Op-amp basics: calculating with the virtual short

Two rules

An ideal op-amp with feedback:

1. No current flows into the input terminals
2. The voltages at the two input terminals become equal (the virtual short)

Non-inverting amplifier

With the input on the + terminal, R2 from the output to the − terminal and R1 from the − terminal to ground:

Vout = Vin × (1 + R2/R1)

R1 = 1 kΩ, R2 = 9 kΩ → a gain of 10. The input impedance is very high, so it takes a sensor signal without loading it. With R2 at 0 it becomes a voltage follower (buffer) with a gain of 1.

Inverting amplifier

Vout = -Vin × (R2/R1). The sign is inverted and the input impedance is R1.

Limits of a real op-amp

Specification	Meaning	Effect
Rail-to-rail input/output	Can it work right up to the supply rails?	Important in single-supply 3.3 V circuits
Offset voltage	The error with zero input	Multiplied by the gain when amplifying small signals
GBW	Gain × bandwidth	At a gain of 100 the bandwidth is GBW/100
Slew rate	The fastest the output can change	Following fast PWM current waveforms

Remember just two rules

An op-amp circuit with negative feedback is calculated with two rules.

1. No current flows into the inputs.
2. The output moves until the two inputs are at the same voltage. (the virtual short)

Three basic circuits

Circuit	Gain	Input resistance	Use
Buffer (voltage follower)	1	Very high	After a divider, in front of an ADC
Non-inverting amplifier	1 + Rf / Rg	Very high	Enlarging sensor signals
Inverting amplifier	−Rf / Rin	Rin	Summing signals, flipping the sign

In a non-inverting amplifier, Rf = 90 kΩ, Rg = 10 kΩ gives a gain of 10. A 0.1 V signal becomes 1.0 V.

Example: measuring current with a shunt

5 A through a 10 mΩ shunt produces 50 mV. To measure it with a 3.3 V ADC, a gain of about 50 is right.

gain 50  →  2.5 V at 5 A
1 ADC LSB (0.8 mV)  →  0.8 mV / 50 / 0.01 Ω = 1.6 mA resolution

If you need to measure current in both directions, raise the middle of the output to 1.65 V and read anything above it as forward and anything below as reverse.

RoadmapSee where this note sits in Electronic Circuits→

What to check on a single supply

Most MCU circuits have only a single 3.3 V supply. Look at two things.

• Input range: does it work with the input down near 0 V? With the shunt on the ground side, the input is almost 0 V.
• Output range: does the output reach close to 0 V and to the supply voltage? An ordinary op-amp falls more than 1 V short at both ends.

A rail-to-rail input/output op-amp meets both conditions. Even then the output only goes down to a few tens of mV above 0 V, so values near 0 A may not be accurate.

Values to look for in the datasheet

Item	Meaning	Effect
Input offset voltage	The error even with equal inputs	Appears at the output multiplied by the gain
Gain-bandwidth product (GBW)	Gain × usable frequency	GBW 1 MHz at a gain of 50 is good to about 20 kHz
Slew rate	The fastest the output can change	Fast step signals become slanted
Input bias current	Current leaking into the inputs	An error when it meets large resistors

Amplify by 50 with an op-amp whose offset is 1 mV and 50 mV rides on the output. In current terms that is 100 mA, so for current measurement choose a low-offset part, or measure the value at 0 A at start-up and subtract it.

Why it should not be used as a comparator

Use an op-amp to compare two voltages without feedback and the output takes time to come out of saturation, and it chatters when the inputs are close. Where a fast decision is needed, such as overcurrent protection, use a dedicated comparator and give it hysteresis so it does not chatter at the threshold.

Problems that come up in practice

• No decoupling capacitor next to the power pin, causing oscillation
• A large capacitor directly on the output, causing oscillation (isolate it with a small series resistor)
• The amplified signal hits the supply rail and clips (recalculate gain and input range)
• Unused op-amp inputs left floating (wire it as a buffer tied to a mid-rail voltage)