The Non-Inverting Amplifier and the Buffer

Same rules, a different doorway

In the last guide you fed the signal into the minus pin and used the virtual ground to build the inverting amplifier. Here we change one thing: the signal goes into the plus pin instead, and the feedback still comes back to the minus pin. That single move builds the non-inverting amplifier — same chip, same two golden rules, but a friendlier circuit whose output rises when the input rises, never flipping its sign.

Remember why the rules work at all: they only hold with negative feedback wrapped around the amplifier. The op-amp has enormous open-loop gain, so the faintest difference between its two inputs slams the output hard one way; the feedback path then feeds enough of the output back to the minus pin to kill almost all of that difference. The chip settles wherever the two inputs are practically equal. That self-balancing is the thermostat you have met before, and it is the engine behind everything in this guide.

Deriving the gain: 1 + Rf/Rin

Apply the rules in order. The first rule says no current flows into either input, so the feedback resistor Rf and the lower resistor Rin form a plain voltage divider hanging off the output, undisturbed by the minus pin. The second rule, the virtual short, says the op-amp drives its output until the minus pin equals the plus pin — and the plus pin is Vin. So the divider's tap is forced to sit at exactly Vin.

Now just read the divider backwards. The minus pin sits at Vout times Rin/(Rin + Rf), and that must equal Vin. Solve for the ratio and the Rin cancels neatly into the closed-loop gain: Vout/Vin = 1 + Rf/Rin. The gain is set entirely by a ratio of two resistors you choose — not by the op-amp's own messy, temperature-drifting open-loop gain. That is the quiet revolution: trade away raw gain you cannot trust for a precise gain you can.

  Vin >--------|+\
               |  \
               |   >-----+------> Vout
          +----|- /      |
          |    |_/       |
          |              |
          +----[ Rf ]----+
          |
        [ Rin ]
          |
         GND

  closed-loop gain = 1 + Rf/Rin
  e.g. Rf = 90k, Rin = 10k  ->  1 + 90/10 = 10

Put numbers on it. With Rf = 90 k and Rin = 10 k the gain is 1 + 90/10 = 10, so a 0.2 V input becomes a 2 V output, same polarity. Notice two things the inverting amp could not offer. First, the gain can never be less than 1 — the leading "1 +" is built in, so this topology amplifies but never attenuates. Second, the signal source looks straight into the plus pin, which (golden rule one) draws essentially no current. The amplifier barely loads whatever feeds it, an advantage we are about to push to its beautiful extreme.

The buffer: a gain of one that earns its keep

Take the non-inverting amp to its simplest extreme. Make Rf = 0 (a plain wire from output to the minus pin) and remove Rin entirely (treat it as infinite). The gain becomes 1 + 0/infinity = 1. The output now simply copies the input, volt for volt. This is the voltage follower, also called the unity-gain buffer — the output faithfully follows wherever the input leads. It is the most-used op-amp circuit on Earth, and at first glance it looks pointless: why build an amplifier that does not amplify?

The answer is impedance, not voltage. A weak source — a high-resistance sensor, a divider made of big resistors — has the right voltage but no muscle to drive a load; ask it for current and its voltage sags. This is the loading effect you met back in the DC rungs: connecting the load changes the very voltage you wanted to read. The buffer breaks that trap. Its plus pin sips almost no current from the source (so the source never sags), while its output, stiffened by feedback, can push real current into the load. Same voltage in and out, but transformed from a frail signal into a sturdy one.

A worked design: sensor into ADC

Picture a real job. A sensor delivers a clean 0 to 0.25 V signal, but it can only supply microamps, and it must drive a circuit that needs the full 0 to 2.5 V range and draws real current. You need a gain of 10 and you must not load the fragile sensor. The non-inverting amplifier solves both at once: it amplifies by the resistor ratio while its plus pin barely touches the source. Here is the walk-through.

1. Pick the gain: you need 0.25 V to become 2.5 V, so gain = 10. Set 1 + Rf/Rin = 10, which means Rf/Rin = 9.
2. Choose real resistors: Rin = 10 k and Rf = 90 k give the ratio 9. Keep them in the kilo-ohm range — too small wastes current heating resistors, too large lets stray currents and noise matter.
3. Wire it: sensor to the plus pin; the 90 k from output back to the minus pin; the 10 k from the minus pin to ground. Check the divider: at Vout = 2.5 V the minus pin sits at 2.5 times 10/(10+90) = 0.25 V, matching the plus pin. The rules hold.
4. Check the load is handled: the op-amp output, not the sensor, supplies whatever current the next stage draws. The sensor only feeds the plus pin, which (rule one) takes almost nothing, so its 0.25 V never sags.

If the sensor already swung the full 0 to 2.5 V and only lacked drive strength, you would drop the gain entirely and use a plain buffer — gain 1, but now able to drive the load. Amplify-and-buffer or just-buffer: same family, you pick the gain you need. This is exactly the kind of stage-interfacing thinking that turns isolated circuits into a working signal chain.

Honest limits, and a glimpse without feedback

The golden rules are an idealization, and they bite when you forget it. The virtual short only holds while the op-amp can actually move its output to balance the inputs — so it fails when you ask for more than the chip can deliver. Demand a swing the supply rails cannot reach and the output clips flat. Demand a fast signal and two real limits appear: slew rate caps how many volts per microsecond the output can move, and the gain-bandwidth product means your gain of 10 only survives up to one-tenth of the part's unity-gain frequency. Above that, the loop runs out of spare gain and the rules quietly stop being true.

There is also the question of speed versus stability. The feedback that grants the rules can also misbehave: if the loop picks up too much phase shift on the way around, the correction arrives late and the amplifier can break into oscillation. That is the dark mirror of the same physics, and the real-op-amp rung studies how to keep a feedback amplifier honest. For now, just hold the caveat: these tidy formulas live inside a supply-, speed-, and stability-bounded box.

Finally, a contrasting glimpse: an op-amp with no feedback at all. Strip the feedback resistor away and the chip runs open-loop, where its huge open-loop gain makes the output slam fully to one rail or the other the instant the plus pin differs from the minus pin. The golden rules no longer apply — there is nothing to balance the inputs. That is not a broken amplifier; it is a comparator, a yes/no decision maker answering "is A above B?". Add a touch of positive feedback to give it a deadband and you get a Schmitt trigger — a thermostat with hysteresis that refuses to chatter on a noisy edge. Feedback to the minus pin makes a faithful amplifier; feedback to the plus pin, or none at all, makes a decider. Same chip, opposite jobs.