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ZHCSNI6A March 2023 – April 2024 OPA928

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7.2.2.2.4 Noise

There are three primary sources of noise to consider in transimpedance amplifiers: the feedback resistor, the op amp (with both current and voltage noise), and the photodiode.

All resistors are sources of thermal noise and the feedback resistor contributes to the total noise of the circuit. In very high transimpedance gain configurations, the photodiode shunt resistance can have a significant affect on the total noise of the circuit. Equation 4 shows the input-referred resistor noise density equation, which can be simplified to show that the input-referred resistor noise of the transimpedance amplifier is given by the thermal noise of R_F divided by the square root of the noise gain. The output-referred resistor noise is given by multiplying Equation 4 by the noise gain. Thus, the output-referred resistor noise increases with the square root of the noise gain and the square root of the resistor value, while the signal gain increases directly with the resistor value. Therefore, increasing R_F provides a signal-to-noise ratio benefit as long as the current noise does not become a dominant source of noise.

Equation 4.

e_{n_R} = \sqrt{4 k T R_{F} (\frac{R_{P D}}{R_{P D} + R_{F}})}

Figure 7-14 shows the output voltage noise of OPA928 in a transimpedance amplifier configuration with R_F = 1TΩ and C_F = 0.15pF. The OPA928 current noise does not significantly contribute to the noise performance of the transimpedance amplifier.

OPA928 OPA928 Transimpedance
Amplifier Output Voltage Noise With a 1TΩ Resistor

Figure 7-14 OPA928 Transimpedance Amplifier Output Voltage Noise With a 1TΩ Resistor

Comparing the input current noise of the OPA928 to the current noise of R_F can be useful to find the dominant noise source. A 1TΩ resistor, for example, is equivalent to 0.1287fA/√Hz of current noise which is well above the measured 0.07fA/√Hz of the OPA928. The OPA928 current noise is equivalent to a 3.34TΩ resistor. For more information on current noise, see the Impact of Current Noise in CMOS and JFET Amplifiers application report.

The total output-referred noise of the transimpedance amplifier is given by Equation 5, where e_n is the amplifier voltage noise (including the 1/f and broadband regions), i_n is the amplifier current noise, i_pd is the photodiode current noise, f_–3dB is the transimpedance bandwidth, G is the dc noise gain, and G(f) is the frequency dependent noise gain.

Equation 5.

E_{n_t o t a l} = \sqrt{\int_{f_{l}}^{f_{h}} {(e_{n} G (f))}^{2} d f + [{(i_{n} R_{F})}^{2} + {(i_{p d} R_{F})}^{2} + 4 k T R_{F} G] \times 1.57 f_{- 3 d B}}

The total output-referred voltage noise calculation requires a complicated analysis of the frequency dependent noise gain and voltage noise density, and is not covered here. Unlike the current and resistor noise which are bandwidth limited by the transimpedance bandwidth given by Equation 3, the op amp voltage noise is only limited by the gain bandwidth of the amplifier. Limit the noise bandwidth with an output filter to reduce the voltage noise contribution.

The ultra-low current noise of the OPA928 is not a significant contributor of noise in most applications, and an output low-pass filter makes the e_n term in Equation 5 negligible. Equation 6 provides a straight-forward calculation for the total output-referred noise for a filtered transimpedance amplifier.

Equation 6.

E_{n_t o t a l} = \sqrt{[{(i_{p d} R_{F})}^{2} + 4 k T R_{F} G] \times 1.57 f_{- 3 d B}}

Figure 7-15 shows the simulated noise of the OPA928 in a transimpedance configuration with R_F = 10GΩ, R_PD = 5GΩ, C_F = 1pF, C_PD = 35pF.

OPA928 Transimpedance Amplifier
RC-Filter Noise Comparison

Figure 7-15 Transimpedance Amplifier RC-Filter Noise Comparison