Op-amps and analog circuits
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An operational amplifier multiplies the difference between its two inputs by a huge gain, about 200,000 for the classic 741. With no feedback its output slams into a supply rail, which makes it a comparator. Add negative feedback and the resistors set the gain instead: -Rf/Rin for an inverting amplifier, 1 + Rf/Rg for a non-inverting one, and exactly 1 for a voltage follower. Work every number on one board, then see where op-amps are used.
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01A 741 op-amp has an open-loop gain of about 200,000. With no feedback, its + input is 1 mV above its - input, on a ±15 V supply. What is the output?
1 mV x 200,000 would be 200 V, but the output cannot go past its supply. On ±15 V a 741 typically stops at about 13 V: the output is saturated.
02An inverting amplifier has Rin = 10 kΩ and Rf = 100 kΩ. The input is 0.5 V. What is the output?
Gain = -Rf/Rin = -100 kΩ / 10 kΩ = -10, so 0.5 V becomes -5.0 V: ten times bigger, with the sign flipped.
03A non-inverting amplifier has Rg = 10 kΩ and Rf = 100 kΩ. What is its gain?
Gain = 1 + Rf/Rg = 1 + 100 kΩ / 10 kΩ = 11. So 0.5 V in gives 5.5 V out, with the same sign.
04In the inverting amplifier, why does all the current through Rin also flow through Rf?
An op-amp input draws almost no current (a 741 has about 2 MΩ input resistance). So the 50 µA that flows through Rin must continue through Rf, and that sets the output voltage.
05What is a voltage follower good for?
The follower's output copies its input (gain 1). Its input barely loads the source, while its output can supply current to the load. It is a buffer.
المسرد
- Op-amp
- Operational amplifier: a chip with two inputs (+ and -) and one output that amplifies the difference between the inputs.
- Open-loop gain
- How much an op-amp multiplies the input difference with nothing fed back: about 200,000 for a 741.
- Saturation
- When the output is stuck at (just inside) a supply rail because the circuit asks for more than the supply allows.
- Comparator
- A circuit that answers 'is this voltage above that one?' with an output at one rail or the other.
- Negative feedback
- Sending part of the output back to the - input, so the op-amp settles where its two inputs are almost equal.
- Virtual ground
- In an inverting amplifier, the - input held at almost 0 V by feedback, even though it is not wired to ground.
- Voltage follower
- An op-amp with its output wired straight to its - input: gain 1. Used as a buffer between a weak source and a load.
- Active filter
- An op-amp with resistors and capacitors around it that passes some frequencies and blocks others.
الملاحظات والمصادر
- The board circuit is a teaching model: the 10 kΩ and 100 kΩ resistors and the 0.5 V input make the arithmetic easy; they are not one application note's circuit.
- Numbers for the 741 are typical values from the Texas Instruments LM741 datasheet at a ±15 V supply: open-loop gain 200 V/mV (200,000), output swing ±13 V into 2 kΩ or more, input resistance 2 MΩ. Real parts vary from these.
- The formulas -Rf/Rin and 1 + Rf/Rg assume an ideal op-amp (infinite gain, no input current). With the 741's real gain the inverting gain is -9.9995 instead of -10: the difference is far smaller than the 1 % or 5 % tolerance of ordinary resistors.
- Real comparators are usually dedicated chips that switch faster than a general-purpose op-amp; the 741 is used here to show the idea.
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