You can calculate the gain of instrumentation amplifier using the formula AV = 2R/RG + 1. This formula shows how resistor values set the amplification. Gain is the ratio between output and input voltage. For example, if you apply a 0.1 V input and set the resistors to R = 20 kΩ and RG = 1 kΩ, you get a gain of 21 and an output of 2.1 V. Accurate gain calculation lets you amplify small signals up to 10,000 times and reject noise over 100 dB.
Key Takeaways
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Use the formula Gain = 1 + (2 × R1 / Rgain) to calculate the gain of an instrumentation amplifier accurately.
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Choose precise resistors with low tolerance (1% or 0.1%) to keep your gain stable and reduce errors.
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Adjust Rgain to set your desired gain, and pick standard resistor values that are easy to find and reliable.
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Double-check your calculations and test your circuit to ensure the gain matches your target value.
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Follow careful steps and use quality components to build accurate and noise-free amplifier circuits.
Gain of Instrumentation Amplifier
Gain Formula
You can find the gain of instrumentation amplifier using a simple formula. The most common formula looks like this:
Gain (G) = 1 + (2 * R1 / Rgain)
Some designs use a slightly different formula, such as:
Gain (G) = (R3 / R2) * ((2 * R1 + Rgain) / Rgain)
You use these formulas to set how much the amplifier boosts your input signal. The gain of instrumentation amplifier tells you how many times the output voltage is larger than the input voltage. For example, if you want to amplify a small signal from a sensor, you can adjust the resistors to get the right gain.
Tip: The gain of instrumentation amplifier does not have a unit. It is a ratio, so you only compare voltages.
Formula Terms
Let’s break down what each part of the formula means:
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R1: This resistor sets part of the gain. You usually find it inside the amplifier circuit.
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Rgain: This resistor lets you adjust the gain. You often connect it between two pins on the amplifier chip.
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R2 and R3: These resistors appear in some amplifier designs. They help set the overall gain and balance the circuit.
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Vout: This is the output voltage from the amplifier.
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Vin: This is the input voltage you want to amplify.
The gain depends on the values of these resistors. If you change Rgain, you change the gain. You can use standard resistor values to get close to your target gain.
Here is a table showing why engineers use instrumentation amplifiers in real projects:
| Feature / Property | Description / Benefit |
|---|---|
| High input impedance | Prevents loading of the signal source, critical for precision measurements |
| Isolated inputs | Ensures input signals do not interfere with each other, improving accuracy |
| High gain | Amplifies low-level signals effectively |
| Excellent Common-Mode Rejection Ratio | Reduces noise and interference from common-mode signals, essential in noisy environments |
| Overcomes limitations of basic differential amplifiers | Avoids input impedance mismatch and gain inaccuracies caused by resistor mismatches |
| Available as integrated circuits | Provides high performance with ease of use and design flexibility |
| Guard drive feature | Reduces cable capacitance effects, improving high-frequency performance |
You will see instrumentation amplifiers in many places, such as medical devices, factory automation, and audio equipment. These amplifiers help you get accurate readings from sensors, even in noisy environments.
Calculate Gain Step by Step
Identify Required Gain
Start by deciding how much you want to amplify your signal. Think about the sensor or device you are using. For example, if your sensor gives a small voltage, you may need a high gain to make the signal readable. Write down the input voltage range and the output voltage you want.
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If your sensor outputs 2 mV and you want 1 V at the output, you need a gain of 500.
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In audio systems, you might need a gain of 10 to 100, depending on the loudness you want.
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For precise sensor readings, the gain of instrumentation amplifier often ranges from 10 up to 1000.
Tip: Most projects use a gain between 10 and 1000. Higher gain helps you see small signals, but too much gain can cause noise or distortion.
Rearrange Formula
Once you know your target gain, use the standard formula for the gain of instrumentation amplifier:
Gain (G) = 1 + (2 * R1 / Rgain)
If you want to solve for Rgain, rearrange the formula:
Rgain = 2 * R1 / (Gain - 1)
This step helps you find the right resistor value to set your desired gain. For example, if you use R1 = 10 kΩ and want a gain of 501, plug the numbers into the formula:
Rgain = 2 * 10,000 / (501 - 1)
Rgain = 20,000 / 500
Rgain = 40 Ω
You can use this method for any gain value. Always double-check your math to avoid mistakes.
Note: The gain of instrumentation amplifier depends on resistor ratios. Changing Rgain changes the gain quickly, so small errors in resistor value can make a big difference.
Select Resistors
Now, choose real resistor values. Use standard resistor values that are easy to buy. Precision resistors with 1% or 0.1% tolerance work best. Lower tolerance means more accurate gain and less error from temperature changes or aging.
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Pick R1 from common values like 1 kΩ, 10 kΩ, or 20 kΩ.
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Calculate Rgain using the rearranged formula.
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Choose the closest standard value for Rgain. For example, if you need 162 Ω, use a 162 Ω resistor with 1% tolerance.
| Desired Gain | R1 (kΩ) | Calculated Rgain (Ω) | Standard Rgain (Ω) | Tolerance (%) |
|---|---|---|---|---|
| 500 | 20 | 162 | 162 | 1 |
| 100 | 10 | 202 | 200 | 1 |
| 21 | 20 | 2,000 | 2,000 | 1 |
Tip: Using precision resistors helps keep your amplifier accurate and stable. Avoid using trimmer potentiometers for Rgain because they can drift with temperature and vibration.
You can see how real-world designs use these steps. For example, the INA126 instrumentation amplifier achieves a fixed gain of 500 by using a 162 Ω resistor for Rgain. This method gives you stable and repeatable results.
When you select resistors, remember that resistor tolerance affects your final gain. If you use 1% tolerance resistors, your gain can vary by up to 1%. For very accurate projects, use 0.1% tolerance resistors.
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Place most of the gain in the first stage of your amplifier. This improves noise rejection and keeps your signal clean.
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Use unity-gain stable op-amps in the input stage to prevent oscillations.
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Distribute gain across stages if you need very high gain, such as 1000x or more.
Note: The classic 3-op amp design lets you set the gain with a single resistor, making it easy to adjust and maintain high common-mode rejection.
By following these steps, you can set the gain of instrumentation amplifier for any project. Always check your resistor values and use the right formula to get the best results.
Gain of Instrumentation Amplifier Example
Example Calculation
You can see how to calculate the gain of instrumentation amplifier with a real-world example. Suppose you want a gain of 500 for your sensor project. You choose R1 as 20 kΩ. To find the right value for Rgain, use the formula:
Rgain = 2 * R1 / (Gain - 1)
Plug in the numbers:
Rgain = 2 * 20,000 / (500 - 1)
Rgain = 40,000 / 499
Rgain ≈ 80.16 Ω
You round Rgain to the nearest standard value, which is 82 Ω. This small change will not affect your circuit much if you use a resistor with 1% tolerance.
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A Texas Instruments INA126 instrumentation amplifier was used in a practical circuit.
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The gain resistor RG was set to 162 ohms with 1% tolerance.
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This configuration achieved a gain of 500 as predicted by theoretical calculations.
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This practical example confirms that the theoretical gain formulas accurately predict real-world instrumentation amplifier gain.
You can trust the formula when you select your resistor values. Real circuits match the calculated gain very closely.
Standard Resistor Values
You often use standard resistor values to set the gain of instrumentation amplifier. These values make it easy to build and adjust your circuit. Precision resistors with low tolerance help you keep the gain accurate.
Two key experiments with the MAX4208 instrumentation amplifier demonstrate how standard resistor values influence gain accuracy. In the first experiment, using only standard low-TCR rejustors configured for a gain of about 360 V/V, the measured gain after trimming was within 0.1% error of the target value. The setup included parallel and series combinations of 1kΩ and 90kΩ rejustors, with precise measurement equipment confirming output voltages closely matched expected values. The second experiment combined fixed standard resistors (0.1% tolerance) with low-TCR rejustors to achieve a gain of 1000 V/V. After trimming, the gain error was again better than 0.1%. These results show that standard resistor values, when paired with adjustable rejustors, do not reduce gain precision in instrumentation amplifiers and allow fine tuning to exact nominal gain values, even with changes in manufacturing or temperature.
Always use resistors with tight tolerance for best results. You can combine standard values in series or parallel to get closer to your target resistance.
Accuracy Tips
Standard Resistors
You can improve the accuracy of your instrumentation amplifier by choosing the right resistors. Standard thin film or metal film resistors work best because they have low temperature coefficients. This means their resistance does not change much when the temperature changes. For example, resistors with a temperature coefficient as low as 15 ppm/°C help keep your gain stable even if your circuit heats up.
When you select resistors, look for ones with tight tolerance, such as 1% or even 0.1%. Tighter tolerance means the resistor value is closer to what is printed on the label. This reduces the chance of gain errors. You can also use resistor networks, which are groups of resistors made together in one package. These networks track temperature changes together, so your gain stays accurate.
Research from Analog Devices and other sources shows that the choice of resistor has a big impact on gain accuracy and drift. If you use standard resistors with low drift and tight tolerance, your amplifier will perform better and stay accurate over time.
Tip: Combine standard resistor values in series or parallel to get as close as possible to your target resistance.
Error Minimization
You can take several steps to minimize errors in your gain calculations and amplifier performance:
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Match Resistors Carefully: Measure and match resistors by hand, or use laser-trimmed resistors found in some amplifier chips. This reduces gain calculation errors.
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Use Precision Op Amps: Choose op amps with low input bias current and low offset voltage. Zero-drift op amps are especially good for amplifying small signals without adding error.
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Optimize Circuit Layout: Place decoupling capacitors near power pins and keep traces short. This prevents noise and keeps your signal clean.
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Check Amplifier Configuration: Make sure you use the correct resistor values for your amplifier setup. For example, using 1k and 39k resistors in different configurations can give you gains of 40 or 39. Small mistakes here can cause big errors.
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Simulate and Test: Use circuit simulation tools like SPICE to check your design before building it. Testing with real components helps you catch errors early.
Practical examples show that using two 20k resistors in series can replace a hard-to-find 40k resistor. This kind of attention to detail helps you achieve the exact gain you need. By following these tips, you can build instrumentation amplifiers that are both accurate and reliable.
You can set the gain of instrumentation amplifier by following a few clear steps.
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Decide your target gain and use the correct formula to calculate resistor values.
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Choose precise resistors and double-check your math for accuracy.
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Record all test details and use repeatable measurements to confirm your results.
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Keep your formula and steps handy for future projects.
Careful calculation and documentation help you achieve reliable and accurate amplifier performance.
FAQ
What happens if you use resistors with high tolerance?
Resistors with high tolerance can cause your gain to change more than you expect. You may see errors in your output voltage. For best results, use resistors with 1% or 0.1% tolerance.
Can you use a potentiometer for Rgain?
You can use a potentiometer for Rgain to adjust gain easily. However, temperature or vibration can make the value drift. For stable circuits, use fixed precision resistors.
Why does the gain formula use ratios?
The gain formula uses ratios because the amplifier boosts voltage based on resistor values. Ratios let you set gain without worrying about units. You only compare resistor values.
How do you check if your gain is correct?
You can measure the input and output voltages. Then, use this formula:
Gain = Vout / Vin
If the result matches your target gain, your circuit works as expected.
Written by Jack from AIChipLink.
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