Application Notes >> Technical Notes >> Frequency Response

Estimating the Frequency Response of Variable Reluctance Pressure Sensors in Gas

Electronic Response

The electronics associated with the pressure sensor provide power to the sensing element, amplify the sensing element signal, and include a low-pass filter for transducer output signal. Some sensing technolgies, such as strain gage pressure transducers, have a DC excitation. Other sensors, such as variable reluctance and capacitive sensors, require an AC excitation and demodulation to provide a high-level DC output. For AC sensing technologies the excitation carrier frequency will also be a factor limiting dynamic response. Validyne variable reluctance sensors use carrier excitation frequencies of 3 or 5 Khz, so this will be the upper limit of dynamic pressure response. The low-pass output filtering of the variable-reluctance demodultor may also limit dynamic response. Typical cut-off frequencies for Validyne carrier demodulators electronics vary from 1 Khz to less than 100 Hz, depending on the application for which the transducer is intended. The output filter stages typically roll-off at -12 to -18 dB/octave.

GO TO TOP

Plumbing Response

Perhaps the most limiting factor in dynamic pressure response is the second-order resonant system created by the tubing leading up to the transducer combined with the pressure cavity of the sensor. The natural frequency of this system depends on the volume of the sensor cavity, the length and diameter of the tubing and the speed of sound in the gas to be measured. The equation is shown.

Fn = Natural Frequency,

Validyne variable reluctance transducers have very small sensor cavity volumes, 0.004 cu inches for the DP15 and 0.01 cu inches for the DP45. Combined with short lengths of tubing, these transducers offer very high dynamic response, even over low pressure ranges.

As with the sensor natural frequency, it is highly undesirable to attempt dynamic pressure measurements at the natural frequency of the plumbing: severe distortion will occur due to the amplification of the pressure waveform. This frequency at which the distortion is tolerable depends on the damping in the system, and this is a difficult variable to determine. The worst distortion occurs when damping is slight, so assuming this, the maximum usable frequency for any given plumbing system is generally taken to be one fifth or one seventh of its natural frequency. Some typical values:

Lightly Damped System = 0.2 per unit critical damping

At 100% Natural Frequency, Amplification = 2 times input
At 50% Natural Frequency, Amplification = 1.25 times input
At 25% of Natural Frequency, Amplification = 1.05 times input
At 20% of Natural Frequency, Amplification = 1.03 times input
At 15% of Natural Frequency, Amplification = 1.02 times input

GO BACK

DP15, DP45 Plumbing Tests

In order to test the relationship between the transducer sensor cavity volume, tubing length and resulting natural frequency, the Validyne DP15 and DP45 (14 In H20 FS pressure range) transducers were tested using air and various lengths of 3/16 inch ID plastic tubing. Each transducer was tested as follows:

The transducer and tubing were pressured to approximately 7 In H2O with air. The three-way solenoid valve was actuated, creating a step-pressure change on the system. The transducer output was sampled at the rate of 5000 samples per second with a UPC-based data acquisition system. The output was graphed for each transducer and tubing length combination, and the natural frequency determined from the period of the ringing part of the waveform. The observed ringing frequency was compared with the calculated value.

A typical waveform captured is shown below.

GO BACK

TOP