Feedback Resistor Calculator: Gain & Bandwidth

This calculator determines the feedback resistor (Rf) needed for a non-inverting or inverting operational amplifier circuit to achieve a desired voltage gain, given a known input resistor (Rin). You enter the op-amp configuration, the value of Rin, and your target gain; the calculator returns the required Rf in ohms, plus the resulting gain if you use a standard resistor value.

Formula

The feedback resistor value depends on the amplifier configuration. For a non-inverting amplifier, the gain is given by:

A = 1 + (Rf / Rin)

Solving for Rf gives:

Rf = Rin × (A − 1)

For an inverting amplifier, the gain magnitude is:

A = −Rf / Rin

Solving for Rf gives:

Rf = Rin × A

Where:

• Rf = feedback resistor (ohms, Ω)
• Rin = input resistor (ohms, Ω)
• A = desired voltage gain (unitless, V/V)

The calculator uses the non-inverting formula by default. If you select “Inverting�, it uses the inverting formula. The “actual gain� output rounds Rf to the nearest standard 5% resistor value (E24 series) and recalculates the gain.

Worked Example

Using the default values: non-inverting amplifier, Rin = 1000 Ω, desired gain = 11 V/V.

1. Apply the non-inverting formula: Rf = Rin × (A − 1) = 1000 × (11 − 1) = 1000 × 10 = 10,000 Ω.
2. The calculator outputs Rf = 10000 Ω (10 kΩ).
3. If you pick the nearest standard 5% resistor, 10 kΩ is already standard, so the actual gain remains 1 + (10000/1000) = 11 V/V.

For an inverting amplifier with the same Rin and gain, Rf = 1000 × 11 = 11,000 Ω, and the nearest standard value is 11 kΩ (gain = 11).

How to Choose the Right Resistor Values

In practice, you don’t need a precise gain in most circuits – you need a gain that is close enough and stable. Here’s how to approach it:

• Pick a standard resistor value for Rin (e.g., 1 kΩ, 10 kΩ) that doesn’t load the source excessively.
• Calculate Rf using the formula.
• Choose the nearest standard resistor value (E12 or E24 series) for Rf.
• Check the resulting gain: if it’s within your tolerance, you’re done.
• If you need a very precise gain, use a trimmer potentiometer in series with Rf to fine-tune.

Remember that the op-amp’s output can only swing within its supply rails, so the gain times the input signal must not exceed the output voltage range.

Common Mistakes and How to Avoid Them

One of the most common errors is mixing up the formulas for inverting and non-inverting amplifiers. The non-inverting gain has a “+1� in the formula; the inverting gain does not. Another mistake is forgetting that the inverting amplifier’s gain is negative – the magnitude is what you usually care about, but the phase inversion matters in AC circuits.

Unit errors also happen: if Rin is in kilo-ohms and you enter it as ohms, the result will be off by a factor of 1000. Always convert to base units (Ω) before calculating.

Finally, don’t ignore the effect of the op-amp’s input bias current and offset voltage. For high-value resistors (above 1 MΩ), these can cause noticeable output offset errors. Use lower resistor values (1 kΩ to 100 kΩ) when possible.

Frequency Response and Bandwidth

The feedback resistor also affects the op-amp’s bandwidth. The gain-bandwidth product (GBP) of an op-amp is constant: if you increase the gain, the bandwidth decreases. For a non-inverting amplifier, the closed-loop bandwidth is approximately:

BW = GBP / A

For example, a 741 op-amp has a GBP of about 1.5 MHz. At a gain of 11, the bandwidth would be roughly 136 kHz. This is a simplified model – the actual bandwidth also depends on the output load and the op-amp’s internal compensation – but it gives you a quick estimate. If you need high bandwidth, use a lower gain or a faster op-amp.

Practical Considerations and Safety

When building a real circuit, always use resistors with a suitable power rating. The power dissipated in Rf is approximately P = V_out² / Rf, where V_out is the RMS output voltage. For most low-voltage op-amp circuits, a 1/4 W resistor is fine, but if you are driving a heavy load or using high supply voltages, check the power.

Also, ensure the op-amp is properly powered and decoupled with capacitors near the supply pins. This prevents oscillation and noise. If you are working with high frequencies, use a resistor with low parasitic inductance (e.g., surface-mount) and keep leads short.

Alternatives to a Fixed Resistor

Sometimes you don’t want a fixed gain. You can use a potentiometer as a variable feedback resistor, but that introduces noise and drift. A better alternative is a digital potentiometer (controlled by a microcontroller) or a programmable gain amplifier (PGA) chip. For AC signals, you might use a resistor in series with a capacitor to create a low-pass or high-pass filter, which changes the gain with frequency.

For very high precision, consider using a precision resistor network or a matched resistor pair. These are available with tight tolerances (0.1% or better) and low temperature coefficients.

Frequently Asked Questions

What is the difference between inverting and non-inverting gain?

In a non-inverting amplifier, the input signal goes to the non-inverting (+) pin, and the output is in phase with the input. The gain formula is 1 + (Rf/Rin). In an inverting amplifier, the input goes to the inverting (−) pin, and the output is inverted (180° phase shift). The gain magnitude is Rf/Rin, but the sign is negative.

Can I use any resistor value for Rin?

Yes, but the value affects input impedance and noise. For a non-inverting amplifier, the input impedance is very high (equal to the op-amp’s input impedance), so Rin is not critical for input loading. For an inverting amplifier, the input impedance is approximately Rin, so choose Rin to match your source impedance. Lower values reduce noise but increase power consumption.

How do I calculate Rf for a specific cutoff frequency in a filter?

In an active filter, the feedback resistor works with a capacitor to set the cutoff frequency. For a first-order low-pass filter using an inverting amplifier, the cutoff frequency is f = 1/(2π·Rf·C). If you know the capacitor value and desired frequency, solve for Rf = 1/(2π·f·C). This is a different calculation than for gain alone.

What if my desired gain is less than 1?

For a non-inverting amplifier, the gain is always ≥ 1 (because of the +1 term). If you need a gain less than 1, use a voltage divider before the amplifier or use an inverting amplifier with Rf < Rin. For example, an inverting amplifier with Rf = 1 kΩ and Rin = 10 kΩ gives a gain of −0.1 (attenuation).

Why does my circuit oscillate when I use a high-value feedback resistor?

High-value resistors (above 1 MΩ) can interact with the op-amp’s input capacitance and the PCB stray capacitance, creating a pole that reduces phase margin and leads to oscillation. To fix this, add a small capacitor (a few pF) in parallel with Rf to roll off the gain at high frequencies, or use lower resistor values.

What is the standard resistor value for Rf if I want a gain of 10 with Rin = 1 kΩ?

For a non-inverting amplifier, Rf = 1 kΩ × (10 − 1) = 9 kΩ. The nearest standard 5% value is 9.1 kΩ (E24 series), which gives a gain of 1 + (9100/1000) = 10.1. For an inverting amplifier, Rf = 1 kΩ × 10 = 10 kΩ, which is a standard value and gives exactly −10 gain.

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sel config | Amplifier type | Non-inverting=1, Inverting=1
in rin | Input resistor (Rin) | Ω | 1000 | 1
in gain | Desired voltage gain (|A|) | V/V | 11 | 1
out rf | Feedback resistor (Rf) | Ω | rin * (gain - 1) | 0
out actual_gain | Actual gain with standard Rf | V/V | 1 + (round(rf / rin * 10) / 10) | 2