Operational Amplifiers

Modified: Mar. 14, 2026

Published: Mar. 6, 2026

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An operational amplifier (op-amp) is an integrated circuit that amplifies the voltage difference between its two inputs. With just a few external resistors, you can build amplifiers, buffers, comparators, filters, and signal conditioning circuits. The op-amp is arguably the most versatile building block in analog electronics. If transistors are individual bricks, an op-amp is a pre-assembled wall section: faster to use and more reliable for most applications. #AnalogElectronics #OpAmps #SignalConditioning

The Ideal Op-Amp

An ideal op-amp has these properties:

Real op-amps approximate these ideals well enough for most applications. The LM358 (dual op-amp, 2 per package) is an excellent beginner part because it works from a single supply (3V to 32V), has rail-to-rail input on the negative side, and costs very little.

Op-Amp Pins

An op-amp has five essential connections:

The Two Golden Rules

When an op-amp operates with negative feedback (output connected back to the inverting input through a resistor network), these two rules apply:

1. No current flows into the inputs. The input impedance is so high that the input current is effectively zero.
2. The op-amp adjusts its output to make both inputs equal. With negative feedback, .

These two rules let you analyze any op-amp circuit by simple algebra.

Five Essential Configurations

1. Voltage Follower (Buffer)

The simplest op-amp circuit connects the output directly back to the inverting input:

         ┌──────────┐
V_in ──>─┤ +     OUT ├──┬── V_out = V_in
         │          │  │
    ┌──>─┤ -        │  │
    │    └──────────┘  │
    └──────────────────┘

Gain is exactly 1. So why bother? The buffer transforms a high-impedance source (like a voltage divider or sensor) into a low-impedance output that can drive loads without affecting the source voltage.

Embedded application: When you connect a voltage divider to an ADC input, the ADC’s sampling capacitor draws a brief current pulse that disturbs the divider voltage. Placing a buffer between the divider and the ADC eliminates this problem. This is the “source impedance” issue mentioned in STM32 ADC lessons.

2. Non-Inverting Amplifier

The non-inverting amplifier amplifies the input signal without inverting it:

               R_f
         ┌────┤├────┐
         │          │
V_in ──>─┤ +    OUT ├──┬── V_out
         │          │  │
    ┌──>─┤ -        │  │
    │    └──────────┘  │
    │                  │
    ├──── R_1 ─── GND  │
    │                  │
    └──────────────────┘

The gain is always 1 or greater (you cannot attenuate with this configuration). The input impedance is very high, so it does not load the source.

Example: To amplify a sensor signal by a factor of 10, use and :

3. Inverting Amplifier

The inverting amplifier inverts and scales the input:

             R_f
        ┌────┤├────┐
        │          │
        │  ┌──────┐│
GND ──>─┤ +│ OUT  ├┤──── V_out
        │  │      │
V_in ──R_in─┤ -   │
        │  └──────┘

The gain can be less than 1 (attenuation), exactly 1, or greater than 1. The input impedance equals (lower than the non-inverting configuration).

The negative sign means the output is inverted: a positive input produces a negative output. With a single-supply op-amp, the output cannot go below ground (0V), so the inverting amplifier needs a virtual ground or a dual supply to handle negative outputs. For single-supply signal conditioning in embedded systems, the non-inverting configuration is usually preferred.

4. Comparator

When used without feedback (open-loop), an op-amp compares two voltages:

The output snaps to the supply rail or ground, producing a digital output from analog inputs. This is useful for threshold detection: “is the temperature above 50 degrees?” or “is the light level below a threshold?”

  Vcc
   |
  [R1] 10K            ┌--------┐
   +------->  V-  (-)  |        |
   |                   |  OUT   +---> Vout
  [R2] 10K            |        |  (HIGH or LOW)
   |         V+  (+)  |        |
  GND   Vsensor -->   └--------┘

  Vref = Vcc x R2/(R1+R2)
  Vsensor > Vref: Vout = Vcc
  Vsensor < Vref: Vout = 0V

Note: Dedicated comparator ICs (like LM393) are better for this purpose because they have faster response times and open-collector outputs that interface directly with digital logic. But an op-amp works for slow signals and prototyping.

5. Differential Amplifier

A differential amplifier amplifies the difference between two input signals while rejecting signals that are common to both inputs (common-mode rejection):

            [R1]         [Rf]
V1 o---+--/\/\/--+--+--/\/\/--+
                 |  |          |
                 | V-  ┌------┐|
                 +---->|  OUT |+-> Vout
                    V+ |      |
V2 o---+--/\/\/--+--->|      |
       |  [R1]   |    └------┘
       |        [Rf]
       |         |
       |        GND
       |
  Vout = (Rf/R1) x (V2 - V1)

This is essential for reading sensors in noisy environments. If electrical noise affects both signal wires equally, the differential amplifier cancels it out. Wheatstone bridges (Lesson 9) produce a differential signal that requires this type of amplifier.

The basic differential amplifier using a single op-amp requires matched resistors for good common-mode rejection. For precision applications, an instrumentation amplifier (three op-amps, or a dedicated IC like the INA128) provides much better performance.

Practical Considerations

Supply Voltage and Output Swing

The LM358 operates from a single supply of 3V to 32V. On a single 5V supply:

• The output can swing from about 0V to about 3.5V (not all the way to 5V)
• This limits the usable output range for ADC input

Rail-to-rail op-amps (like MCP6002, OPA2340) can swing their output to within millivolts of the supply rails. For 3.3V single-supply systems, rail-to-rail op-amps are strongly recommended.

Bandwidth and Slew Rate

The LM358 has a gain-bandwidth product (GBW) of about 1 MHz. This means:

• At gain = 1, bandwidth is 1 MHz
• At gain = 10, bandwidth is 100 kHz
• At gain = 100, bandwidth is 10 kHz

For audio and low-frequency sensor signals, this is plenty. For high-speed signals, you need a faster op-amp.

Slew rate is how fast the output can change: about 0.3 V/us for the LM358. If you need to amplify a fast signal (like a square wave), the output will round off the edges if the slew rate is insufficient.

Stability and Oscillation

Op-amp circuits can oscillate if the feedback path has too much delay or if the load is capacitive. For most breadboard circuits with resistive feedback, this is not a problem. On PCBs, keep feedback traces short and add a small capacitor (10 to 100 pF) across the feedback resistor if you see oscillation.

Practical Build: Thermistor Signal Conditioning

This is the key project for this lesson. We will read a thermistor voltage, amplify it to fill the 0 to 3.3V range of an ADC, and add a buffer stage for clean readings.

Components Needed

The Problem

A 10k NTC thermistor in a voltage divider with a 10k fixed resistor produces a voltage that varies from about 0.4V (hot) to 4.6V (cold) on a 5V supply. But the variation over the useful temperature range (say, 20 to 50 degrees Celsius) might only be 1V to 2.5V. If your ADC input range is 0 to 3.3V with 12-bit resolution (4096 counts), using only 1.5V of the 3.3V range wastes half your resolution.

The solution: amplify and offset the signal so that the temperature range of interest fills the entire ADC input range.

Circuit Design

We will use a two-stage approach:

  Thermistor       Buffer        Amplifier
  Divider         (Op-amp A)    (Op-amp B)
                 ┌--------┐    ┌--------┐
  VCC--[Rf]--+-->| +  OUT |+-->| +  OUT |--> Vout
             |   |        |    |        |    (to ADC)
          [NTC]  | -      |    | -      |
             |   └---+----┘    └---+----┘
            GND      |    Rf pot   |
              (output to   |       |
               inv. input) +--[R1]-+
                           |
                          GND

Stage 1: Voltage follower (buffer) The thermistor divider output connects to the non-inverting input of the first LM358 section, with the output connected back to the inverting input. This isolates the thermistor from the amplifier loading.

Stage 2: Non-inverting amplifier The buffered signal goes to the second LM358 section configured as a non-inverting amplifier with adjustable gain.

Build Steps

1. Power the LM358 Connect pin 8 () to 5V and pin 4 (GND) to ground. Place a 100 nF ceramic capacitor between pin 8 and pin 4, as close to the IC as possible. This is the decoupling capacitor.

2. Build the thermistor voltage divider Connect a 10k fixed resistor from 5V to a node. Connect the 10k NTC thermistor from that node to ground. The voltage at the node varies with temperature.

3. Connect the buffer (Op-amp A) Connect the thermistor node to pin 3 (non-inverting input of op-amp A). Connect pin 1 (output A) directly to pin 2 (inverting input A). The output on pin 1 is now a buffered copy of the thermistor voltage.

4. Build the amplifier (Op-amp B) Connect pin 1 (buffer output) to pin 5 (non-inverting input of op-amp B). Connect a 10k resistor () from pin 6 (inverting input B) to ground. Connect a 10k potentiometer () from pin 6 to pin 7 (output B).

5. Set the gain With the potentiometer at minimum resistance (~0 ohm), gain is about 1. At maximum (10k), gain is . For higher gain, replace with a smaller value. With and (pot) at 10k, gain is .

6. Measure the output Use your multimeter to measure the voltage at pin 7 (amplifier output). Warm the thermistor by pinching it between your fingers. The voltage should change noticeably as the thermistor heats up.

7. Adjust for your ADC range If your MCU ADC accepts 0 to 3.3V, adjust the gain so the output stays within this range across your expected temperature span. Measure the output at room temperature and while gently warming the thermistor, then set the potentiometer so the maximum output does not exceed 3.3V.

8. Verify linearity Note: the thermistor response is not linear. The op-amp amplifies whatever it receives faithfully. Linearization is typically done in software on the MCU using a lookup table or the Steinhart-Hart equation.

LM358 Pinout Reference

Verification Checklist

Dealing with LM358 Output Limitations

You will notice that the LM358 cannot swing its output all the way to 5V. The maximum is typically about . This is actually fine for our purpose, since we want to stay within the 3.3V ADC range. But if you need full rail-to-rail output, consider the MCP6002 (rail-to-rail, works at 3.3V supply) as a drop-in replacement for the LM358 in single-supply circuits.

Common Mistakes

How This Connects to Embedded Systems

Summary

Next lesson: power supply design. Every circuit needs clean, stable power. We will build a regulated 3.3V supply from a 9V battery and understand why decoupling matters so much.