Photodiode TIA Noise
Photodiode + transimpedance amplifier: Butterworth bandwidth, input-referred noise including the e_n·C term, and NEP.
Responsivity
384.73 mA/W
TIA Bandwidth
3.99 MHz
√(GBW/2πR_f·C_S); Butterworth C_f = 0.0563 pF
Noise Bandwidth (ENBW)
4.43 MHz
Set by the TIA roll-off (B > f_TIA); the e_n·C noise peaks near f_TIA
Input Noise Current
2.605e-9 A rms
Dominant: e_n·2πf·C_S; 1237.3 fA/√Hz band average
NEP (in the noise band)
6.770e-9 W
Output noise 2.60 mV rms
f_TIA = √(GBW / (2π·R_f·C_S)) for a Butterworth (Q = 0.707) response
i²(f) = i_n² + 4kT/R_f + (e_n/R_f)² + (e_n·2πf·C_S)²
i²_rms = ∫₀ᴮ i²(f) / (1 + (f/f_TIA)⁴) df (Butterworth response, brick-wall post-filter B)
B ≫ f_TIA: ENBW = 1.11·f_TIA, and the e_n·C term weighs (e_n·2π·C_S)²·1.11·f_TIA³
NEP = i_rms / ℛ. Photocurrent and dark-current shot noise are left out.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Single-pole op amp with a Butterworth-compensated feedback R_f ∥ C_f; input-referred noise is weighted by the 2-pole Butterworth response 1/(1 + (f/f_TIA)⁴) up to a brick-wall post-filter B. Photocurrent and dark-current shot noise, 1/f noise and the C_f term of the noise gain are left out.
- Ramus X. (2009). Transimpedance Considerations for High-Speed Amplifiers. Texas Instruments application report SBOA122. Butterworth TIA bandwidth √(GBP/2πR_F·C_S) (eq. 12) and input-referred noise (eq. 13). ti.com
- Graeme J. G. (1996). Photodiode Amplifiers: Op Amp Solutions. McGraw-Hill. Transimpedance stability, feedback-capacitor compensation and the e_n·C noise gain.
- Nyquist H. (1928). Thermal agitation of electric charge in conductors. Phys. Rev. 32, 110. Derivation of 4k_B·T·R per unit bandwidth. doi:10.1103/PhysRev.32.110