🔁 Op-Amp Basics: Inverting and Non-Inverting Amplifiers

Now that you understand the ideal op-amp concept, let’s look at the two most fundamental op-amp configurations:

• Non-Inverting Amplifier
• Inverting Amplifier

Almost every op-amp circuit you’ll ever design is built from these two ideas.

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➕ Non-Inverting Amplifier

This is the most intuitive op-amp configuration.

🔌 Configuration

• Input signal → Non-inverting input (+)
• Feedback → From output to inverting input (−) using resistors

🔄 Behavior

• Input goes up → Output goes up
• Input goes down → Output goes down

The signal is not flipped.

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📐 Gain Formula

$$A_v = 1 + \frac{R_f}{R_s}$$

Where:

• $R_f$ = feedback resistor (output → − input)
• $R_s$ = resistor from − input to ground

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📊 Example

If:

• $R_f = 9k\Omega$
• $R_g = 1k\Omega$

Then:

$$A_v = 1 + \frac{9k}{1k} = 10$$

So:

• $100mV \rightarrow 1V$
• $200mV \rightarrow 2V$

Very predictable and stable.

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✅ Advantages

• Very high input impedance
• Does not load sensors
• No phase inversion
• Can be unity gain (buffer)

📌 Unity gain buffer:

$$R_f = 0,\; R_s = \infty \Rightarrow A_v = 1$$

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➖ Inverting Amplifier

Here the signal is applied to the inverting input.

🔌 Configuration

• Input signal → Inverting input (−) through a resistor
• Non-inverting input (+) → Ground
• Feedback from output → − input

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🔄 Behavior

• Input goes up → Output goes down
• Input goes down → Output goes up

The output is 180° out of phase (inverted).

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📐 Gain Formula

$$A_v = -\frac{R_f}{R_{s}}$$

Where:

• $R_{s}$ = input resistor
• $R_f$ = feedback resistor

The negative sign means inversion.

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📊 Example

If:

• $R_f = 10k\Omega$
• $R_{in} = 1k\Omega$

Then:

$$A_v = -10$$

So:

• $+100mV \rightarrow -1V$

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✅ Advantages

• Precise, stable gain
• Gain can be less than 1
• Easy to sum multiple inputs
• Defined input impedance ($R_{in}$)

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⚖️ Key Differences at a Glance

Feature	Non-Inverting	Inverting
Phase	Same as input	Inverted (180°)
Input impedance	Very high	Set by resistor
Gain formula	$1 + R_f/R_s$	$-R_f/R_{s}$
Unity gain	Yes	Yes
Signal summing	Harder	Easy

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🔁 Feedback – The Secret Sauce

Both circuits rely on negative feedback.

Golden rule applies:

$$V_{+} \approx V_{-}$$

Feedback forces the op-amp to settle at a stable output instead of saturating.

Without feedback:

• Output slams to supply rails
• Circuit becomes a comparator

With feedback:

• Linear
• Predictable
• Stable

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🧪 Practical Beginner Example (Non-Inverting)

Sensor output:

$$50mV \rightarrow 1V \text{ required}$$

Required gain:

$$A_v = \frac{1V}{50mV} = 20$$

Choose:

$$R_f = 19k\Omega,\; R_s = 1k\Omega$$

Perfect for temperature, pressure, light sensors.

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➕ Practical Example (Inverting)

Want to add signals:

$$V_{out} = -(V_1 + V_2 + V_3)$$

Use:

• Multiple input resistors
• One feedback resistor

This is the foundation of summing amplifiers.

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🚫 Common Beginner Misconception

“Inverting means something is wrong”

❌ False.

Inversion just means:

$$\text{Phase shift} = 180^\circ$$

In audio, control systems, and signal processing, inversion is often intentional.

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🧭 Choosing the Right One

Use Non-Inverting when:

• Sensor has high impedance
• Phase must be preserved
• You want a buffer or voltage follower

Use Inverting when:

• You need exact gain control
• You’re summing signals
• Input impedance must be known
• Phase inversion doesn’t matter

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✅ The Bottom Line

• Non-inverting: signal stays upright, high input impedance
• Inverting: signal flips, precise gain control
• Both rely on negative feedback
• These two circuits form the foundation of all op-amp designs

Master these, and op-amps become predictable, powerful tools instead of mysterious black boxes.