I found an anti-aliasing circuit on the 40m wiki. It consists of A differential LPF made using THS4131 low noise differential op-amp (one of the main applications of which is preprocessing before the ADC), and a notch. I modified it to arrange for the desired bandwidth (about 8 kHz) and notch after the Nyquist frequency at 36 kHz. I simulated it to get the attached results:
Attachment 1: It shows the input PSD (same as the one posted in the previous elog), the filter transfer function, and The resulting output.
Attachment 2: The circuit schematic. The initial part using THS4131 is a differential LPF and the subsequent RC network is the notch.
Attachment 3: This shows the ratio of the aliased downconverted signal to the the in-band signal, representative of the contamination in each bin. Here too, the aliased signals are negligible as compared to the low frequencies but they are not negligible as compared to the higher frequencies (above 10 kHz) into which they would get downconverted due to sampling. However, here, the attenuation at 8kHz is less than 6 dB while in the previous circuit, it was about 12 dB. One problem with this circuit is at about 6kHz, there is aliased signal from the 65k to 98kHz band, but this can be taken care of by adding an LPF later.
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Summary: The aim is to design an analog anti-aliasing (AA) filter placed before the ADC, whose function is to filter out components of the input spectrum that have frequencies higher than the Nyquist frequency. This needs to be done so that there is no contamination of aliased downconverted high-frequency signals into the ADC output. I have put down and simulated a circuit to do this, based on the spectra of a few interferometer signals that eric Provided. Attachment 1 shows such an input PSD, treated with whitening filter, before the AA. The sampling rate is 65536 Hz and hence the Nyquist freq. is 32768 Hz.
Motivation: Attachments 2 and 3 show the plot of required attenuation for various frequencies above the Nyquist. We can see a peak at 36 kHz, which will alias to about 29kHz. It will require about 70 dB attenuation here. This indicates that use of a notch filter combined with a low pass filter can be used.
Details of Schematic: Attachment 4 shows the schematic of a Boctor low pass notch filter, cascaded by a 2nd order LPF. The stopband frequency of the boctor filter can be tuned to around 36 kHz. Its main advantage for the boctor is better insensitivity to component value tolerances, use of a single op amp, and relatively independent tuning of parameters. The various component values are calculated from here. The transfer functions for the circuit shown in attachment 4 were simulated using TINA - a spice based simulation software. The transfer function is shown in attachment 5.
A few more calculations: Attachment 6 shows the output psd after the signal has been treated with AA. Attachments 7 and 8 show the ratio of aliased downconverted signal and the unaliased signal of the output. Here, we can see that above about 13 kHz, the ratios go above -40dB, which is apparently undesirable. However, we also see from the transfer function of the filter that the gain falls to less than -20dB after about this frequency, and the aliased signals are atleast 20 dB lower than this, atleast upto about 29 kHz in attachment 7 and about 25 kHz in attachment 8. This means that the aliased signals are negligible as compared to the low frequencies even if they are not negligible as compared to the higher frequencies (above 13 kHz) into which they would get downconverted due to sampling. But these higher frequencies (above 13 kHz) themselves are small.
The filter overall, is 4th order. Considering this and the above discussion, I need to decide what changes to make in the existing schematic. For now, I could discuss with eric to finalize the opamp and start building the pcb board design.
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