I'm trying to understand the noise I measure in a couple of versions of a trans-impedance pre-amp that I'm using with a quartz tuning fork, such as is used in digital watches, but removed from its can and used to measure acoustic signals from a laser beam focused between the tines of the tuning fork. The output noise spectra do not match what I calculate using the Johnson noise of the feedback resistor, the specified voltage and current noise of the op-amps, the measured feedback capacitance and my estimate of the capacitance at the input of the op-amp.
The initial version of the trans-impedance amp used a Burr-Brown OPA656 with a 10 Mohm feedback resistor on a 2-sided board. I measure an output noise of 410 nV/rt-Hz at frequencies below 1 kHz, which matches the Johnson noise of the 10 Mohm feedback resistor, but the noise floor starts increasing above 1 kHz. This increasing output noise floor is qualitatively similar to that due to the voltage noise of the op-amp amplified by the noise gain. However the numbers don't workout. The specified input capacitance of the OPA656 is 4.5 pF common mode, 0.7 pF differential. There are the capacitances of the 1/2" long traces from the op-amp inputs to an SMA connector soldered to the board, the SMA connector, an SMA to BNC adapter, and a bulkhead BNC connector to which the fork is soldered. I estimate these connector capacitances total about 3 pF. Adding in the shunt capacitance of the quartz tuning fork, about 1 pF, the I estimate the total input capacitance to be 9.2 pF. I measure a 3 dB bandwidth of 106 kHz from which I conclude the stray capacitance of surface mount feedback resistor is
0.15 pF. With these capacitances and the 10M feedback resistor, I calculate that the output noise should not rise above the Johnson noise of the feedback resistor by 5% until about 100 kHz.However I measure the noise reaching 500 nV/rt-Hz at 30 kHz. (With a quartz tuning fork connected that is still in its can, there is a noise peak at the fork resonance of 32764 Hz, but this noise peak has a width of 0.4 Hz and doesn't not contribute significantly to the noise spectrum except within about 20 Hz of the resonance frequency.)
This pre-amp has another problem, the trans-impedance gain varies with the equivalent series resistance of the tuning fork's equivalent series RLC circuit. The fork series resistance changes with pressure and temperature, so the system gain changes with gas pressure. The change in trans-impedance gain with source resistance is well fit by a model using a finite open-loop gain of 62 dB for the OPA656 which is in fair agreement with the "typical" open loop gain of 65 dB up to about 100 kHz.
So to reduce the variation in trans-impedance gain with source resistance, I decided to replace the OPA656 with the OPA657. The OPA657 has a higher typical open loop gain (75 dB) and a larger gain bandwidth product, but the same specified input capacitance and resistance as the OPA656, the same current noise (1.3 fA/rt-Hz), and slightly lower voltage noise (5 nV/rt-Hz for the OPA657 and 7 nV/rt-Hz for the OPA 656). To my surprise and disappointment, with the OPA 657, the noise increased at 30 kHz from 500 nV/rt-Hz to 600 nV/rt-Hz and peaks at 50 kHz. With the OPA656, the noise kept increasing to 100 kHz, the upper limit of my spectrum analyzer.
To further confuse me, another version of this pre-amp was made with a
4-layer board that has provision for doing active bandpass filtering. We found that the trans-impedance input stage with an OPA657 has twice the noise at 30 kHz as the previous board with an OPA657. This higher noise level is present when the components for filtering are removed. Even when a quartz tuning fork is soldered to the 4-layer circuit board, the noise level near 30 kHz is still about 3 times the Johnson noise level of the feedback resistor.I have measured the noise spectrum at the power pins for the OPA657 and it is flat at 200 nV/rt-Hz from about 128 Hz until it starts rolling off at about 40 kHz. I have also looked at the output of these pre-amps with a 400 MHz bandwidth scope and can not find evidence of oscillation. I found a problem with current leakage on one of these boards that was fixed by scrubbing with isopropyl alcohol and cotton swabs, so we've periodically cleaned these boards without any reduction in noise since that first time.
The one other obvious difference in the two circuit boards is that on the
4-layer board, the ground plane extends under the op-amp and perhaps under the traces from the op-amp inverting input to the fork connections, while the original 2-layer board does not have a ground plane under the op-amp and the inverting input.My basic questions are:
1) What could be the cause of the excess noise that became significantly worse when switching to a faster and higher gain op-amp that has less voltage noise and that depends on the layout of the circuit board?2) What things should be done in the layout of the next circuit board to minimize the noise near 32 kHz for a trans-impedance pre-amp with gains of 1 to 10 Mohms?
Thanks for any suggestions, Bret Cannon