all points connected to ground are wired together using wires whichare not shown. [Draw figure on the blackboard now!]R1and R2make a voltage divider between the Op Amp input and outputconnected to the inverting input. It provides negative feedback.Find viand the voltage gain with feedback, AvF≡ vo/vin.Use nodal analysis at node 1 where v1= −vi.7Inverting Amplifier – Finite-Gain Op Amp,Find viusing nodal analysis at node 1:i1= i2vin− v1R1=v1− voR2vin+ viR1= −vi+ voR2R2(vin+ vi) = −R1(vi+ vo) = −R1vi(1 + Av)vi(R1(1 + Av) + R2) = −R2vinvi= −vin1 +R1R2(1 + Av)In the limit Av→ ∞,vi= 0.8Inverting Amplifier, Gain → ∞This means node 1 (the inverting input) is a “virtual ground”(held at ground by the negative feedback). This requires the non-inverting input to be grounded, as is the case for the invertingamplifier.More generally, the negative feedback insures thatv+= v−in the limit that the Op Amp gain, Av→ ∞.This is the other “golden rule.” It is true for any circuit involvingan ideal Op Amp with negative feedback.9Inverting Amplifier – Finite-Gain Op Amp,Find AvF:vo= Avvi= −Avvin1 +R1R2(1 + Av)AvF≡ vo/vin= −11/Av+R1R2(1/Av+ 1).Again, in the limit Av→ ∞,AvF= −R2/R1.You can get this result directly using the ideal op amp golden rules:v+= v−andi+= i−=


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UCD PHY 116A - LECTURE NOTES

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