Mar 01, 2012

Fz: Noise gain zero frequency

Fp: Noise gain pole frequency

Fc: Intersection frequency of noise gain and open loop gain

Margin: Phase margin of loop gain at intersection frequency (stable for margin >45deg)

NG(Fc): Noise gain at intersection frequency Fc

f3dB: 3dB bandwidth relative to DC value

Q: Quality factor of resonant peaking

Fpeak: Frequency of resonant peaking

Peak: Resonant peaking value in dB

Cf(flat): Cf value for maximally flat (Q=1/Sqrt(2)) response for Tz and INV circuits, if possible

The last term in the In_eq expression is a result of the noise-gain zero which gains-up the op-amp noise voltage at frequencies higher than the noise-gain zero. Note that this current-density term is EXPLICITLY bandwidth dependent and can in many cases dominate the other noise current components, particularly in high-bandwidth circuits with large input capacitance and high gain (Rf). The op-amp input noise current term and the thermal noise term of Rf don't experience the same enhanced noise effect and their noise contributions start rolling off at about the pole frequency in a similar way to the transimpedance output signal voltage rolloff.

Generally speaking, to maximize transimpedance circuit sensitivity, it is desirable to use as high a gain (Rf) as possible provided there is enough signal bandwidth for the intended application and to choose an op-amp with very low input voltage noise en and input capacitance to lower the gaining-up effect. For maximum sensitivity, the goal is to select an op-amp with low en, in and Cin to achieve a noise performance in the Tz circuit which is limited only by the intrinsic thermal noise of Rf, for the particular photodiode and with the required bandwidth. The diagram below which corresponds to the default parameters in the calculator above, shows how the noise-gain curve starts to increase (gaining up the op-amps voltage noise en at a rate of 20 dB/decade) above the noise-gain's zero frequency ~ 1.7 kHz and continues to increase, raising the noise, and finally levelling off at the pole frequency 106 kHz and finally rolling off as limited by the op-amp GBW limit:

For a more detailed discussion of noise considerations for transimpedance circuits, see:

**Photodiode Amplifiers Op Amp Solutions**, J. Graeme, McGraw Hill, 1996, p. 87.

- Photodiode Monitoring with OP AMPS, TI Technical Document SBOA035 1995

- OPA656 Wideband, Unity-Gain Stable, FET-Input OpAmp, OPA656 Data Sheet.

For example, for In_tot = 27 pA, and with Responsivity = 0.5A/W, the minimum detectable optical power in this Tz circuit with the specified bandwidth would be 54 pW.

Photodiodes are typically reverse biased to reduce junction capacitance. However a biased photodiode, like any reverse biased PN junction exhibits leakage ("dark") current. This dark current introduces extra shot noise to the circuit characterized by a constant spectral density:

or, using convenient units:

Evaluation of this expression from the photodiode specifications will indicate if it contributes significantly to input-referred current noise. If so, it should be added to the RMS noise-current summation above. Generally smaller photodiodes will have less dark current. For example the commercial Vishay Semiconductors BPW24R Si photodiode exhibits a dark current of ~ 3nA at reverse voltages of less than 10 V. This corresponds to a shot-noise current density of ~ 31 fA/Sqrt(Hz) (or 0.03 pA/Sqrt(Hz). In the default calculator example, this is comparable to the final noise-gain term.

The photodiode dark current will also contribute to an output DC offset voltage by an amount Id*Rf or for the 5 Mohm case above and a 3nA dark current, an offset of 15 mV.

Transimpedance Amplifier Circuit Configuration:

Inverting Amplifier Circuit:

Non-inverting Amplifier Circuit: