6. The Operational Amplifier

Transcription

1 1 6. The Operational Amplifier This chapter introduces a new component which, although technically nonlinear, can be treated effectively with linear models This element known as the operational amplifier (op amp), which has been used in a large variety of electronic applications This chapter covers the following topics: Op amp basics Op amp models Practical op amps

2 2 6.1 Background The origins of op amps back to 1940 when the basic circuits were designed to perform mathematical operations such as addition, subtraction, multiplication, division, differentiation, and integration K2-W was the first commercial vacuum tubed op amp device The modern integrated circuit (IC) op amps are constructed using perhaps 25 or even more transistors all on the same silicon chip The op-amp is defined as a DC-coupled high-gain electronic voltage amplifier with a differential input and, usually, a single-ended output V output input V

3 3 6.2 The Ideal Op Amp Ideal Op Amp Rules No current ever flows into either input terminal There is no voltage difference between the two input terminals Inverting Amplifier We use the rule 1 (no current flows into the inverting input terminal) v in ir 1 ir f v out =0 v out=v in i R 1 R f We use the rule 2 (the non inverting input is grounded then the inverting input is zero) v in ir 1=0 v in i= R 1

4 4 We obtain an expression for vout in terms of vin Rf v out= R v in 1 v in=5 sin 3t Rf AC input: v out = R 5 sin 3t 1 DC input: Voltage (V) 10-2 R f /R 1 =5 vout t (s) v in

5 Non Inverting Amplifier We use the rule 2 (the non inverting input is vin then the inverting input is vin) Since there is no current flows into the inverting input terminal, we have v in v in v out R1 = R f Rf v out= 1 R v in 1 Voltage Follower We use the rule 2 (the non inverting input is vin then the inverting input is vin) v out=v in It is typically used as a buffer amplifier to connect a source with a high impedance to a low-impedance load 5

6 Summing Amplifier Since no current can flow into the inverting input terminal, we can write i 1 i 2 i3 =i v1 0 v 2 0 v vout R R R = Rf Rf v out= R v1 v 2 v3 Difference Amplifier At node b, we have (voltage divider) R v b = R R v 2 1 = 2 v2 At node a, we have (use KCL) v1 0.5 v v 2 v out = R R v out =v 2 v1 6

7 7 6.3 Cascaded Stages Cascading several individual op amps together in the same circuit can be used to meet some application requirements A two-stage op amp circuit consisting of a summing amplifier cascaded with an inverting amplifier circuit Rf v x= R v1 v 2 R2 vout = R1 v x R 2 Rf R v out = R 1 v 1 v 2

8 8 6.4 Circuits for Voltage and Current Sources So far, we have made use of ideal current and voltage sources il il is vs vl vl = constant, no matter what the load current is vl il = constant, no matter what the load voltage is For practical voltage and current sources, we discussed the effect of the internal resistors in reducing the source outputs as more current or more voltage are supplied, respectively il il vs/r is vs vl isr vl

9 9 A Reliable Voltage Source One of the most common means of providing a stable and consistent reference voltage is to make use of a Zener diode Vout Vref Vin Vout Vref Vin Zener diode is a special type of diode designed to be used in a reverse biased mode As Vin goes greater than Vref, the voltage across the diode is essentially constant Rref in the circuit should be chosen to ensure that the diode is operating at its Zener voltage but below its maximum rated current

10 10 Design a circuit based on the 1N750 Zener diode (max current rating is 75 ma) that runs on a single 9 V battery and provides a reference voltage of 4.7 V From the circuit, we have R ref = 9 V ref I ref We design for 50 percent of the maximum rated current (Iref =0.075/2 A) R ref = =115 We may use the Zener reference circuit in conjunction with a simple amplifier stage to provide a reliable voltage source The result is a stable voltage that can be controlled by adjusting the value of either R1 or Rf, without having to switch to a different Zener diode

11 11 A Reliable Current Source We may use the Zener reference circuit in conjunction with a simple inverting op amp to design a reliable current source Regarding the ideal op amp rules IS V ref I S = R ref Thus, the current supplied to RL does not depend on its resistance The op amp circuit can be used as independent current source with the essential ideal characteristic (up to the maximum rated o/p current of the used op amp)

12 6.5 Practical Considerations The piratical op amp model can be represented as a dependent voltage source with voltage gain A, an output resistance Ro, and an input resistance Ri The parameter A is the open-loop voltage gain of the op amp, and is typically in the range of 105 to 106 The data sheet of the op amp describes several parameters such as the open loop gain, the input resistance, the output resistance, an input bias current, an input offset voltage, CMRR, slew rate, and the PSpice model 12

13 Using the practical op amp model reanalyze the inverting amplifier circuit Thus, we write two nodal equations: v in v d v out v d v d R1 Rf = Ri Av g v out v out v d = Rf R0 we eliminate vd and combine these two equations to obtain the following expression for vout in terms of vin: vout = [ R 0 R f R 0 AR f 1 R1 1 Rf 1 Ri ] 1 1 v in Rf R1 Using the typical values of the op amps parameters, we can compute the actual closed-loop gain of the op amp circuit Note that if we allow A, Ro 0, and Ri, we have Rf vout = R1 v in 13

14 Derivation of the Ideal Op Amp Rules The open circuit voltage of a practical op amp is vout =A v d The difference input voltage, can be given as v d= v out A since the o/p voltage is limited by the supplied voltage (5 to 24 V) and the open-loop gain in the range of 105 to 106, the practical value of vd is on the order of μv The input bias current of an op amp is simply vd iin = R i since the input resistance of an op amp is in the range of the mega ohms to the tera ohms, we expect an extremely small input current The o/p voltage can be given as vout =A v d R 0 iout a nonzero value of R0 acts to reduce the output voltage 14

15 Common-Mode Rejection The ideal op amps should amplify the difference between its two input terminals (v1-v2) with an infinite deferential-mode gain A=vout/(v1-v2) The input voltages can be expressed in terms of Differential mode component and common mode component as v1 =v cm v d /2 v 2=v cm v d / 2 where vd=v1-v2 and vcm=(v1+v2)/2 When v1=v2=vcm, the output should be zero, but real op amps produce a small common mode voltage vocm. The common mode gain of the op amp v ocm A CM = vcm We then define CMRR in terms of the ratio of differentialmode gain A to the common-mode gain ACM, or A CMRR= ACM 15

16 Negative Feedback The enormous but unpredictable gain of the op amp is made usable through negative feedback The closed-loop gain of the op amp is dominated by the ratio Rf/R1 Power Supplies The op amp requires power supplies Usually, equal and opposite voltages are connect to the V+ and V- terminals Typical values are 5 to 24 volts The power supply ground must be the same as the signal ground 16

17 17 Saturation The power supply voltages represent the maximum possible output voltage of the op amp The output of a real op amp cannot exceed its supply voltages vout Positive saturation region V+ Linear region vin negative saturation region V-

18 Offset Voltage Input offset voltage (VOS) arises as a result of the unavoidable mismatches The offset voltage and its polarity vary from one op-amp to another The analysis can be simplified by using the circuit model with an offset-free op amp and a voltage source VOS at input terminal Typical offset voltage is a few mv Effect of offset voltage for a closed-loop amplifier A dc voltage VOS(1+R2/R1) exists at the output at zero input voltage The input offset voltage is effectively amplified by the closed-loop gain as the error voltage at output Some op amps are provided with two additional terminals for offset nulling 18

19 Slew Rate One measure of the frequency performance of an op amp is its slew rate The slew rate is the rate at which the output voltage can respond to changes in the input (expressed in V/μs) Packaging 19

20 Comparators and The Instrumentation Amplifier The Comparator Since the open-loop gain of op amps is so high, small differences in the inputs will rapidly drive the output voltage to its maximum or minimum value The op amps in an open-loop configuration can be used as a comparator device A comparator circuit compares two input voltages and outputs either a 1 (the voltage at the positive terminal V+) or a 0 (the voltage at the negative terminal V-) to indicate which is larger vout 12 vin< vin vin>2.5

21 Design a circuit that provides a logic 1 5 V output if a certain voltage signal drops below 3 V, and zero volts otherwise. 21

22 The Instrumentation Amplifier An instrumentation amplifier is a type of differential amplifier that has been outfitted with input buffer amplifiers, which eliminate the need for input impedance matching and thus make the amplifier particularly suitable for use in measurement and test equipment Differential-mode gain can be adjusted by tuning RG=2R1 Common-mode gain is zero Input impedance is infinite Output impedance is zero 22

23 Homework Assignments 5 P6.2, P6.4, P6.9, P6.12, P6.14, P6.17, P6.18, P6.21, P6.30, P6.34, P6.40, P6.50, P