Operational Amplifiers

Transcription

1 Monolithic Amplifier Circuits: Operational Amplifiers Chapter Jón Tómas Guðmundsson Week Fall 200 Operational amplifiers (op amps) are an integral part of many analog and mixedsignal systems The op amp is a highgain differential amplifier Modern op amp design involves a tradeoff between parameters such as voltage gain, input impedance, speed and power dissipation 2 The operational amplifier can be looked at as a black box having two inputs and one output The term operational amplifier (op amp) was coined in the 940s That is well before the invention of the transistor and the integrated circuit They were first realized by vacuum tubes to create integrators and differentiators etc. referred to as analog computers it performed mathematical operations thus operational amplifier The op amp is a circuit that amplifies the difference between the two inputs = ( 2 ) 3 4

2 Actual op amps are not ideal Ideal op amps have infinite voltage gain, = infinite input impedance, R in = zero output resistance, R 0 = 0 infinite speed zero output voltage when input voltage is zero infinite bandwidth infinite slew rate v2 i2 v R i i R o A(v 2 v ) Equivalent circuit of an op amp i o v o finite voltage gain, finite bandwidth, bw finite input impedance, R in finite input capacitance, C in finite output resistance, R 0 generates noise input bias currents input offset currents and voltages finite output swing and all of these effects are temperature dependent v2 i2 v R i i R o A(v 2 v ) Equivalent circuit of an op amp i o v o 5 6 The main objective of this course is to understand what causes the nonidealities and to develop design strategies to get around them The first step towards analyzing and designing op amps is to understand the transistor technologies upon which they are based The very high gain of the op amp leads to an important observation The difference between and 2 is always small 2 = 7 8

3 Unitygain buffer Unitygain buffer If the voltage gain of the op amp were infinite For a finite gain = ( 2 ) = ( ) and = 2 = = or = The gain approaches unity as becomes large 9 0 Noninverting amplifier Inverting amplifier Noninverting amplifier consists of an op amp and a voltage divider 2 = = R R If the op amp has finite gain = where is the open loop gain and / is the closed loop gain R Now node X bears zero potential referred to as virtual ground so 0 R This is the inverting amplifier = = R 2

4 Inverting amplifier Integrator If we assume a finite gain = ( ) R R With an ideal op amp C = s = R R C s = Example. so the circuit operates as an integrator (and low pass filter) 3 4 Integrator Differentiator Also or d = C R dt = dt RC Here = R V = R C s in C s which acts as a differentiator and a high pass filter Similarly or C d dt = R = R C d dt 5 6

5 Precision rectifier Precision rectifier Recall that simple rectifier circuits suffer from a dead zone due to the finite voltage required to turn on a diode (0.7 V) This drawback prevents the use of simple diode circuits in high precision applications A solution to this problem is to place a diode around an op amp for a precision rectifier to rectify very small signals If = 0 the op amp raises V Y to approximately V D,on so turning D barely on with little current so V X 0 If becomes slightly positive V Y rises further so that current flowing through D and R yields A diode D is placed in the feedback loop If becomes negative D turns off 7 8 Logarithmic amplifier Squareroot amplifier Here also = V BE so V BE = V T ln /R I s = V T ln I s R Logarithmic amplifiers are useful in applications where the input signal level may vary by a large fraction Here = R 2 µ W nc ox L (V GS V TH ) 2 and since V GS = 2 = W µ n C ox L R V TH 9 20

6 DC offsets Op amp Nonidealities Input offset voltage is the voltage that must be applied to the two input terminals to null the output In practice op amps suffer from imperfections that may influence circuit performance significantly So far we have assumed that = 0 if = 2 In reality, a zero input difference may not give a zero output In op amp design the tradeoffs between parameters requires a multidimensional compromise If the speed is critical while the gain error is not we choose a topology that favors the former The internal circuit of the op amp may have random asymmetries from fabrication E.g. the bipolar transistor sensing the input may have different baseemitter voltages 2 22 Input bias current Input bias current is the average of the currents that flow into the inverting and noninverting terminals of an op amp I B = I B I B2 2 The high frequency behavior of op amps plays a critical role in many applications In reatility, the internal capacitances of the op amp degrade the performance at high frequency Op amps implemented in bipolar technology draw a base current from each input They are small ( 0. µa) but may create inaccuracies in some circuits The open loop gain begins to fall as the operational frequency exceeds f 23 24

7 Note that for low frequencies This gainroll off can be approximated by a first order model where 2 (s) = s ω the gain is equal to At very high frequencies s/ω s/ω ω = 2πf The smallsignal bandwidth is often defined as the unitygain frequency f u and the gain of the op amp falls to unity at ω u = ω f u can exceed GHz for modern CMOS op amps For the noninverting amplifier (s) = s ω R s ω = s ω R The bandwidth of the closedloop circuit is significantly higher than that of the op amp itself The system is of first order and the pole of the transfer function is given by ( ) ω p,closed = ω R This improvement is at the cost of a reduced gain, from to (R ) = Example

8 Slew rate Slew rate Slew rate is defined as the maximum rate of change of the output voltage per unit of time SR = d [V/µs] dt maximum In reality the output first rises with a constant slope (i.e. as a ramp) and eventually settles as in the linear case Slewing is a nonlinear phenomena It indicates how rapidly the output of an op amp can change in response to changes in the input frequency Slew rate If and (t) = V 0 sinωt ( (t) = V 0 R ) sinωt d dt ( = V 0 R ) ω cosωt Slew rate The output exhibits a maximum slope of V 0 ω( R / ) and the op amp must have SR with higher value to avoid slewing and ω FP = is the fullpower bandwidth and is a measure of the largesignal speed of the op amp SR V max V min 2 = Example

9 Operational Amplifiers in circuits Operational Amplifiers in circuits Operational amplifiers are everywhere in practical circuits The operational amplifier 74 has been a workhorse in circuits for decades Operational Amplifiers in circuits Further reading This discussion is based on Chapter 8 in Razavi (2008) and section 9.. of Razavi (200). A nice summary of op amp parameters is also found in chapter 2 of Gayakward (2000). References Gayakward, R. A. (2000). Opamps and Linear Integrated Circuits (4 ed.). Upper Saddle River, NJ: Prentice Hall. The operational amplifiers are often included in application specific integrated circuits (ASIC) Razavi, B. (200). Design of Analog CMOS Integrated Circuits. New York, NY: McGrawHill. Razavi, B. (2008). Fundamentals of Microelectronics. Hoboken, NJ: John Wiley & Sons. Here we see a CMOS op amp on the die level 35 36