A guide to using FETs for sensor applications, Part 2
In some JFET op amps such as the AD743, the input capacitance is in the order of 18 to 20 pF. In comparison, with an LSK489 dual FET, the input capacitance is in the order of 3 pF, which will be suitable for low noise photodiode applications. In this section we will see why it is important to have low equivalent input noise and low input capacitance in a photodiode preamp.
A simple photodiode is shown in Figure 8, which uses an op amp.
Figure 8 - A simple photodiode transresistance amplifier.
In the photodiode amplifier above, when light is shined onto the photodiode, current is generated by the photodiode, PD1. As configured with the cathode of PD1 connected to the (-) input terminal of U1, Vout generates a positive voltage proportional to the amount of light into the photodiode. Also shown in Figure 8 are the equivalent capacitances from the photodiode, Cpd, and (-) input terminal, Cin(-), which are connected in parallel. To minimize Cpd, the photodiode capacitance, the anode of PD1 is connected to the minus 12 volt power supply for maximum reverse bias to lower its junction capacitance. For example, if a BPV10 photodiode is used, Cpd is about 2.7 pF at 12 volts reverse bias. At a lower reverse bias voltage such as 1 volt, Cpd is about 7 pf.
For low noise considerations, these two capacitances, Cpd and Cin(-), should be low as possible. The reason is that the equivalent input noise density voltage, Vnoise_input of the op amp will be amplified in the following manner at Vout, neglecting any noise current from the photodiode:
Vout_noise for a bandwidth of 1 Hz = (Vnoise_input) √(1+ωRFCt)2 + √4kTRF (1)
ω = 2πf, RF = feedback resistor, k = 1.38 x10-23 Joules per degrees Kelvin, T = 298 degrees Kelvin
Ct = Cpd||Cin(-) = total capacitance at the (-) input terminal, and
Ct = Cpd + Cin(-)
√4kTRF = thermal noise voltage of the feedback resistor RF for a bandwidth of 1 Hz.
As we can see from the equation above, the output noise, Vout_noise, goes higher if Ct is increased.
In designing a low noise transresistance preamps the goals are to:
1) Minimum equivalent input noise voltage. Equation (1) above shows that the output noise voltage is dependent on the equivalent input noise voltage, Vnoise_input.
2) Minimize noise current from the (-) input because the noise current at the input will form a noise voltage across the feedback resistor. Generally, a JFET is desirable for the (-) input because of its low gate noise current.
3) Minimize the capacitance from the (-) input to ground. The equation (1) shows that more noise is generated at the output when the capacitance, Ct = Cpd + Cin(-), at the (-) input terminal is increased.
4) Use as large value RF as possible. At first glance, it would appear increasing the resistance in RF would increase the output noise because of the resistor’s thermal noise. This is true but the signal amplification from the photodiode is increased more so that results in a net increase in signal to noise ratio when RF is increased in value. For example, doubling the value in RF increases the resistor noise from RF by √2 = 1.41 while increasing the photodiode signal output voltage by 2. Thus, there is a net gain of √2 or + 3 dB, in terms of signal to noise ratio in this example.