Op-Amp Series – Part 7: The Differentiator Amplifier

The Differentiator Amplifier

Final Build

A differentiator amplifier is an operational amplifier circuit that produces an output proportional to the rate of change of the input signal.

Instead of amplifying the voltage itself, it amplifies how fast the voltage is changing.

In simple mathematical terms:

Vout = -RC × (dVin/dt)

This means:

• If the input changes slowly → small output
• If the input changes quickly → large output
• If the input is constant (DC) → output is zero

Why is that powerful?

Because many real-world systems care about change, not steady values.

The Basic Differentiator Circuit

Basic Circuit

A basic differentiator uses:

• One capacitor
• One resistor
• One op-amp

Key layout:

• Capacitor in series with the input
• Resistor in the feedback path
• Non-inverting input connected to ground

This is almost the reverse of the integrator circuit.

How the Circuit Works

Let’s break it down conceptually.

1. The capacitor allows current to flow only when the input voltage is changing.
2. The faster the voltage changes, the more current flows.
3. That current flows through the feedback resistor.
4. The op-amp converts that current into a voltage at the output.

Since capacitor current is:

I = C × (dV/dt)

And voltage across a resistor is:

V = I × R

Combining them gives:

Vout = -RC × (dVin/dt)

The negative sign comes from the inverting configuration.

Understanding the RC Term

The product R × C determines how strongly the circuit responds to changes.

• Larger R or C → larger output for the same rate of change
• Smaller R or C → smaller output

It effectively sets the sensitivity to change.

What Happens With Different Input Signals?

1) DC Input

If the input is constant:

dVin/dt = 0

So:

Vout = 0

The differentiator completely ignores DC.

2) Ramp Input

If the input increases steadily (a straight-line ramp):

• The rate of change is constant
• The output becomes a constant voltage

So a ramp in gives a flat output.

3) Square Wave Input

A square wave changes very quickly at its edges.

• Rising edge → large negative spike
• Falling edge → large positive spike

Between transitions → zero output

This makes differentiators useful as edge detectors.

Why Differentiators Are Useful

Differentiators are used for:

• Edge detection in digital circuits
• Pulse generation
• High-pass filtering behaviour
• Detecting sudden changes
• Audio transient detection
• Wave-shaping circuits

Because they ignore slow changes and respond strongly to fast ones, they naturally behave like a high-pass filter.

The Practical Differentiator (Important!)

The ideal differentiator is rarely used exactly as shown.

Why?

• It amplifies high-frequency noise
• It can become unstable
• Real op-amps are not ideal

In practice, we often:

• Add a small resistor in series with the capacitor
• Add a small capacitor in parallel with the feedback resistor

This limits extreme high-frequency gain and improves stability.

Practical Build

Let’s build a simple differentiator using an LM358.

We’ll power it from a single 6 V supply, just like previous builds.

The goal will be to create a differentiator that produces visible spikes when a square wave is applied.

Component Values

• R = 10 kΩ
• C = 0.1 µF

This gives:

RC = 10,000 × 0.0000001

RC = 0.001

So:

Vout = -0.001 × (dVin/dt)

Parts Required

• LM358
• 10 kΩ resistor
• 0.1 µF capacitor
• Breadboard
• 6 V DC supply
• Jumper wires
• Function generator
• Oscilloscope

Circuit Diagram

Practical Circuit Build

Step-by-Step Wiring

1. Place the LM358

Insert the LM358 across the breadboard gap.

LM385 Pinout

We’ll use Op-Amp 1:

Pin 1 → Output
Pin 2 → Inverting Input (–)
Pin 3 → Non-inverting Input (+)
Pin 4 → Ground
Pin 8 → +6 V

2. Power Connections

Pin 8 → +6 V
Pin 4 → Ground

3. Input Capacitor

Connect 0.1 µF capacitor from signal input → Pin 2

4. Feedback Resistor

Connect 10 kΩ resistor from Pin 1 → Pin 2

5. Non-Inverting Input

Pin 3 → Ground

Applying a Test Signal

Connections for Function Generator and Oscilloscope

The easiest way to test this is with:

Function Generator Settings

• A square wave
• 1 kHz frequency
• 0 V to 5 V amplitude

Bench Power Supply Settings

If you don’t have a function generator, a 555 timer oscillator works well.

What You Should See

Oscilloscope Readings

On an oscilloscope:

• Sharp negative spike at rising edge
• Sharp positive spike at falling edge
• Flat line (0 V) between transitions

Important Real-World Note

Just like your earlier LM358 builds:

• The output cannot swing below ground.
• Negative spikes may clip at 0 V.

If you want full positive and negative spikes, you need a dual supply (positive and negative rails).

What Happens If You Change R or C?

Increase C → spikes get larger
Increase R → spikes get larger
Decrease either → spikes get smaller

But:

Too large → instability
Too small → barely visible output

It’s a balancing act.

YouTube Video

Key Takeaway

A differentiator:

• Responds to change, not level
• Ignores DC
• Produces spikes from square waves
• Acts like a high-pass filter

Mathematically:

Vout = -RC × (dVin/dt)

Conceptually:

The output shows how fast the input is moving.

Thanks

Hope you enjoyed this one.

Thanks for reading,
Matty