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
① 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.
② Condition 2: Virtual short : Voltages at the input nodes are the same.
③ 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.
⑵ 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
③ 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.
⑷ Example 1: Inverting Amplifier : Voltage gain is negative. AC signal is inverted in the output.
Figure 8. Inverting Amplifier
⑸ Example 2: Non-Inverting Amplifier : Node at virtual short point is interpreted as vin.
Figure 9. Non-Inverting Amplifier
⑹ Example 3: Summing Amplifier : Multiple inverting amplification circuits are interpreted using the principle of superposition.
Figure 10. Inverting Summing Amplifier
⑺ 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
⑻ 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
⑼ 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
⑽ Example 7: Integrating Amplifier
Figure 15. Integrating Amplifier
⑾ 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