Transimpedance Circuit Output Noise-Voltage Calculator

Aug 26, 2012

This output noise voltage calculator applies to the transimpedance circuit shown below. Parameter names are described below the calculator:

Transimpedance Total Noise Calculator
  GBW (MHz):      en (nV/√Hz):      in (pA/√Hz):   
  Rf (k):      Ri (k):      Cf (pF):      Ci (pF):   
  Resp(A/W):      Id(nA):      Psig (µW):   
  Q:   Fz (Hz):     Fp (Hz):   F0 (Hz):
  f3db (Hz):   NBWen (Hz):   NBWin_th (Hz):
  Ven (µV):   Vth (µV):   Vin(µV):
  Vtotal(µV):   VId(µV):   VPsig(µV):
Transimpedance Cumulative Noise Calculator
  fmax (MHz):      xm:   F0:
    I1(xm,Q):   I2(xm,Q):
  VenC(µV):   VthC(µV):   VinC(µV):
  VtotalC(µV):   VIdC(µV):   VPsigC(µV):

Calculating The Noise With The Calculator

The calculator above can be used to compute the total (integrated over all frequency) and the cumulative (up to frequency fmax) output noise voltage. The noise sources include op-amp voltage and current noise sources, thermal noise sources and photodiode signal current and dark current shot noise sources. The calculation for both the total and cumulative noise integrates over the exact transfer function of the circuit, thereby taking into account the second-order nature of the response.
The steps are: Note that clicking Get Params & Noise does NOT update the data in the Cumulative Noise section of the calculator. If only TOTAL noise up to infinite frequency is required, the upper section of the calculator can be used independently of the lower section.
For convenience, 3 special buttons are provided which automatically calculate the required exact Cf value (given GBW, Rf, Ri and Ci) and all other parameters in the upper section of the calculator for the 3 useful cases of: The calculator is also available separately and also with a minimal interface.

Note on Special Conditions:
Depending on the component values of Rf, Ci and GBW, a solution for Cf for underdamped responses, such as the maximally flat condition Q=1/√2 or the popular Q=1.0 case may not be possible. This may occur for small values of Rf or Ci or GBW. (However, a Cf solution for the critically damped case Q = 0.5 will always be possible). For the "maximally flat" case with Q = 1/√2, a Cf solution will only be possible under this condition:

For the common case with Q = 1.0, a Cf solution will only be possible under this condition:

In both cases, this means that the zero frequency of the noise gain (or equivalently the pole frequency of the feedback factor β(f)) must be comparable to or less the op-amp GBW for a Cf solutions with these Q values to exist. This condition will NOT be satisfied if the zero and pole frequencies of the noise-gain are considerably higher than the op-amp GBW. In that case, the transimpedance f3db bandwidth will simply be controlled by the op-amp open-loop rolloff and f3db will be comparable to the op-amp GBW. Under this condition, the circuit will typically have a Q value < 0.5 with Cf set to zero (or some nominally small stray value such as 0.3 pF) and there will be negligible noise-gain peaking in the pass-band of the transimpedance response. The circuit will have considerable phase margin and will be stable so that no compensation capacitance Cf will be required. Of course Cf could be added to reduce f3db and total output noise.

Calculator Parameters