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Estimating the Frequency Response of Variable Reluctance Pressure Sensors in Gas

Results

The observed natural frequencies were lower than the calculated natural frequencies, as the tubing lengths were shortened. The lower observed frequencies may be the result of restrictions in the solenoid valve and in the transducer porting and fittings. The actual natural frequencies may be somewhat higher in the absence of the solenoid valve.

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Frequency Response Recommendations - Transducers and Carrier Demodulator Selection

For pressures above 2 Inches H2O, the DP15 is the best transducer because of its smaller sensor cavity volume. Below 2 In H2O the DP45 has better sensitivity and only slightly lower natural frequency for any given tubing length. For static line pressures greater than 15 psig, the DP15 must be used. The CD15 or CD101 have the highest low-pass filters, flat to within +/-5% at 1 Khz, and are the best choice for single-channel applications. For multiple pressure readings, theUPC601-L may be used for transient capture to a PC; the AC excitation, demodulation and software is included.

Here are some guidelines to assure the best possible dynamic frequency response:

Plumb the transducers as closely as possible to the source of the pressure waveform. Close coupling is best. This should keep the natural frequency of the plumbing as high as possible: approximately 400 Hz for a DP15 and 330 Hz for the DP45. (in air) Assuming minimal damping, flat response should be 80 to 100 Hz for DP15s in air and 65 to 80 Hz for the DP45.

If the data is to be recorded using a data acquisition system, a sample rate of 5000 samples per second will insure that a digital low-pass filter can be constructed that will eliminate any frequencies present above the system flat response. A multi-tap FIR filter, applied in software after data collection, would insure that the waveforms captured were free from distortion within the flat response range of the transducer and its plumbing.

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Example of System Response Estimate

Consider the following system:

DP15-26 transducer is connected by 3 feet of 3/16 in ID tubing to a pneumatic system where +/- 10 In H2O differential pressure fluctuations ranging in frequency to 5 Hz are to be investigated. What is the usable response of such a system if the companion electronics consists of a 3 Khz carrier demodulator having a 250 Hz low-pass third order filter ? What sampling rate should be used by the data acquisition system?

The graph below shows the response of the various system elements. The 3 Khz carrier frequency represents the upper limit of the frequency response in the system, as shown by the line on the extreme right side of the graph. From the graph showing sensor natural frequency as a function of range, 2500 Hz represents the mechanical sensor response for a 0.5 psid transducer. The plumbing natural frequency was observed to be about 100 Hz (see previous graph from test results). The third-order analog filter response is also shown, with its cut-off of 250 Hz. Note that the distortion due to the resonance of the plumbing would be mostly passed by this filter, yielding measurement errors should frequencies above about 25 Hz be present.

The data acquisition system can be constructed so that the flat response of the transducer/plumbing system is optimized. The analog filter will attenuate frequncies above 2500 Hz to a very small amplitude. If the sampling rate is set to 5000 Hz, a minimal distortion will result from any aliasing frequencies present above 2500 Hz. A multi-tap digital FIR filter can be constructed with a cut-off of 25 Hz, so the data can be processed such that the total system response is flat to about 20 Hz. Thus the system is adequate for accurately measuring pressure fluctuations on the order of 5 Hz.

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