Chapter 6: Operational Amplifier (Op Amp)

Transcription

1 Chapter 6: Operational Amplifier (Op Amp) 6.1 What is an Op Amp? 6.2 Ideal Op Amp 6.3 Nodal Analysis of Circuits with Op Amps 6.4 Configurations of Op Amp 6.5 Cascaded Op Amp 6.6 Op Amp Circuits & Linear Algebraic Eqs 6.7 Applications Digital to Analog Conerter Instrumentation Amplifier 6.8 Characteristics of Practical Op Amps 6.9 Summary 1

2 6.1 What is an Op Amp (1) An operational amplifier (op amp) is a integrated circuit (IC) composed of perhaps 30 BJTs and/or FETs, 10 resistors, and seeral capacitors. The functions like a oltage controlled oltage source. It is an actie circuit element designed to perform mathematical operations of addition, subtraction, multiplication, diision, differentiation and integration. Pin configuration Circuit symbol Powering the op amp 2

3 6.1 What is an Op Amp (2) (a) μa741 IC with has 8 connecting pins. (b) Correspondence btw circled pin numbers of the IC and the nodes. (c) An op amp, including power supplies + and -. (a) (b) (c)

4 6.1 What is an Op Amp (3) The equialent circuit of the non ideal op amp Op Amp output: o as a function of d d = 2 1 o = A d = A( 2 1 ) Typical ranges for op amp parameters Parameter Typical range Ideal alues Open loop gain, A 10 5 to 10 8 Input resistance, i 10 5 to Output resistance, o 10 to Supply oltage, V CC 5 to 24 V o o i i d () t S dt sat o sat 4

5 6.1 What is an Op Amp (4) Equialent circuit of the op amp: 5

6 6.2 Ideal Op Amp An ideal op amp has the following characteristics: 1. Infinite open loop gain, A 2. Infinite input resistance, i 3. Zero output resistance, o 0 Example: Determine the alue of i o. 6

7 6.3 Nodal Analysis of Circuits with Op Amps (1) Use node equations to analyze circuits containing ideal Op amps. There are 3 things to remember: 1. The node oltages at the input nodes of ideal op amps are equal. Thus, one of these two node oltages can be eliminated from the node equations can be eliminated from the node equations. 2. The currents in the input leads of an ideal op amp are zero. These currents are inoled in the KCL equations at the input nodes of the op amp. 3. The output current of the op amp is not zero. This current inoled in the KCL Equations at the output node of the operational amplifier. Applying KCL at this node adds another unknown to the node equations. If the output current of the op amp is not to be determined, then it is not necessary to apply KCL at the output node of the operational amplifier. 7

8 6.3 Nodal Analysis of Circuits with Op Amps (2) Example: Analysis of a Bridge Amplifier The operational amplifier and resistors, 5 and 6, are used to amplify the output of the bridge. As a consequence, 1 = 0 and i 1 = 0, determine the output oltage, o, in terms of the source oltage, s. (a) (b) (c) (d) (a) A bridge amplifier, including the bridge circuit. (b) The bridge circuit and (c) its Théenin equialent of the bridge. 8

9 6.3 Nodal Analysis of Circuits with Op Amps (3) First, notice that the node oltage a is gien by (using KVL) Because 1 = 0 and i 1 = 0, i a 1 oc t 1 Now, writing the node equation at node a a o a i Because a = oc and i 1 = 0, Soling for o, we hae a oc oc o oc o oc s

10 6.4 Configurations of Op amp (1) Inerting Amplifier: reerses the polarity of the input signal while amplifying it. Negatie feedback btw the inerting input ( i ) & output ( o ) i is connected to the inerting input ia 1 Equialent Noninerting circuit input is grounded To find the relationship btw i & o : By KCL at node 1, i 1 1o i1 i2 1 f for an ideal op amp since the noninerting terminal is grounded. f o i 1 Closed-loop oltage gain is A o i f Example: Find o & i in 1 if i = 0.5 V, 1 = 10 kω, & f = 25 kω. 1 10

11 6.4 Configurations of Op amp (2) Current to oltage conerter (trans resistance amplifier) PD is adopted to use an inerting current o i s 3 3 o 11 i 1 2 s 11

12 6.4 Configurations of Op amp (3) Noninerting Amplifier: designed to produce positie oltage gain. To find the relationship btw i & o : i connected to noninerting input terminal f 1 0 (short circuit) or (open circuit) o i By KCL at inerting terminal, i i2 f 1 2 i o 1 1 Voltage gain: A 1 1 o i f To isolate two cascaded stage: as oltage follower Has a ery high input impedance and 12 thus eliminate interstage loading f o i 1

13 6.4 Configurations of Op amp (4) Circuit 1 (a) before and (b) after circuit 2 is connected. (c) Preenting loading, using a oltage follower. A oltage diider (a) before and (b) after a 30 kω resistor is added. (c) A oltage follower is added to preent loading. 13

14 6.4 Configurations of Op amp (5) A common application of op amp is to scale a oltage, that is, to multiply a oltage by a constant, K, so that o Kin The input oltage, in, is proided by an ideal oltage source. The output oltage, o, is the element oltage of a 100 kω resistor. Circuits that perform this operation are usually called amplifiers. The constant K is called the gain of the amplifier. There are four cases to consider: (b) K = -5 (< 0), (c) K = 5 (> 1), (d) K = 1, and (e) K = 0.8 (0 < K < 1). (a) (b) (c) (d) (e) 14

15 6.4 Configurations of Op amp (6) Example: calculate the output oltage o. 15

16 6.4 Configurations of Op amp (7) Summing Amplifier: combines seeral inputs and produces an output that is the weighted sum of the inputs. Example: calculate o & i o. To find the relationship btw i & o : By KCL at node a, i i1i2 i3 But i, i, i, i a 1 a 2 a 3 a a o f 0o f f f

17 6.4 Configurations of Op amp (8) Differential Amplifier: amplifies the difference between two inputs but rejects any signals common to the two inputs. Example: Design an op amp circuit with 1 & 2 such that o = By KCL at node a, 1a a o 2 2 o 1a By KCL at node b, 0 2 b b 4 b (1 1/ 2) 2 But a b o 2 1 1(1 3/ 4) 1 To reject a signal common to the two inputs, o 0 when 1 2, if To become a subtractor, o , if

18 6.4 Configurations of Op amp (9) 18

19 6.4 Configurations of Op amp (10) 19

20 6.5 Cascaded Op Amp (1) Cascaded Connection: a head to tail arrangement of two or more op amp circuits such that the output of one is the input of the next. Op amp circuits hae the adantage that they can be cascaded without changing input output relationships. This is due to the fact that each (ideal) op amp circuit has i & o 0. Note that to design an actual op amp circuit must ensure that the load due to the next stage in the cascade does not saturate the op amp. Oerall gain: 20

21 6.5 Cascaded Op Amp (2) Example : If 1 = 1 V & 2 = 2 V, find o 21