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3.1 Operational Amplifiers • properties of an ideal amplifier • equivalent circuit and performance of a real operational amplifier • three example circuits P voltage follower circuit - used as an impedance buffer P non-inverting amplifier circuit - works by voltage feedback P inverting amplifier circuit - works by current feedback • Bode plot showing the dependence of gain on frequency 3.1 : 1/8 Ideal Amplifiers • operational amplifiers evolved from the field of analog computation where they were designed to perform mathematical operations • they are currently used as building blocks in constructing electronic instrumentation • they are available as integrated circuits and cost just a few dollars - the circuit detail at the transistor level can be ignored • properties of an ideal amplifier (op-amps come close!) P an infinite input impedance that draws no current from the preceding circuit P a zero output impedance so that a voltage divider is not formed with the following circuit P an infinite gain so that the smallest signal can be amplified to a useful level P respond to any frequency 3.1 : 2/8 Equivalent Circuit and Performance inverting input + 15 V • the signal is connected to one or both inputs ! • any current passing between the Rout two inputs will cause a voltage, RS GVS ! VS, across RS + • VS is amplified by a factor of G + to create Vout Vout = -GVS • when the signal is connected noninverting ! 15 V between the common and input inverting inputs, the output is the circuit common negative of the input • when the signal is connected between the common and noninverting inputs, the output is the same sign as the input • typical performance P open loop gain, G, of ×104 to ×109 P effective input impedance (given by RSG) of 109 to 1015 Ω P effective output impedance (given by Rout/G) of < 1 Ω P frequency response into the megahertz domain 3.1 : 3/8 Op-Amps with Negative Feedback There are two equivalent methods for determining how Vout depends upon the input signal. circuit V! circuit ! VS = 0 V+ 1. Using voltage: Vout will adjust itself so that V- = V+. This makes VS = 0. + V out if circuit 2. Using current: Vout will adjust itself so that if = iin. This makes iS = 0. ! i in iS = 0 + V out 3.1 : 4/8 Voltage Follower A voltage follower is often used as an impedance buffer between a high Z source and low Z circuit. The voltage approach can be used. In order that VS = 0, it is necessary that Vout = Vin. Thus the output voltage follows the input voltage. ! VS + V out high Z V in Note that the above relationship is an approximation since Vin + VS = Vout. Vin + VS = Vout Vout = Vout G ⎛ G ⎞ = Vin ⎜ ⎟ ⎝ G −1 ⎠ Vin + Vout 3.1 : 5/8 for a gain of 104 and larger the discrepancy from Vout = Vin is trivial low Z Non-Inverting Amplifier Rf The op-amp will increase Vout until V− equals Vin . At that point VS = 0. R1 R1 Vin = V− = Vout R1 + R f Rf Vout R1 + R f = = 1+ Vin R1 R1 ! + V! Vin positive attributes • output voltage is the same sign as the input voltage • very high input impedance given by G×Rs negative attributes • the high input impedance will combine with stray capacitance to limit the amplifier bandwidth • the non-zero voltage at both inputs stresses the op-amp 3.1 : 6/8 V out Inverting Amplifier The op-amp will increase Vout until if = i1. At that point VS = 0, the + input is at true ground, and the − input is at "virtual" ground. i1 = i f Vin − 0 0 − Vout = R1 Rf Rf R1 i1 iS if ! V in VS + V out Rf Vout =− G= Vin R1 negative attributes • output voltage is opposite in sign from the input • input impedance given by R1 + Rf/G, not G×RS positive attributes • the low input impedance does not combine with stray capacitance to limit the bandwidth • the zero voltage at both inputs maximizes op-amp performance 3.1 : 7/8 Frequency Dependent Gain A(dB) 741 Operational Amplifier Bode Plot The gain curve of an op100 dc gain 86 dB amp depends upon G 90 80 and the unity gain 70 bandwidth. Draw a open loop gain x100 60 horizontal line at G (dB), bandwidth 50 x10 and a line with a slope 40 bandwidth unity gain of 20 dB/decade upward 30 bandwidth from the unity gain (0 1.2 MHz 20 dB) bandwidth. Where 10 0 the two lines cross the 0 1 2 3 4 5 6 7 gain is down by 3 dB, log(f) just as the filter Bode plots. To obtain a Bode plot for a given amplifier, draw a horizontal line at the amplifier gain. Where it intersects the open loop line, the gain is down by 3 dB. Shown above are lines for ×10 and ×100 amplifiers. 3.1 : 8/8