TIA Feedback Capacitor (Stability)
Cf = √(Cin / (2π · Rf · fGBW))
Quick answer
This calculator solves Cf = √(Cin / (2π × Rf × fGBW)) for Feedback Capacitor. With Input Capacitance 0.22 nF, Feedback Resistor 2.2 MΩ, Gain-Bandwidth 10 MHz, the result is 1.262 pF. It solves in 4 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
A transimpedance amplifier (photodiode amplifier) is destabilised by the input capacitance interacting with the feedback resistor, which creates a noise-gain peak. A small feedback capacitor across Rf cancels this by adding a pole. This formula gives the value that yields about 45° of phase margin—the maximally-flat (Butterworth-like) compromise between stability and bandwidth.
Variables
- Cf — Feedback capacitor (F)
- Cin — Total input capacitance (photodiode + amp) (F)
- Rf — Feedback (gain) resistor (Ω)
- fGBW — Amplifier gain-bandwidth product (Hz)
Practical Notes
Too little Cf rings and may oscillate; too much needlessly limits bandwidth. Minimise Cin (small photodiode, low input capacitance op-amp) to allow a smaller Cf and wider bandwidth.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Cf | Feedback Capacitor | pF | pF, nF, µF, mF, F |
| Cin | Input Capacitance | pF | pF, nF, µF, mF, F |
| Rf | Feedback Resistor | MΩ | mΩ, Ω, kΩ, MΩ |
| fGBW | Gain-Bandwidth | MHz | Hz, kHz, MHz, GHz |
Step by step
- 1. What you know: Input Capacitance 0.22 nF, Feedback Resistor 2.2 MΩ, Gain-Bandwidth 10 MHz
- 2. The relation: Cf = √(Cin / (2π × Rf × fGBW))
- 3. Substitute: Cin = 0.22 nF, Rf = 2.2 MΩ, fGBW = 10 MHz
- 4. Result: Feedback Capacitor = 1.262 pF
Nearest standard component values
| Series | Nearest value | Error |
|---|---|---|
| E12 | 1.2 pF | 4.9% |
| E24 | 1.3 pF | 3% |
Worked examples
Minimum range
Given: Input Capacitance 2.2 pF, Feedback Resistor 100 kΩ, Gain-Bandwidth 100 kHz
Result: Feedback Capacitor = 5.917 pF
Low range
Given: Input Capacitance 22 pF, Feedback Resistor 1 MΩ, Gain-Bandwidth 1 MHz
Result: Feedback Capacitor = 1.871 pF
Typical
Given: Input Capacitance 0.22 nF, Feedback Resistor 2.2 MΩ, Gain-Bandwidth 10 MHz
Result: Feedback Capacitor = 1.262 pF
High range
Given: Input Capacitance 2.2 nF, Feedback Resistor 10 MΩ, Gain-Bandwidth 100 MHz
Result: Feedback Capacitor = 0.5917 pF
Maximum range
Given: Input Capacitance 22 nF, Feedback Resistor 100 MΩ, Gain-Bandwidth 1 GHz
Result: Feedback Capacitor = 0.1871 pF
Solving for each variable
Solve for Feedback Capacitor
Input Capacitance 2.2 pF, Feedback Resistor 100 kΩ, Gain-Bandwidth 100 kHz → 5.917 pF
Solve for Input Capacitance
Feedback Capacitor 1 pF, Feedback Resistor 100 kΩ, Gain-Bandwidth 100 kHz → 0.06283 pF
Solve for Feedback Resistor
Feedback Capacitor 1 pF, Input Capacitance 2.2 pF, Gain-Bandwidth 100 kHz → 3.501 MΩ
Solve for Gain-Bandwidth
Feedback Capacitor 1 pF, Input Capacitance 2.2 pF, Feedback Resistor 100 kΩ → 3.501 MHz
How Feedback Capacitor changes with Input Capacitance
| Input Capacitance (input) | Feedback Capacitor (result) |
|---|---|
| 48.4 pF | 0.269 pF |
| 121 pF | 0.4253 pF |
| 0.242 nF | 0.6014 pF |
| 0.363 nF | 0.7366 pF |
| 0.484 nF | 0.8505 pF |
| 0.726 nF | 1.042 pF |
| 0.968 nF | 1.203 pF |
| 1.936 nF | 1.701 pF |
| 3.388 nF | 2.25 pF |
| 4.84 nF | 2.69 pF |
The same result in other units
| Unit | Value |
|---|---|
| pF | 1.262 |
| nF | 0.001262 |
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<p><a href="https://vbatpower.com/formulas/tia-feedback-capacitor/">TIA Feedback Capacitor (Stability)</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate TIA Feedback Capacitor (Stability)?
Use Cf = √(Cin / (2π × Rf × fGBW)). With Input Capacitance 0.22 nF, Feedback Resistor 2.2 MΩ, Gain-Bandwidth 10 MHz, Feedback Capacitor works out to 1.262 pF.
How do you calculate tia feedback capacitor?
Rearrange for Feedback Capacitor: with Input Capacitance 22 pF, Feedback Resistor 1 MΩ, Gain-Bandwidth 1 MHz, Feedback Capacitor is 1.871 pF.
What is the formula for TIA Feedback Capacitor (Stability)?
The formula is Cf = √(Cin / (2π × Rf × fGBW)). A transimpedance amplifier (photodiode amplifier) is destabilised by the input capacitance interacting with the feedback resistor, which creates a noise-gain peak.
How do you find Input Capacitance when you know the other values?
Rearrange for Input Capacitance: with Feedback Capacitor 1 pF, Feedback Resistor 100 kΩ, Gain-Bandwidth 100 kHz, Input Capacitance is 0.06283 pF.
How do you find Feedback Resistor when you know the other values?
Rearrange for Feedback Resistor: with Feedback Capacitor 1 pF, Input Capacitance 2.2 pF, Gain-Bandwidth 100 kHz, Feedback Resistor is 3.501 MΩ.
What units does TIA Feedback Capacitor (Stability) use?
Feedback Capacitor is shown in pF, nF. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
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