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NONIDEAL OP AMP CIRCUITS Objective of Lecture • Describe the impact of real operational amplifiers on the models used in simulation and on the design approaches that have to be used. • The output voltage of the amplifier is limited by the values of the • • • • power supplies. Rin and current does enter the two input terminals The open-loop gain, AOL, of an op amp is not infinite. The gain of an op amp is dependent on the frequency of the signal. The slew rate of the op amp can cause oscillations rather than amplification, particularly when the amplifier gain is high. Inverting Amplifier: Voltage Supplies if is i2 = 0 i1 = 0 V+ = 15V V– = -10V i Example #1 (con’t) if is i2 = 0 i i1 = 0 V+ = 15V V– = -10V Example #1 (con’t) is i f i2 i f i2 i1 0mA is VS / R1 if i f Vo / R f is Av Vo Vs R f R1 i1 = 0 i i2 = 0 R f 10k R1 1k Av 10 Example #1 (con’t) • SinceAv = -10 • If VS = 0V, then Vo = -10(0V) = 0V • If VS = 0.5V, then Vo = -10(0.5V) = -5V • If VS = 1V, then Vo = -10(1V) = -10V • If VS = 1.1V, then Vo = -10(1.1V) < V–, Vo = -10V • If VS = -1.2V, then Vo = -10(-1.2V) = +12V • If VS = -1.51V, then Vo = -10(-1.51V) > V+, Vo = +15V Example #1 (con’t) • Voltage transfer characteristic Slope of the voltage transfer characteristic in the linear region is equal to AV. Rails • Rails is another turn for the voltage supplies that power the operational amplifier. • Rail-to-rail operation means that the output voltage can equal V+ and V– at some points during its operation. • 15 mV away from the voltage supplies is close enough to be called rail- to-rail. LM 741 Operational Amplifier http://www.ti.com/lit/ds/symlink/lm741.pdf Non-symmetrical Swing • LM324 operational amplifier where VCCmax = 32 V Inverting Amplifier: Finite Rin if is i2 0 i i1 0 Example #2 (con’t) if is i2 0 i i1 0 Rin ∞ Example #2 if iS i2 i f i2 i1 if i is VS V2 V2 V2 VO R1 Rin Rf R Rin VS 1 1 R f V2 R1 R1Rin VO AOL vd AOL V1 V2 AOLV2 VO Rf i2 i1 i _ vd + AOLvd R Rin VO VS 1 1 Rf R1 R R 1 in AOL Rf Rf AOL AOL VO VS V S R1 R1 R1 Rin R1 Rin R f A 1 Rf AOL 1 OL R1Rin R R in 1 VO Rf Gain • The gain of the amplifier is a function of R1, Rf, and Rin. VO G ACL VS Rf AOL ACL R R1 R1 Rin f AOL 1 R R 1 in Rf If Rin , ACL R1 Differential Voltage (vd ) ∞, then i1 and i2 are not equal to zero. • That means that the voltages at the input terminals of the op amp are not equal • Since Rin • V1 V2 • vd 0 V • Because of nonideal operation of the transistors inside the operational amplifier, vd 0 V even when VO = 0 V. • Thus, there is an input offset voltage V1 – V2 0V. • Some transistors have a pin that allow you to counterbalance this offset voltage. Gain • As the open-loop gain, AOL, of the op amp is finite, the closed-loop gain is a function R1, Rf, Rin, and AOL. VO G ACL VS Rf AOL ACL R R1 R Rin f AOL 1 1 R R in 1 Rf R Rin Let G and 1 R1 Rin 1 ACL G 1 G 1 AOL Gain-Bandwidth Product • Over a certain range of frequencies: f unity f max ACL 1 If ACL 1, f max f unity f max ACL f unity ACL f unity LM 741 1MHz 10k 10 1k f unity 100kHz ACL ACL f max Note ACL dB 20 log ACL Slew Rate • The speed at which the output voltage changes after a change in the input voltage. • When the closed-loop gain is very large and the operating frequency is high, there is a chance that the output voltage will not follow the input voltage because it didn’t have time to reach the desired value before the input voltage changed. • When this happens, it is possible for the op amp circuit to start oscillating. Electronic Design Project • The time-varying signal will be very small. • To maximize the range of the mbed ADC that will be used to digitize the analogue signal, the amplifier will have to have a large gain. • Because there will be significant noise on the signal that you want to detect, a bandpass filter will have to be designed that removes dc and very low frequency ac signals and removes high frequency noise. • Given the frequency range that the bandpass filter must operate and that we would like the pulse meter to be powered by a battery, the resistors used in the filters will be large. Op Amp Circuits to Consider • Buffers (Voltage Followers) • Isolate one subsystem from another • Used in impedance matching • Cascade Amplifiers • Several amplifiers in series where the overall gain is the multiplication of the gain of each amplifier in series • Active Filter • An op amp with a combination of resistors and capacitors at the input termal and/or in the feedback loop. • This is considered to be a filter (low, high, or bandpass) with gain. • Passive filters (RC networks) are always lossy • VO never is exactly equal to Vin Op Amp Circuits to Consider (con’t) • Because there is only +9V, +5V, +3.3V, and ground available (the battery, the voltage regulator output, and the logical high voltage on the mbed), inverting amplifiers should not be used because at least half of the signal will be lost. • Consider non-inverting amplifiers and difference amplifiers.