Section 6 Chapter 2: Operational Amplifiers

Transcription

1 03 Section 6 Chapter : Operational Amplifiers eference : Microelectronic circuits Sedra sixth edition 4//03

2 4//03 Contents: - DC imperfections A. Offset voltage B. Solution of offset voltage C. Input bias current D. SOLUTION OF BIAS CUENT E. Offset current - Finite open loop gain and bandwidth a. Frequency Dependence of the Open-Loop Gain b. Frequency esponse of Closed Loop Amplifiers 3- Large signal operation a. Output voltage saturation b. SLEW ATE c. FULL BANDWIDTH POWE 4- AC Coupled Amplifiers 5- ASSIGNMENT

3 4//03 - Dc Imperfection A. Offset Voltage If the two input terminals of the op amp are connected to ground, it will be found that a finite dc voltage exists at the output V o =V os (+ / ) B. It s Solution Capacitive coupling This circuit will have high pass filter response. For dc input bias V o =V os (+ /Z ) Z = V o = V os So the aim of this solution is that V os will not be amplified at dc gain C. Input bias current I B =I B =I B V O =I B = I B

4 4//03 D. Solution of bias current To make V o =0 We put 3 = // Proof??? E. Offset current Having selected 3 as above, let us evaluate the effect of a finite offset current I os I B = I B + l os / and I B = I B l os / The result is V o =I os Proof??? We conclude that to minimize the effect of the input bias currents, one should place in the positive lead a resistance equal to the equivalent dc resistance seen by the inverting terminal. Example Effect of offset voltage: V o =V os + 3

5 4//03 Problem 98 A particular inverting amplifier with nominal gain of 00 VN uses an imperfect op amp in conjunction with 00-kΩ and 0-MΩ resistors. The output voltage is found to be +9.3 V when measured with the input open and V with the input grounded. (a) What is the bias current of this amplifier? In what direction does it flow? (b) Estimate the value of the input offset voltage. (c) A 0-MΩ resistor is connected between the positive input terminal and ground. With the input left floating (disconnected), the output dc voltage is measured to be 0.8 V. Estimate the input offset current. Solution a. If the input is open V o - V os =I B 9.3 = V os I B If the input is grounded I B = I B = - From & I B =930 na b. V os = -.mv c. As 0-MΩ resistor is connected between the positive input terminal and ground = V o =I os 0.8=0000 I os I os = -80 na - Finite open loop gain and bandwidth A. Frequency Dependence of the Open-Loop Gain The differential openloop gain A of an op amp is not infinite but it is finite and decreases with frequency. Its 4

6 4//03 5 response is similar to the response of low pass filter and its gain can be written as A(s) For high frequencies w>>> w o A(jw) A(jw) To reach unity gain, let s define gain bandwidth product or unity gain bandwidth W t =A o W o B. Frequency esponse of Closed Loop Amplifiers For inverting configuration For very small w b (w o ) G As 0 b G s A t G s 3 t db 0 3 db b A 3 db G s

7 4//03 Problem A particular op amp characterized by a gain bandwidth product of 0 MHz is operated with a nominal closed-loop gain of 00 V/V. What 3-dB bandwidth results? At what frequency does the closed-loop amplifier exhibit -6 o phase shift? 84 o phase shift? Solution F t = 0 MHz + F 3db = =00 KHz G(jw)= Ø=tan - ( ) =-6 f=tan (-6)* f 3db = KHz 3- Large signal operation A. Output voltage saturation Similar to all other amplifiers, op amps operate linearly over a limited range of output voltages. Specifically, the op-amp output saturates in the manner shown with L and L within V or so of the positive and negative power supplies, respectively. Thus, an op amp that IS operating from + 5-V supplies will saturate when the output voltage reaches about + 3 V in the positive direction and 3 V in the negative direction. For this particular op amp the rated output voltage IS said to be ± 3 Y. To avoid saturation the input signal must be kept correspondingly small. 6

8 4//03 B. Slew rate Another phenomenon that can cause nonlinear distortion when large output signals are present is slew-rate Limiting. The name refers to the fact that there IS a specific maximum rate of change possible at the output of a real op amp. This maximum is known as the slew rate (S) of the op amp and is defined as C. Full power bandwidth dv S dt O max The op-amp data sheets usually specify a frequency f M, called the full-power bandwidth, It IS the frequency at which an output sinusoid with amplitude equal to the rated output voltage of the op amp begins to show distortion due to slew-rate limiting. If we denote the rated output voltage V omax then f M is related to S as follows v Vˆ sin t v I O v GVˆ sin t O dvo GVˆ i cos t dt S GVˆ cos t S GVˆ i G v S V i M i i i OMax S V OMax 7

9 4//03 Problem 4 For operation with 0 V output pulses with the requirement that the sum of the rise and fall times represent only 0% of the plus width (at half amplitude). What is the slew-rate requirement for an op amp to handle pulses µs wide? (Note: The rise and fall times of the pulse signal usually measured between the 0% and 90% height points). Solution: 4- AC Coupled Amplifiers The concept of AC coupled is not to pass the dc voltage to the circuit Also we need to decrease all Dc imperfections as offset voltage, bias current and offset current, all this can done by a. selecting 3 = b. selecting 3 = 8

10 4//03 Biomedical department nd year st term 03 Electronics course Assignment no.6 Student name: Problem 05 An op amp intended for operation with a closed loop gain of -00 V\ V uses resistors of 0 kω and MΩ with a bias-current-compensation resistor, What should the value of be with input grounded. The output offset voltage is found to be +0. V. Estimate the input offset current assuming zero input offset voltage. If the input offset voltage can be as large as mv of unknown polarity, what range of offset current is possible? Solution 9

11 4//03 Problem 7 This problem illustrates the use of cascaded closed-loop amplifiers to obtain an overall bandwidth greater than can be achieved using a singlestage amplifier with the same overall gain. (a) Show that cascading two identical amplifier stages. Each having a lowpass STC frequency response with a 3-dB frequency f, results in an overall amplifier with a 3-dB frequency given by (b) It is required to design a non-inverting amplifier with a dc gain of 40 db utilizing a single internally compensated op amp with f = I M Hz. What is the 3-dB frequency obtained? (c) edesign the amplifier of (b) by cascading two Identical non-inverting amplifies each with a dc gain of 0 db. What is the 3-dB frequency of the overall amplifier? Compare this to the value obtained In (b) above. Solution 0

12 4//03 Problem 8 A designer wanting to achieve a stable gain of 00 V/V at 5 MHz. considers his choice of amplifier topologies. What unity-gain frequency would a single operational amplifier require to satisfy his need? Unfortunately the best available amplifier has an f of 40 MHz. How many such amplifiers connected in a cascade of identical non-inverting stages would he need to achieve his goal? What is the 3-dB frequency of each stage he can use? What is the overall 3-dB frequency? Solution