Non-inverting amplifier
16 minutes · Advanced
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The non-inverting amplifier is the most widely used op-amp circuit. It amplifies the signal in phase (as the input rises, the output rises too) and its input resistance is very high, so it hardly loads the source it measures at all. It's the first choice for enlarging sensor signals.
The circuit
The signal goes to the op-amp's + input. A resistor Rf goes from the output to the − input, and a resistor Rg from the − input to ground. These two resistors feed part of the output back to the − input: they form a voltage divider.
Finding the gain with the two rules
- Rule 2: V− = V+ = Vin.
- Rule 1: no current enters the − input; the same current flows through Rf and Rg. Rf and Rg are a voltage divider dividing the output voltage: V− = Vout × Rg / (Rf + Rg).
- Set the two equations equal: Vin = Vout × Rg / (Rf + Rg) → Vout = Vin × (Rf + Rg) / Rg.
Gain = 1 + Rf / Rg
Question: A microphone gives a 20 mV signal. We want 1 V at the output. If Rg = 1 kΩ, what should Rf be?
Gain = 1 V / 20 mV = 50
50 = 1 + Rf / 1k → Rf = 49 kΩ → standard value 47 kΩ (gain 48)
Try it yourself
Set the gain by changing Rf. Then increase the amplitude: the output clips when it reaches the rails. Set the model to LM358, raise the gain to 101 (Rf 100k, Rg 1k) and increase the frequency: see how the bandwidth narrows.
Non-inverting amplifier
Vout = (1 + Rf/Rg) × Vin = 2.00 × Vin
Input signal
Components
Supply and op-amp
Infinite speed and bandwidth; the output swings all the way to the rails.
Why is it so useful?
- Very high input resistance: the signal goes straight to the op-amp input; almost no current is drawn from the source. Ideal for high-impedance sensors (piezo, pH probe).
- The gain depends on the resistors: even though the op-amp's own gain varies with temperature and from part to part, the circuit's gain depends only on the Rf/Rg ratio. With 1% resistors you get a gain accurate to 2%.
What should the resistor values be?
Even if the ratio stays the same, very small resistors (e.g. Rf = 100 Ω) load the op-amp's output unnecessarily. Very large resistors (e.g. 10 MΩ) bring noise and bias-current errors. In practice, values between 1 kΩ and 100 kΩ are chosen for Rf and Rg.Common mistakes
- Thinking the gain is Rf/Rg: in a non-inverting amplifier you add 1.
- Connecting Rg to the supply instead of ground.
- Not allowing for the op-amp's GBW at high gain (LM358 with a gain of 100 → ~10 kHz).
- Trying to amplify an AC signal on a single supply without giving the input a DC offset.
Test yourself
1. Rf = 22 kΩ, Rg = 2.2 kΩ. The gain?
2. What is the phase of the output in a non-inverting amplifier?
3. Can we bring the gain below 1?
4. Which circuit has the highest input resistance?
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