# DC Circuits: Operational Amplifiers Hasan Demirel

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1 DC Circuits: Operational Amplifiers Hasan Demirel

2 Op Amps: Introduction Op Amp is short form of operational amplifier. An op amp is an electronic unit that behaves like a voltage controlled voltage source. An operational amplifier has a very high input impedance and a very high gain.

3 Op Amps: Use of Op Amps Op amps can be configured in many different ways using resistors and other components. Most configurations use feedback. An op amp can be designed to perform mathematical operations of addition, subtraction, multiplication, division, differentiation, and integration.

4 Op Amps: Applications of Op Amps Amplifiers provide gains in voltage or current. Op amps can convert current to voltage. Op amps can provide a buffer between two circuits. Op amps can be used to implement integrators and differentiators. Op amps can be used to design filters (i.e. lowpass and bandpass filters).

5 Op Amps: Op Amp Symbol A typical op amp: (a) pin configuration, (b) circuit symbol.

6 Op Amps: Schematic diagram of op amp

7 A is the open-loop voltage gain. Op Amps: The Op Amp Model Inverting input Output Non-inverting input The differential input voltage The output voltage

8 Op Amps: Typical op amp parameters

9 Op Amps: Example 5.1: A 741 op amp has an open-loop voltage gain of 2x10 5, input resistance of 2 MΩ, and output resistance of 50 Ω. The op amp is used in the circuit shown in Fig. 5.6(a). Find the closed- loop gain v 0 /v s. Determine current i when v s = 2 V. Figure 5.6: (a) original circuit, (b) the equivalent circuit.

10 Op Amps: Example 5.1: A 741 op amp has an open-loop voltage gain of 2x10 5, input resistance of 2 MΩ, and output resistance of 50 Ω. The op amp is used in the circuit shown in Fig. 5.6(a). Find the closed- loop gain v 0 /v s. Determine current i when v s = 2 V. Apply KCL at node 1: (1) Apply KCL at node 0: (2)

11 Op Amps: Example 5.1: A 741 op amp has an open-loop voltage gain of 2x10 5, input resistance of 2 MΩ, and output resistance of 50 Ω. The op amp is used in the circuit shown in Fig. 5.6(a). Find the closed- loop gain v 0 /v s. Determine current i when v s = 2 V. Substituting v 1 from Eq. (1) into Eq. (2) gives: This is called closed-loop gain, because the 20-kΩ feedback resistor closes the loop between the output and input terminals. From Eq. (1)

12 Op Amps: Ideal Op Amp An ideal op amp is an amplifier with infinite open-loop gain, infinite input resistance, and zero output resistance. To facilitate the understanding of op amp circuits, we will assume ideal op amps. An op amp is ideal if it has the following characteristics: 1. Infinite open-loop gain, A = 2. Infinite input resistance, R in = 3. Zero output resistance, R o =0

13 Op Amps: Ideal Op Amp An ideal op amp is an amplifier with infinite open-loop gain, infinite input resistance, and zero output resistance. 1. Ideal Op Amp Model 1. Infinite open-loop gain, A = 2. Infinite input resistance, R in = 3. Zero output resistance, R o =0

14 Op Amps: Ideal Op Amp Two important characteristics of the ideal op amp are: 1. The currents into both input terminals are zero. This is due to infinite input resistance. An infinite resistance between the input terminals implies that an open circuit exists there and current cannot enter the op amp. 2. The voltage across the input terminals is equal to zero. An ideal op amp has zero current into its two input terminals and the voltage difference between the two input terminals is equal to zero.

15 Op Amps: Ideal Op Amp Example 5.2: Use the ideal op amp model to calculate the closed-loop gain v 0 /v s. Find i o when v s = 1 V. v 2 vs v1 v2 v s KCL at inverting terminal (v 1 ): vs vo vs v v s KCL at output (v o ): o v 1 v o i o v v v 10 o s o (if v s = 1 V, then v o = 9V) i o ( ) ma

16 Op Amps: Inverting Amplifier Both the input signal and the feedback are applied at the inverting terminal of the op amp. Applying KCL at node 1: Noninverting terminal is grounded. An inverting amplifier reverses the polarity of the input signal while amplifying it.

17 Op Amps: Inverting Amplifier Example 5.3: Refer to the op amp in Fig If v i =0.5 V, calculate: (a) the output voltage v o, and (b) the current in the 10-kW resistor. (a) (b)

18 Op Amps: Inverting Amplifier Practice Problem 5.3: Find the output of the op amp circuit shown in Fig Calculate the current through the feedback resistor.

19 Op Amps: Example 5.1: A 741 op amp has an open-loop voltage gain of 2x10 5, input resistance of 2 MΩ, and output resistance of 50 Ω. The op amp is used in the circuit shown in Fig. 5.6(a). Find the closed- loop gain v 0 /v s. Determine current i when v s = 2 V. Repeat Ex. 5.1 by using ideal op amp model.

20 Op Amps: Review To solve an op amp circuit, we usually apply KCL at one or both of the inputs. We then use the properties of the ideal model. The currents into both input terminals are zero. The voltage across the input terminals is equal to zero. We solve for the op amp output voltage.

21 Op Amps: Noninverting Amplifier A noninverting amplifier is an op amp circuit designed to provide a positive voltage gain. Apply KCL at inverting terminal: (1) Apply eq. (1) into eq (2): (2) Then:

22 Op Amps: Voltage Follower A voltage follower (or unity gain amplifier) has the output voltage equal to the input voltage. Voltage follower is a noninverting amplifier with:

23 Op Amps: Noninverting Amplifier Example 5.5: For the op amp circuit below, calculate the output voltage v o.

24 Op Amps: Summing Amplifier (Inverting Summer) Apply KCL at node a:

25 Op Amps: Summing Amplifier (Inverting Summer) Apply KCL at node a: Note that Then,

26 Op Amps: Summing Amplifier (Inverting Summer) Example 5.6: Find v o and i o in the op amp circuit shown below.

27 Op Amps: Difference Amplifier Apply KCL at node a: Apply KCL at node b: But

28 Op Amps: Difference Amplifier Difference amplifier must reject a signal common to the two inputs, the amplifier must have the property that v o =0, when v 1 = v 2. This property exists when: When this property is satisfied The op amp circuit is a difference amplifier If R 2 = R 1 and R 3 = R 4 The difference amplifier becomes A subtractor circuit:

29 Op Amps: Cascaded Op Amp Circuits A cascade connection is a head-to-tail arrangement of two or more op amp circuits such that the output of one is the input of the next. The overall gain of the cascade connection is the product of the gains of the individual op amp circuits

30 Op Amps: Cascaded Op Amp Circuits Example 5.9: Find v 0 and i 0 in the circuit below.

31 Op Amps: Cascaded Op Amp Circuits Example 5.10: Find v 1 = 1 V and v 2 = 2 V, find v 0 in the circuit below.

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