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Lesson 10. Op Amp (Operational Amplifier)

Higher category : [Circuit Theory] Circuit Theory Table of Contents


1. Overview

2. Ideal Op Amp

3. Practical Op Amp

4. Parameters of Op Amp


a. Floating Capacitor and Feedback Direction of Op Amp


**1. Overview **

⑴ Definition : A component that amplifies the potential difference between two input terminals and outputs it in the form of voltage.

⑵ Structure of Op Amp Component

Figure 1. Structure of Op Amp Component

① The top part of the component is marked, making it distinguishable between top and bottom.

② output voltage = A × (non-inverting input voltage + (-1) × inverting input voltage)

○ Also referred to as non-inverting input voltage: v2

○ Also referred to as inverting input voltage: v1

③ Op Amp is supplied with energy from power sources (④, ⑤) : Requires two power terminals.

④ Offset null : Used to adjust the output error of the Op Amp (⑥, ⑦)

⑤ NC (no connection) : Unused area (⑧)

⑶ Op Amp Equivalent Circuit Stage 1 : Capacitors and other omissions

Figure 2. Op Amp Equivalent Circuit Stage 1 [Note:1]

⑷ Op Amp Equivalent Circuit Stage 2 : Omitting offset null (⑥, ⑦)

Figure 3. Op Amp Equivalent Circuit Stage 2 [Note:2]

⑸ Op Amp Equivalent Circuit Stage 3 : Omitting (+), (-) power supplies (④, ⑤)

① Schematic

Figure 4. Op Amp Equivalent Circuit Stage 3

② The simplified equivalent circuit of the Op Amp does not satisfy KCL (Kirchhoff’s Current Law)

○ Ground connections to the Op Amp are omitted

○ Leakage current flows through the ground connections

○ Formulation

Figure 5. Current Flow through Op Amp (including leakage current)

⑹ Op Amp Equivalent Circuit Stage 4 : Assuming ib1, ib2, vos = 0

Figure 6. Op Amp Equivalent Circuit Stage 4



2. Ideal Op Amp

⑴ Conditions

Condition 1: Virtual ground : Input current is 0. Input resistance is infinite.

○ To achieve this, a virtual ground must be connected to the input node.

○ The simplified equivalent circuit of the Op Amp does not satisfy KCL : This is due to the omission of ground connections to the Op Amp.

○ Leakage current flows through the ground connections.

Condition 2: Virtual short : Voltages at the input nodes are the same.

Condition 3: R o __= 0. In other words, the output resistance is 0 and the voltage gain A0 is infinite.

○ The voltage gain should always be infinite regardless of frequency.

v i __- v o curve

① Graph : The magnitude of the output voltage cannot exceed the power supply voltage.


Figure 7. Graph of Real Op Amp

② Op Amp Amplification Range

v+ = v- applies in the solution examples below as well.

⑶ Feedback

① Definition : Feedback loop : Connection between output terminal and input terminal

② Purpose : The amplification range is quite narrow, so Op Amp is not often used without feedback loop.

○ In other words, constructing an open-loop circuit makes it difficult to adjust the amplification ratio and saturation occurs easily.

○ Constructing a feedback loop allows users to adjust the amplification ratio.

Example 1: Inverting Amplifier : Voltage gain is negative. AC signal is inverted in the output.

Figure 8. Inverting Amplifier

Example 2: Non-Inverting Amplifier : Node at virtual short point is interpreted as vin.

Figure 9. Non-Inverting Amplifier

Example 3: Summing Amplifier : Multiple inverting amplification circuits are interpreted using the principle of superposition.

Figure 10. Inverting Summing Amplifier

Example 4: Voltage Follower : Strategy to eliminate loading effect.

Figure 11. Voltage Follower

① When there is a loading effect : vb = 0.5 vin (O), va = 0.75 vin (X)

Figure 12. When there is a loading effect

② When there is no loading effect : Due to the virtual short of Op Amp, vc = va

Figure 13. When there is no loading effect

Example 5: Differential Amplifier

Figure 14. Differential Amplifier

① Circuit interpretation

○ When Rb = kRa and Rd = kRc : vo = k (vb - va)

② Advantages of the difference amplifier

○ Can eliminate the influence of common errors when measuring va and vb

○ Application in sensors : Can read values proportional to the measured physical quantities

Example 6: Differentiating Amplifier

Figure 15. Differentiating Amplifier

① Circuit interpretation

② Features

○ All signals have some degree of noise

○ Due to noise, the output voltage value changes very irregularly

○ The differentiator is not widely used in practice

Example 7: Integrating Amplifier

Figure 15. Integrating Amplifier

Example 8:

Figure 16. Example 1

① Circuit interpretation

○ Applying KCL to the inverting input node

○ Applying KCL to the non-inverting input node

○ Applying characteristics of ideal Op Amp

○ Conclusion

② The 50 kΩ resistor does not affect the circuit interpretation at all : The current created by the 50 kΩ resistor escapes as supply current



3. Practical Op Amp

⑴ Real Inverting Op Amp : Considering Ri ≠ ∞, Ro ≠ 0 as practical Op Amp

Figure 17. Real Inverting Op Amp

(The arrows all indicate grounding)

① Represented as 1/R is denoted as G

② In the case of ideal Op Amp : A → ∞, Gi → 0, Go →

∞, when substituted, this matches the previous conclusion

③ Offset null

Figure 20. Offset Null

○ Circuit interpretation

○ vpractical - videal according to R1

○ In the case of R1 = 0 : Vos term appears, so vpractical - videal = (1 + R3 / R2)vos + R3 ib1

○ In the case of R1 ≪ 1, R1 ≠ 0 : vpractical - videal = R3 ib1 = R3 × (bias current)

○ In the case of R1 = (R2-1 + R3-1)-1 : vpractical - videal = R3 (ib1 - ib2) = R3 × (offset current)

○ Offset

○ Deviation between control quantities in actual situation and control quantities in ideal situation

○ Generally, bias current is about 4 times offset current : R1 as a variable resistor reduces the error of the actual Op Amp, which is offset null

⑵ SR (Slew Rate) : A measure of the rate at which a signal is transmitted from the input terminal to the output terminal

Figure 21. Slew Rate

① Mathematical expression

② All input signals can be represented as the integral sum of a step function : An accurate output function can be found

⑷ Asymmetry of Op Amp

① Negative Feedback Op Amp : Feedback circuit connected to the inverting input node

○ Feedback Circuit : Circuit connecting the output terminal and input terminal

Figure 22. Negative Feedback Op Amp

○ Ideal Op Amp : vo = A (v2 - v1)

○ Real Op Amp : vo = A (v2 - v1)

② Positive Feedback Op Amp : Feedback circuit connected to the non-inverting input node

○ Feedback Circuit : Circuit connecting the output terminal and input terminal

Figure 23. Positive Feedback Op Amp

○ Ideal Op Amp : vo = A (v2 - v1)

○ Real Op Amp : vo = v+ or v- (Op Amp’s supply voltage)

③ Reason : Related to stray capacitor



4. Parameters of Op Amp

Table 1. Parameters of Op Amp



Input: 2016-01-09 21:30

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