🎯 Instrumentation Amplifiers: Precision Measurement

We've learned about difference amplifiers. They subtract signals. But they have a problem:

Input impedance is only okay, not great.

When measuring tiny signals from sensors (thermocouples, strain gauges, medical electrodes), you need:

• Very high input impedance (GΩ range)
• Very high CMRR (Common-Mode Rejection Ratio)
• Precise, adjustable gain
• Low noise and drift

This is where Instrumentation Amplifiers (In-Amps) shine.

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🔍 What is an Instrumentation Amplifier?

An instrumentation amplifier is a precision differential amplifier designed specifically for measurement applications.

Key Features

Feature	Regular Diff Amp	Instrumentation Amp
Input impedance	~10kΩ to 100kΩ	>1GΩ (both inputs)
CMRR	40-60dB	80-120dB
Gain accuracy	Moderate	Excellent (<0.1% error)
Gain adjustment	Multiple resistors	Single resistor
DC offset	Higher	Ultra-low
Noise	Moderate	Very low

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🏗️ Three Op-Amp Instrumentation Amplifier

The Architecture

• Input V1 to non-inverting of Op-Amp 1
• Input V2 to non-inverting of Op-Amp 2
• Gain resistor Rg between inverting inputs of Op-Amp 1 and 2
• Resistors R from each output to respective inverting inputs
• Op-Amp 1 and 2 outputs feed difference amplifier (Op-Amp 3)
• Final output Vout

How It Works

Stage 1 & 2: Input buffers with gain

• Very high input impedance (op-amp inputs)
• Differential gain set by single resistor $R_g$

Stage 3: Difference amplifier

• Subtracts the two buffered signals
• Fixed gain (usually 1)
• Very high CMRR

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📐 The Magic Equation

For the three op-amp instrumentation amplifier:

$$V_{out} = \left(1 + \frac{2R}{R_g}\right)(V_2 - V_1)$$

Where:

• $V_1, V_2$ = input voltages
• $R$ = input stage resistors (matched pair)
• $R_g$ = gain-setting resistor (the only one you change!)

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🎚️ Setting the Gain

Want gain of 100?

$$100 = 1 + \frac{2R}{R_g}$$ $$\frac{2R}{R_g} = 99$$

If $R = 10k\Omega$:

$$R_g = \frac{2 \times 10k}{99} = 202\Omega$$

Use standard value $R_g = 200\Omega$

That's it! One resistor controls the entire gain.

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Gain Resistor Selection

• High gain (100-1000): $R_g$ = 100Ω to 1kΩ
• Medium gain (10-100): $R_g$ = 1kΩ to 10kΩ
• Low gain (1-10): $R_g$ = 10kΩ to 100kΩ or even open circuit

For variable gain, use a potentiometer for $R_g$!

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🌡️ Real-World Example: Thermocouple Amplifier

Problem: K-type thermocouple produces 41µV/°C

Measure temperature range: 0-500°C
Output range needed: 0-5V for ADC

Signal from thermocouple: $0 to 20.5mV$ (500°C × 41µV/°C)

Required gain:

$$A_v = \frac{5V}{20.5mV} = 244$$

Design:

• Choose $R = 10k\Omega$ (typical)
• Calculate $R_g$:

$$244 = 1 + \frac{2 \times 10k}{R_g}$$ $$R_g = \frac{20k}{243} = 82.3\Omega$$

Use standard value: $R_g = 82\Omega$ (1% tolerance)

Result:

• 0°C → 0V
• 500°C → ~5V
• Perfect for 10-bit ADC (0-1023 counts)

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💪 Why Common-Mode Rejection Matters

The Problem

Sensors often pick up noise:

• 50/60Hz mains hum
• EMI from motors, switching supplies
• Ground potential differences

This noise appears equally on both inputs = common-mode signal

Example

• $V_1 = 1.000mV + 100mV_{noise}$
• $V_2 = 1.005mV + 100mV_{noise}$

What we want: $V_2 - V_1 = 5\mu V$

With poor CMRR (40dB):

• Noise rejection: 100:1
• Remaining noise: 1mV
• Signal: 5µV
• Signal drowned in noise!

With excellent CMRR (100dB):

• Noise rejection: 100,000:1
• Remaining noise: 1µV
• Signal: 5µV
• Clean signal!

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🔬 Common-Mode Rejection Ratio (CMRR)

Definition:

$$CMRR_{dB} = 20 \log_{10}\left(\frac{A_{differential}}{A_{common-mode}}\right)$$

CMRR	Rejection Ratio	Application
40dB	100:1	Basic measurements
60dB	1,000:1	General instrumentation
80dB	10,000:1	Precision measurements
100dB	100,000:1	Medical, strain gauges
120dB	1,000,000:1	Ultra-precision

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Practical CMRR Considerations

CMRR depends on:

• Resistor matching (use 0.1% or better)
• Frequency (CMRR decreases at high frequencies)
• Op-amp quality (use precision op-amps)
• PCB layout (symmetric, short traces)
• Temperature (use low-drift resistors)

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⚖️ Wheatstone Bridge + In-Amp = Perfect Match

We'll cover Wheatstone bridges in detail soon, but here's a preview:

Strain Gauge Measurement

Bridge output: Typically ±10mV full scale
With 10V excitation: 0.1% change = 10mV

In-Amp makes it easy:

• Connect bridge to In-Amp inputs
• Set gain = 500
• Output: ±5V full scale
• Perfect for ADC!

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🧬 Medical Applications

ECG (Electrocardiogram)

Challenge:

• Heart signal: 1mV
• 50Hz interference: 100mV
• Electrode offset: up to 300mV

Solution: Instrumentation amplifier with

• CMRR > 90dB (rejects 50Hz)
• High input impedance (doesn't load electrodes)
• Gain = 1000 (1mV → 1V)
• Input protection (for defibrillator shocks)

Result: Clean ECG waveform!

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🏭 Industrial Sensing

Load Cell (Weight Measurement)

Sensor: 4-wire strain gauge bridge
Output: 2mV/V (20mV at 10V excitation)
Load range: 0-1000kg

With In-Amp:

• Gain = 250
• Output: 0-5V for 0-1000kg
• Resolution: 5V/1000kg = 5mV/kg
• With 12-bit ADC: 5V/4096 = 1.22mV → 0.24kg resolution

Perfect for industrial scales!

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🎛️ Two Op-Amp Instrumentation Amplifier

A simpler version exists using only two op-amps:

• Simplified structure
• Lower cost
• Still good performance

Trade-offs:

• Input impedance: Lower (but still high)
• CMRR: Slightly lower
• Gain range: More limited
• Cost: Lower

Use when: Budget is tight, moderate performance is acceptable

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💎 Integrated Instrumentation Amplifiers

Instead of building from discrete op-amps, use dedicated ICs:

Popular IC In-Amps

Part Number	CMRR	Gain Range	Features	Application
INA128	120dB	1-10,000	Low cost, general purpose	Sensors, bridges
AD620	100dB	1-10,000	Industry standard	Data acquisition
INA114	115dB	1-10,000	Ultra-low noise	Medical, audio
INA333	100dB	1-1000	Single supply, micro-power	Portable devices
AD8221	100dB	1-1000	Rail-to-rail, precision	Battery-powered

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🎯 Design Example: Pressure Sensor Interface

Sensor: Piezoresistive pressure sensor
Output: 0-100mV (0-10 bar)
Desired output: 0-5V

Component Selection:

In-Amp: AD620

• Low cost
• Excellent CMRR
• Easy to use

Gain needed:

$$A_v = \frac{5V}{100mV} = 50$$

For AD620, gain formula:

$$G = 1 + \frac{49.4k\Omega}{R_g}$$

Solving for $R_g$:

$$50 = 1 + \frac{49.4k}{R_g}$$ $$R_g = \frac{49.4k}{49} = 1.008k\Omega$$

Use $R_g = 1k\Omega$ (exact value!)

Additional circuitry:

• 0.1µF ceramic caps on power pins
• 10µF tantalum for supply filtering
• Optional: Low-pass filter at output (anti-aliasing)

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🛡️ Input Protection

Instrumentation amplifiers are sensitive. Protect them:

Protection Strategies

1. ESD diodes: Clamp overvoltage to rails
2. Series resistors: Limit current (1kΩ typical)
3. RC filter: Remove high-frequency transients
4. Zener clamps: Limit voltage to safe range

• Series resistors
• Zener diodes to ground
• Capacitors for filtering

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⚡ Key Specifications to Know

Input Offset Voltage

Voltage at output when inputs are at same potential.

• Typical: 50µV to 5mV
• Precision: <25µV
• Effect: Adds DC error to measurement

Mitigation: Calibration, auto-zero techniques

Input Bias Current

Current flowing into/out of input terminals.

• Typical: 1nA to 100nA
• Low bias: <1nA
• Effect: Creates voltage drop across source impedance

Noise

Random voltage fluctuations.

• Voltage noise: 5-50 nV/√Hz
• Current noise: 0.1-10 pA/√Hz
• Effect: Limits minimum detectable signal

Bandwidth

Frequency range of accurate operation.

• Low power: 1kHz to 100kHz
• High speed: 1MHz to 10MHz
• Effect: Limits signal frequency

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🔧 Practical Design Guidelines

When to Use In-Amps

✅ Use In-Amp when:

• Measuring differential signals < 100mV
• High CMRR needed (>80dB)
• High input impedance required
• Single resistor gain adjustment desired
• Bridge sensors (load cells, strain gauges)
• Medical/bio-potential measurements

❌ Don't use In-Amp when:

• Signals are already large (>1V differential)
• High speed needed (>1MHz)
• Cost is critical and simple diff amp sufficient
• Single-ended measurement (use regular op-amp)

Component Selection Tips

1. Gain resistor: Use 0.1% tolerance, metal film
2. Power supply: Use low-noise regulator, decouple well
3. Input filtering: Add small cap (10pF-100pF) to reduce noise
4. Output filtering: Low-pass for anti-aliasing before ADC
5. Ground: Star grounding, separate analog and digital

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🧪 Lab Exercise: Build a Weight Scale

Objective: Create a digital weight scale using load cell

Components:

• Load cell (strain gauge bridge)
• INA128 or AD620 instrumentation amplifier
• Arduino or similar ADC
• Power supply (±15V or +5V)

Steps:

1. Connect load cell to bridge excitation (10V)
2. Connect bridge outputs to In-Amp inputs
3. Calculate and set gain ($R_g$) for 0-5V output
4. Connect In-Amp output to ADC
5. Calibrate with known weights
6. Display weight on LCD/serial

Challenges:

• Zero offset adjustment (potentiometer)
• Temperature compensation
• Mechanical mounting
• Noise reduction

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✅ Key Takeaways

• Instrumentation amplifiers are precision differential amplifiers
• Three op-amp architecture provides best performance
• Single resistor ($R_g$) sets gain
• CMRR is critical for rejecting common-mode noise
• High input impedance doesn't load sensors
• IC in-amps (AD620, INA128) are easy to use
• Essential for sensors, bridges, and medical applications

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🎓 Looking Ahead

Instrumentation amplifiers are often used with:

• Wheatstone bridges (next topic!)
• Active filters (for noise reduction)
• ADCs (for data acquisition)
• Isolated amplifiers (for safety)

They're the foundation of precision measurement systems!

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📚 Further Study

• Experiment with different gain settings
• Measure CMRR experimentally
• Interface with various sensors
• Study datasheets of commercial in-amps
• Learn about chopper-stabilized in-amps for ultra-low offset