By Kennedy R.J., Thorndike E.M.
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Extra resources for A Search for an Electrostatic Analog to the Gravitational Red Shift
5 nA rms. 5 mV root mean squared (rms). 5 = 15 mV peak-to-peak (pk-pk). Hence it should be clearly visible and a signiﬁcant fraction of the 1 V mean voltage. I tried this and saw nothing! Why not? One of the problems is that the bandwidth of the scope, driven like this from a current source, is not really the 20 MHz you paid for but only a few kilohertz. Yes, it has an input DC impedance of 1 MW, but this is shunted by several picofarads. The speciﬁcation for mine claims 1 MW ± 1 percent in parallel with 20 pF ± 2 pF.
So, how do we improve the detection performance of the LED transceiver? We showed above that the design cannot be shot-noise-limited, as the detected signal voltage is less than 2 kT/q, or 52 mV. How about increasing the load resistor RL to 1 GW? With the increase in load resistor, its thermal noise voltage has increased by a factor of 1000 = 32 times to 4 mV/ Hz, which seems like a retrograde step. However, the signal from the 100 pA photocurrent has increased by 100 times to 10 V. In the 20 MHz bandwidth the thermal noise of the resistor is 18 mV rms.
10 uses two opamps arranged respectively as a follower with gain and an inverting gain stage. The combination is inverting, just as in a conventional transimpedance ampliﬁer. Ideally, the ﬁrst device can be chosen for low bias current and low noise, such as the AD711 (GBW = 4 MHz) mentioned earlier, and the second device can be a high-bandwidth bipolar unit, such as an LM833 (GBW = 15 MHz). By choosing the stage gains to be 52 and 192, the respective bandwidths are both equal to 77 kHz. Both ampliﬁers then act as low-pass ﬁlters at 77 kHz, with a combined cutoff frequency of about 54 kHz.
A Search for an Electrostatic Analog to the Gravitational Red Shift by Kennedy R.J., Thorndike E.M.