Enter the temperature and the capacitance into the calculator to determine the kT/C sampling noise as noise voltage in dBV (decibels relative to 1 V RMS).
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kT/C Noise Formula
kT/C noise is the thermal noise stored on a capacitor after a sampling or reset event. It is a fundamental limit in sample-and-hold circuits, switched-capacitor stages, image sensor sense nodes, and many ADC front ends. After the capacitor has fully settled through a resistive path, the final sampled noise is set by absolute temperature and capacitance.
V_n^2 = \frac{kT}{C}V_{n,\mathrm{rms}} = \sqrt{\frac{kT}{C}}N_{\mathrm{dBV}} = 20\log_{10}\!\left(\frac{V_{n,\mathrm{rms}}}{1\ \mathrm{V}}\right) = 10\log_{10}\!\left(\frac{kT}{C}\right)Variable Definitions
- Vn,rms: RMS noise voltage on the capacitor, in volts
- NdBV: noise voltage expressed in dBV, referenced to 1 V RMS
- k: Boltzmann constant, 1.380649 × 10-23 J/K
- T: absolute temperature in kelvin
- C: capacitance in farads
Because dBV is referenced to 1 V RMS, kT/C noise values are usually negative. A more negative dBV value means less noise voltage.
Rearranged Equations
If you know the target noise and want to solve for the required capacitance or temperature, these forms are the most useful:
V_{n,\mathrm{rms}} = 10^{N_{\mathrm{dBV}}/20}\ \mathrm{V}C = \frac{kT}{V_{n,\mathrm{rms}}^2} = \frac{kT}{10^{N_{\mathrm{dBV}}/10}}T = \frac{C V_{n,\mathrm{rms}}^2}{k} = \frac{C \cdot 10^{N_{\mathrm{dBV}}/10}}{k}How to Use the kT/C Noise Calculator
- Enter any two known values: temperature, capacitance, or noise voltage in dBV.
- Select the correct units for temperature and capacitance.
- Click calculate to solve for the missing quantity.
- Interpret the result in the context of your circuit noise budget, not as the only possible noise source.
The calculator handles user-friendly units, but the underlying physics always uses kelvin and farads. If temperature is entered in Celsius or Fahrenheit, it must first be converted to absolute temperature before applying the equation.
Design Interpretation
These quick scaling rules help when estimating how design changes affect sampled thermal noise:
| Design Change | Effect on RMS Noise | Effect in dBV |
|---|---|---|
| Temperature doubles | Noise increases by about 41.4% | +3.01 dB |
| Capacitance doubles | Noise drops to about 70.7% | -3.01 dB |
| Capacitance increases 10× | Noise drops to about 31.6% | -10 dB |
| Capacitance increases 100× | Noise drops to about 10% | -20 dB |
In practical design, capacitance is usually the strongest lever for reducing kT/C noise at room temperature. Lower temperature helps, but increasing capacitor size is often the more direct electrical tradeoff.
Typical kT/C Noise Values at 300 K
| Capacitance | Approx. RMS Noise | Approx. Noise Level |
|---|---|---|
| 0.1 pF | 203.5 µV | -73.83 dBV |
| 1 pF | 64.36 µV | -83.83 dBV |
| 10 pF | 20.35 µV | -93.83 dBV |
| 100 pF | 6.44 µV | -103.83 dBV |
| 1 nF | 2.04 µV | -113.83 dBV |
This table makes the inverse relationship easy to see: every 10× increase in capacitance reduces the noise by about 10 dB.
Common Applications
- Sample-and-hold capacitor sizing
- Switched-capacitor filter design
- Reset noise estimation on floating diffusion or sense nodes
- ADC front-end noise budgeting
- Comparing capacitor tradeoffs against speed, area, and power
Practical Notes
- Switch resistance affects settling time, not the final fully-settled kT/C value. If the sample period is too short, the capacitor may not reach the theoretical noise level predicted here.
- Larger capacitors reduce noise, but they also increase area, loading, and charge/discharge energy.
- Use absolute temperature. For example, 25°C is 298.15 K, not 25 K.
- Watch the capacitance units carefully. Confusing pF, nF, and µF can shift the result by large multiples.
- kT/C is only one part of total noise. Real systems can also include amplifier noise, 1/f noise, leakage, charge injection, clock feedthrough, reference noise, and quantization noise.
Why kT/C Noise Matters
kT/C noise is important because it sets a floor on how quiet a sampled capacitor node can be. If your required signal resolution is close to the predicted kT/C level, capacitor sizing becomes a first-order design choice. This is why the calculator is useful both for quick estimates and for checking whether a chosen capacitor is consistent with your target noise specification.
