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| learn:courses:real-analog-chapter-5:start [2017/01/19 23:26] – [Real Analog: Chapter 5] Martha | learn:courses:real-analog-chapter-5:start [2023/02/10 12:34] (current) – external edit 127.0.0.1 | ||
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| - | ====== Real Analog: Chapter 5 ====== | + | ===== Real Analog: Chapter 5 ====== |
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| + | * Lecture Material: | ||
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| + | * Chapter 5 Video: | ||
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| - | ====== 5. Introduction and Chapter Objectives | + | ===== 5. Introduction and Chapter Objectives ===== |
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| The above constraint is based on pure inequalities – in general, the output voltage range will be somewhat less than the range specified by V- and V+. The margin between the output and the supply voltages will vary depending on the specific op-amp. Any attempt to drive the output voltage beyond the range specified by the supply voltages will cause the output to // | The above constraint is based on pure inequalities – in general, the output voltage range will be somewhat less than the range specified by V- and V+. The margin between the output and the supply voltages will vary depending on the specific op-amp. Any attempt to drive the output voltage beyond the range specified by the supply voltages will cause the output to // | ||
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| - | Similarly it makes sense that the power supply voltages will constrain the range of allowable input voltages, as provided below: | ||
| **Input Voltage Constraint**: | **Input Voltage Constraint**: | ||
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| * The voltages at the input terminals are the same: $v_n = v_p$ | * The voltages at the input terminals are the same: $v_n = v_p$ | ||
| * The output voltage is constrained to be between the positive and negative power supply voltages: $V^- < v_{OUT} < V^+$ | * The output voltage is constrained to be between the positive and negative power supply voltages: $V^- < v_{OUT} < V^+$ | ||
| - | * The input voltages are constrained to be between | + | * Nothing is known about the current out of the op-amp, $i_{OUT}$ |
| * All voltages on the above diagram are relative to the same reference. | * All voltages on the above diagram are relative to the same reference. | ||
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| $$V_{OUT} = K \left(v_p - v_n \right) = K \cdot \Delta v_{in} | $$V_{OUT} = K \left(v_p - v_n \right) = K \cdot \Delta v_{in} | ||
| - | Where in $\Delta v_{in}$ is the difference between the voltages at the input terminals and //K// is a very large number. (Values of //K// for typical commercially available operational amplifiers can be on the order of $10^6$$ or higher.) Since the output voltage is constrained to be less than the supply voltages, | + | Where in $\Delta v_{in}$ is the difference between the voltages at the input terminals and //K// is a very large number. (Values of //K// for typical commercially available operational amplifiers can be on the order of $10^6$ or higher.) Since the output voltage is constrained to be less than the supply voltages, |
| $$V^- < K \cdot \Delta v_{in} < V^+$$ | $$V^- < K \cdot \Delta v_{in} < V^+$$ | ||
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| ==== Exercises ==== | ==== Exercises ==== | ||
| - | - An operational amplifier has a gain K = 10,000. The voltage supplies are $V+ = 20V$ and $V-= -10V$. Determine the output voltage if the voltage difference between the input terminals $\left( v_p - v_n \right) is: | + | - An operational amplifier has a gain K = 10,000. The voltage supplies are $V+ = 20V$ and $V-= -10V$. Determine the output voltage if the voltage difference between the input terminals $\left( v_p - v_n \right)$ is: |
| - 1mV | - 1mV | ||
| - 2mV | - 2mV | ||
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| * The effect of a non-zero output resistance on an operational amplifier’s operation is that the power output of the amplifier is limited. Thus, a realistic operational amplifier will not be able to provide any arbitrary current to a load. Whether this has a significant effect on the overall circuit’s operation is primarily dependent upon the value of the load resistance. | * The effect of a non-zero output resistance on an operational amplifier’s operation is that the power output of the amplifier is limited. Thus, a realistic operational amplifier will not be able to provide any arbitrary current to a load. Whether this has a significant effect on the overall circuit’s operation is primarily dependent upon the value of the load resistance. | ||
| * The effect of a finite op-amp gain is that the voltage difference across the input terminals may not be identically zero. | * The effect of a finite op-amp gain is that the voltage difference across the input terminals may not be identically zero. | ||
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