Simulation Control
Change anything on the op amp or on the water model; the two are always the same circuit. Restart from 0 V puts both inputs back at 0 V, with feedback off, a gain of 105 and a ±15 V supply.
Op Amp
The circuit: vo = A(V+ − V−), held inside the supply rails. The Water Model shows the same op amp as flowing water, and every control here has a twin there.
−PS is drawn at the top here to match the water model, where the supply (PS−) is at the top. Most textbooks draw +PS at the top; the circuit is the same either way.
Key to the op amp drawing
- V+ input: green wire
- V− input: orange wire
- Feedback wire: violet, or dashed grey when off
- Supply pins: dashed
- Partner of the part you point at or focus: thick blue lines
Now: op amp state
- Inputs
- Difference, vs
- Output, vo
Water Model
The same op amp as a trough of flowing water. Water stands for electrons, so it runs from PS− to PS+, and the fuller a column, the more negative its voltage. Every column reads 0 V on the same dotted line.
Key to the water model
- V+ float and left gate: green
- V− float and right gate: orange
- Output float and its linkage: violet, dashed
- Water: the streaks run faster where more flows
- 0 V line: dotted
- Output limits: dashed
- Partner of the part you point at or focus: thick blue outline
Now: water model state
- V+ column
- V− column
- Water split
- Output column
Output Over Time
- V+: green line
- V−: orange line
- vo: thick blue line
- ±limit: dashed grey
- ±PS: dotted grey
Each line is named at its right-hand end.
Show recent values as a table
Transfer Curve
Output against the input difference. The axis rescales with the gain.
- vo = A·vs, clipped at the limits
- Linear operating range
- Filled dot: now (an arrow when off scale)
Show the curve as a table
Op Amp and Water Model, Part by Part
Point at a row, a part of the op amp or a part of the water model to highlight its partner in both drawings.
| In the op amp | In the water model | What it does |
|---|---|---|
| Supply pins, −PS (top) and +PS (bottom) | Pump, supply reservoir (PS−, top) and drain (PS+, bottom) | Provide all the water (current). The output can never go beyond them, which is why the op amp is powered: it is the source of any gain. |
| Noninverting input, V+ | V+ column, its float and the left gate | The column's level is V+. Filling it (more negative) pushes the left gate shut, more water reaches the output, and vo goes more negative with it. |
| Inverting input, V− | V− column, its float and the right gate | Filling it pushes the right gate shut, less water reaches the output, and vo goes the other way: the inverting input flips the sign. |
| Open-loop gain, A | Gate sensitivity | How much of the supply's water the gates send down one channel for a small difference between the input columns. Too much, and all of it goes one way: the output is at a limit. |
| The op amp's transistors | Channels around the central block | The paths the gates steer the supply's water through. |
| Output, vo | Corner outlet and output column | Fuller column, more electrons at the output: a more negative vo. |
| Feedback wire from vo to V− | Float in the output column | Works the right gate in place of the V− column. The output settles level with the V+ column: vo = V+. |
| Circuit common | The dotted 0 V line | Every column reads its voltage from this line; the gate pivots sit on it too. |
About the Model
The water model
Water stands for electrons. It enters from the supply at the top (PS−), splits around the central block and leaves through the drain at the bottom (PS+). The two hinged gates, level with each other, are the op amp's inputs. Each is worked by a float in its own small input column: the V+ column on the left and the V− column on the right. Fill or drain a column with its taps to change that input. A column's level is its voltage, read from the dotted 0 V line that runs through all three columns; the fuller the column, the more electrons and so the more negative the voltage. A fuller input column pushes its gate shut.
The gates are sensitive: a small difference between them decides how the supply's water divides between the two channels, and the gate sensitivity (the gain) sets how much of it goes to one side for a given difference. The streaks show the split; at a limit, all of the water that can be steered goes one way. Closing the left gate leaves more water for the right side, so the outlet at the bottom-right corner pushes water up into the output column: vo goes more negative, the same way V+ went. Closing the right gate starves the corner, the output column drains, and vo goes the other way: the inverting input flips the sign. The gates only steer water; they never supply it, so the output column can never fill above the supply or drain below the drain. That is saturation at the output limits, and it is why the op amp must be powered.
Why the input columns change scale
Without feedback, a gain of 105 means a few microvolts between the inputs is enough to swing the output across its whole range, so the input columns are drawn magnified: a column's full range is ±67.5 µV. Over the gates' whole travel the output then changes all the way, reaching a limit only at the very ends. With feedback on (the float in the water model), the op amp itself keeps the inputs within microvolts of each other, so the inputs can span volts: the input columns then read ±8 V on the same scale as the output column, and the output settles exactly level with the V+ column.
The equations
- Open loop: vo = A(V+ − V−), limited to ±(PS − 1.5 V). With far more gain than the gates' travel needs (try 107), most of the travel drives the output to a limit: the op amp is a comparator.
- With the float (the feedback wire), V− = vo, so vo = V+ · A/(1 + A), which is V+ to within a few parts per million at A = 105.
- The difference the op amp needs to hold that output is vs = vo/A, a few microvolts: the gates end up balanced.
Time
After any change, the output moves toward its new value no faster than the slew rate, 10 V/µs (typical of a general-purpose op amp), and settles with a time constant of 0.5 µs. Time is slowed about a million-fold so the response can be seen: at 1× speed, 1 s on screen is 1 µs in the op amp. The same settling is used with and without feedback; open loop, a real op amp's small-signal response is far slower (its dominant pole sits near 10 Hz), which is one more reason op amps are almost always used with feedback. The taps fill and drain the input columns at 20 % of a column per second of real time.
What is simplified
- The water picture is an analogy. The flow streaks, ripples, gate angles and linkages are illustrative; the numbers under Now come from the op amp model.
- The output limits sit 1.5 V inside each supply rail, the same on both sides.
- The inputs draw no current, and there is no offset voltage or bias current.
Keyboard
Tab moves between controls. Arrow keys move a slider in small steps, Page Up and Page Down in larger ones, or type a value in the box beside it and press Enter (for example 27, −40 or 1e5; SI prefixes such as 100k or 27µ work too). Fill and Drain add or remove a little water each press. The op amp's controls and the water model's are the same settings in different words, so moving one moves its twin, and focusing a control highlights its part in both drawings. On the water model you can also drag an input column's water level or hold down its taps. Alt + Shift + P (Option + Shift + P on a Mac) switches presentation mode on and off, and Escape leaves it.