6: Operational Amplifiers 6: Operational Amplifiers •Operational Amplifier •Negative Feedback •Analysing op-amp circuits •Non-inverting amplifier •Voltage Follower •Inverting Amplifier •Inverting Summing Amplifier •Differential Amplifier •Schmitt Trigger •Choosing Resistor Values •Summary E1.1 Analysis of Circuits (2017-10110) Operational Amplifiers: 6 - 1 / 12 6) Solve for I (KCL at Op Amp output): 1) 0A into the op amp. 2) By voltage division: 3) 0V across op amp inputs 12 3V 5 15 5 0 3 3 12 3 vL vL 12 3 15V 2.5 15 12 3 15 I I 7mA EEL 3111: Circuits 1 1) By formula (inv. op amp) 2) KCL at - (vir. gnd) Cascaded Op Amp Find vO Ex 5 1.5 4.5V 2 6 1 in i f v R R v Small Signal Model of the op amp Alternate equivalent small signal model obtained by Norton to Thevenin transformation M V G A = - G. 28 Single-stage single-input low-gain op amp M v L-G A = sC +G GB and A VO are two of the most important parameters in an op amp V 1 G M V 1 V G IN V OUT C L A V M v0-G G L G C MM LL 2/21/2011 Example An op amp circuit analysis lecture 3/23 Jim Stiles The Univ. of Kansas Dept. of EECS The search for a template… Q: I looked and looked at the notes, and I even looked at the book, but I can't seem to find the right equation for this configuration! A: That's because the "right equation" for this circuit does not exist—at least The name Op Ampcomes from "operational amplifier." Op Amp Golden Rules(memorize these rules) 1)The op amp has infinite open-loop gain. 2)The input impedance of the +/− inputs is infinite. (The inputs are ideal voltmeters). The output impedance is zero. (The output is an ideal voltage source.) 3)No current flows into the +/− inputs of the op amp. Lab 2 - Op Amps Lab 2-1 Lab 2 - Op Amps Format This lab will be conducted during your regularly scheduled lab time in a group format. Again, it is strongly recommended that you rotate roles during the lab. You may ask the lab instructor for assistance if needed, but successful completion of the lab it is each individual's responsibility. Report Op-Amp with Single Supply Examples from Last Class • ideal case (gain = ∞) • V = 2.5 V V = 2.5 V V+ VO 2.5 V 5 V ∞∞∞∞ Mixed Signal Chip Design Lab + O (V + = V-for finite V O and V O centered at 2.5 V) • V+ = 2.501 V VO = 2.5 + A(V +-V-) = ∞ VO = 5 V (limited to supply) • V+ = 2.449 V VO = 2.5 + A(V +-V-) = -∞ VO = 0 V (limited to supply) Lecture 8: Op-Amps; About this Video. Circuit design is complicated by interactions among elements, but these interactions can be reduced or eliminated by using an op-amp as a buffer. This lecture covers how to analyze and design op-amp circuits. Lecture handout (PDF) Lecture slides (PDF) Recitation Video Op Amps: Ideal Op Amp • An ideal op amp is an amplifier with infinite open-loop gain, infinite input resistance, and zero output resistance. • To facilitate the understanding of op amp circuits, we will assume ideal op amps. An op amp is ideal if it has the following characteristics: 1. Infinite open-loop gain, A = ∞ 2. Infinite input 7 Feedback •Most op-amp circuits are designed to use feedback. •Feedback is defined as taking a portion of the output of a circuit and coupling or feeding it back into the input. •If the output fed back is in phase with the input then the circuit has positive feedback. •If the output fed back is out of phase with the input then the circuit has negative feedback. An op-amp is a differential amplifier, that is it amplifies the difference between the two input terminals. If we have a source with voltage Vp connected to the +