Experiment 4

1. Experiment 4 * Operational Amplifiers * Op-Amp Circuits * Op-Amp Analysis

2. Operational Amplifiers • Op-Amps are possibly the most versatile linear integrated circuits used in analog electronics. • The Op-Amp is not strictly an element; it contains elements, such as resistors and transistors. • However, it is a basic building block, just like R, L, and C. • We treat this complex circuit as a black box! • Do we know all about the internal details? No! • Do we know how to use it and interface it with other electronic components? Yes, we must!

3. Op-Amp Circuits perform Operations • Op-Amps circuits can perform mathematical operations on input signals: • addition and subtraction • multiplication and division • differentiation and integration • Other common uses include: • Impedance buffering • Active filters • Active controllers • Analog-digital interfacing

4. The Op-Amp Chip • The op-amp is a chip, a small black box with 8 connectors or pins (only 5 are usually used). • The pins in any chip are numbered from 1 (starting at the upper left of the indent or dot) around in a U to the highest pin (in this case 8). 741 Op Amp

5. Op-Amp Input and Output • The op-amp has two inputs, an inverting input (-) and a non-inverting input (+), and one output. • The output goes positive when the non-inverting input (+) goes more positive than the inverting (-) input, and vice versa. • The symbols + and – do not mean that that you have to keep one positive with respect to the other; they tell you the relative phase of the output. (Vin=V1-V2) A fraction of a millivolt between the input terminals will swing the output over its full range.

6. Powering the Op-Amp • Since op-amps are used as amplifiers, they need an external source of power. • The op-amp must be connected to an external constant DC source in order to function. • Typically, this source will supply +15V at +V and -15V at -V. The op-amp will output a voltage range of of somewhat less because of internal losses. The power inputs determine the output range of the op-amp. It can never output more than you put in. Here the maximum range is about 28 volts.

7. Op-Amp Intrinsic Gain • Amplifiers increase the magnitude of a signal by multiplier called a gain -- “A”. • The internal gain of an op-amp is very high (105-106). • The exact gain is often unpredictable. • We call this gain the open-loop gain or intrinsic gain.

8. Op-Amp Saturation • Note that in spite of the huge gain, the maximum or minimum output is still limited by the input power. • When the op-amp is at the maximum or minimum extreme, it is said to be saturated. • Ideally, the saturation points for an op-amp are equal to the power voltages, in reality they are 1-2 volts less.

9. Internal Model of a Real Op-amp • Zin is the input impedance (very large ≈ 2 MΩ) • Zout is the output impedance (very small ≈ 75 Ω) • Aol is the open-loop gain

10. Real Op-Amp Characteristics • dc-coupled: the op amp can be used with ac and dc input voltages • differential voltage amplifier: the op amp has two inputs (inverting and non-inverting) • single-ended low-resistance output: the op amp has one output whose voltage is measured with respect to ground. The output looks like a voltage source. • very high input resistance: the op-amp input looks like a load circuit to any circuit connected to its input (ideally 0 current; actually < 1nA) • very high voltage gain: the op-amp will saturate either positive or negative depending on the inputs

11. Problems using op-amps directly as amplifiers • The op-amp intrinsic gain, Aol, can be relied upon to be very large (1 to 5 million V/V ) but cannot be relied upon to be an accurate stable value. • Using op-amps, we can construct circuits whose performance depends mainly on passive components selected to have accurate and stable values. • As long as Aol is large enough, the behavior of our circuits will depend upon the values of the stable components rather than Aol • Feedback is the process of coupling the op-amp output back into one of the inputs.Understanding feedback is fundamental to understanding op-amp circuits.

12. Types of Feedback • Negative Feedback • As information is fed back, the output becomes more stable. Output tends to stay in the desired range. • Examples: cruise control, heating/cooling systems • Positive Feedback • As information is fed back, the output destabilizes. The op-amp will saturate. • Examples: Guitar feedback, stock market crash

13. Op-Amp Circuits use Negative Feedback • Negative feedback couples the output back in such a way as to cancel some of the input. • This lowers the amplifier’s gain, but improves: • Freedom from distortion and nonlinearity • Flatness of frequency response or conformity to some desired frequency response • Stability and Predictability • Insensitivity to variation in Aol • Amplifiers with negative feedback depend less and less on the open-loop gain and finally depend only on the properties of the feedback network itself.

14. Op-Amp Circuits • Op-Amp circuits we will do now • inverting amplifier (multiply signal by negative gain) • non-inverting amplifier (multiply signal by positive gain) • differential amplifier (multiply difference between two signals by a positive gain) • Op-Amp circuits we will do in experiment 8 • weighted adder • integrator • differentiator • buffer (voltage follower)

15. Inverting Amplifier

16. Non-inverting Amplifier

17. Differential (or Difference) Amplifier

18. PSpice circuit you will use in exp 4

19. Op-Amp Analysis • We assume we have an ideal op-amp: • infinite input impedance (no current at inputs) • zero output impedance (no internal voltage losses) • infinite intrinsic gain • instantaneous time response

20. Golden Rules of Op-Amp Analysis • Rule 1: VA = VB • The output attempts to do whatever is necessary to make the voltage difference between the inputs zero. • The op-amp “looks” at its input terminals and swings its output terminal around so that the external feedback network brings the input differential to zero. • Rule 2: IA = IB = 0 • The inputs draw no current • The inputs are connected to what is essentially an open circuit

21. How to analyze a circuit with an op-amp 1) Remove the op-amp from the circuit and draw two circuits (one for the + and – input terminals of the op amp). 2) Write equations for the two circuits. 3) Simplify the equations using the rules for op amp analysis and solve for Vout/Vin

22. Analysis of Non-inverting Amplifier Note that step 2 uses a voltage divider to find the voltage at VB relative to the output voltage.

23. Analysis of Difference Amplifier(1)

24. Analysis of Difference Amplifier(2) Note that step 2(-) here is very much like step 2(-) for the inverting amplifier and step 2(+) uses a voltage divider. What would happen to this analysis if the pairs of resistors were not equal?

25. Op-Amp Cautions (1) • In all op-amp circuits, the “golden rules” will be obeyed only if the op-amp is in the active region, i.e., inputs and outputs are not saturated at one of the supply voltages. • Typically it can swing only to within 1-2V of the supplies. • There must always be negative feedback in the op-amp circuit. Otherwise, the op-amp is guaranteed to go into saturation. • Do not not mix the inverting and non-inverting inputs.

26. Op-Amp Cautions (2) • Many op-amps have a relatively small maximum differential input voltage limit. The maximum voltage difference between the inverting and non-inverting inputs might be limited to as little as 5 volts in either polarity. Breaking this rule will cause large currents to flow, with degradation and destruction of the op-amp. • Note that even though op-amps themselves have a high input impedance and a low output impedance, the input and output impedances of the op-amp circuits you will design are not the same as that of the op-amp.