Active Filter Gain (MFB)
Gain = −Rf / Ri
Quick answer
This calculator solves Gain = −Rf / Ri for Voltage Gain. With Feedback Resistor 10 kΩ, Input Resistor 22 kΩ, the result is -0.4545. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The multiple feedback (MFB) topology is a second-order active filter that provides inverted output. Its passband gain is set by the ratio of feedback to input resistor, identical to a simple inverting amplifier. The MFB topology uses five components (two resistors and three capacitors, or three resistors and two capacitors) to implement a complete second-order filter section with independent control of gain, cutoff frequency, and Q factor. It has lower sensitivity to op-amp gain-bandwidth limitations compared to Sallen-Key at high Q values.
Variables
- Gain — Passband voltage gain (negative, indicating inversion)
- Rf — Feedback resistor (Ω)
- Ri — Input resistor (Ω)
Practical Notes
MFB advantages: lower component sensitivity at high Q, better high-frequency stopband rejection, gain and frequency can be independently tuned. Disadvantages: inverting output, higher component count than Sallen-Key, requires matched component values for proper response shape. MFB is preferred for bandpass filters where Q > 5.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Gain | Voltage Gain | — | — |
| Rf | Feedback Resistor | kΩ | mΩ, Ω, kΩ, MΩ |
| Ri | Input Resistor | kΩ | mΩ, Ω, kΩ, MΩ |
Step by step
- 1. What you know: Feedback Resistor 10 kΩ, Input Resistor 22 kΩ
- 2. The relation: Gain = −Rf / Ri
- 3. Substitute: Rf = 10 kΩ, Ri = 22 kΩ
- 4. Result: Voltage Gain = -0.4545
Worked examples
Minimum range
Given: Feedback Resistor 100 Ω, Input Resistor 0.22 kΩ
Result: Voltage Gain = -0.4545
Low range
Given: Feedback Resistor 1 kΩ, Input Resistor 2.2 kΩ
Result: Voltage Gain = -0.4545
Typical
Given: Feedback Resistor 10 kΩ, Input Resistor 22 kΩ
Result: Voltage Gain = -0.4545
High range
Given: Feedback Resistor 100 kΩ, Input Resistor 0.22 MΩ
Result: Voltage Gain = -0.4545
Maximum range
Given: Feedback Resistor 1 MΩ, Input Resistor 2.2 MΩ
Result: Voltage Gain = -0.4545
Solving for each variable
Solve for Voltage Gain
Feedback Resistor 100 Ω, Input Resistor 0.22 kΩ → -0.4545
Solve for Feedback Resistor
Voltage Gain -0.025, Input Resistor 0.22 kΩ → 5.5 Ω
Solve for Input Resistor
Voltage Gain -0.025, Feedback Resistor 100 Ω → 4 kΩ
How Voltage Gain changes with Feedback Resistor
| Feedback Resistor (input) | Voltage Gain (result) |
|---|---|
| 1 kΩ | -0.04545 |
| 2.5 kΩ | -0.1136 |
| 5 kΩ | -0.2273 |
| 7.5 kΩ | -0.3409 |
| 10 kΩ | -0.4545 |
| 15 kΩ | -0.6818 |
| 20 kΩ | -0.9091 |
| 40 kΩ | -1.818 |
| 70 kΩ | -3.182 |
| 100 kΩ | -4.545 |
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<p><a href="https://vbatpower.com/formulas/active-filter-gain/">Active Filter Gain (MFB)</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Active Filter Gain (MFB)?
Use Gain = −Rf / Ri. With Feedback Resistor 10 kΩ, Input Resistor 22 kΩ, Voltage Gain works out to -0.4545.
What is the formula for Active Filter Gain (MFB)?
The formula is Gain = −Rf / Ri. The multiple feedback (MFB) topology is a second-order active filter that provides inverted output.
How do you find Feedback Resistor when you know the other values?
Rearrange for Feedback Resistor: with Voltage Gain -0.025, Input Resistor 0.22 kΩ, Feedback Resistor is 5.5 Ω.
How do you find Input Resistor when you know the other values?
Rearrange for Input Resistor: with Voltage Gain -0.025, Feedback Resistor 100 Ω, Input Resistor is 4 kΩ.
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