Hydrophone Loading Corrections

The sensitivity of a hydrophone is often specified as the end-of-cable open-circuit sensitivity. This is the sensitivity of the hydrophone at the end of its cable when not connected to an electrical load. When a specific electrical load, such as an oscilloscope, an amplifier or extra cable is used at the output of the hydrophone, the end-of-cable loaded sensitivity of the hydrophone at a given frequency may be related to the open-circuit sensitivity in the following ways:

• Loading due to measurement instrumentation
• Loading due to added extension cable
• Corrections using only capacitance values
• Electrical impedance correction

Loading due to measurement instrumentation

Consider the general case in which the hydrophone is considered as a two-terminal network of complex impedance Z_H connected to an electrical load of complex impedance Z_L. The end-of-cable loaded sensitivity of the hydrophone, M_L, when connected to the specified load is related to the end-of-cable open-circuit sensitivity, M_O, by:

where Re and Im denote the real and imaginary parts of the relevant complex impedance.

Often, as in the case of a preamplifier or oscilloscope input, the electrical load can be assumed to be a parallel combination of a resistance R_L and capacitance C_L. In this case, Re(Z_L) and Im(Z_L) are given by:

where ω is the angular frequency.

Loading due to added extension cable

For hydrophones without an integral preamplifier, the effect on the sensitivity due to the addition of an extension cable can be calculated using the formula below. This formula requires complex impedance measurements of the hydrophone with extension cable and the extension cable alone in order to determine the change to the open-circuit sensitivity of the hydrophone caused by the addition of the extension cable.

The open-circuit sensitivity measured at the end of the extension cable, M_L, can be derived from the open-circuit sensitivity of the hydrophone at the end of the integral hydrophone cable, M_O, as follows:

where:

Z_HC  is the complex impedance of the hydrophone and extension cable

Z_OC  is the complex impedance of the extension cable alone measured with the free ends open-circuit

Z_SC  is the complex impedance of the extension cable alone measured with the free ends short-circuit

Corrections using only capacitance values

A simplified correction is possible if the impedances of both the hydrophone and the load can be assumed to be purely capacitive. This is often a valid assumption for a hydrophone at frequencies much less than the resonance frequency and for loads such as extension cables.

If C_H is the end-of-cable capacitance of the hydrophone (including any integral cable and connector) and C_L is the capacitance of the load (e.g. the extension cable), the correction factor is calculated as below:

The low frequency, end-of-cable capacitance of a hydrophone is often quoted in the manufacturer's documentation and the capacitance of extension cable is usually specified in pF/m by the cable manufacturer. It is therefore possible to calculate an approximate sensitivity correction without the need for an impedance analyser or LCR meter.

Electrical impedance correction

Where it has been necessary to measure the electrical impedance of a hydrophone via an extension cable, the complex impedance of the hydrophone (with its integral cable) can be determined from further measurements of the complex impedance of the extension cable alone.

The complex impedance of the hydrophone (with its integral cable), Z_H, is given by:

where:

Z_HC  is the complex impedance of the hydrophone and extension cable

Z_OC  is the complex impedance of the extension cable alone measured with the free ends open-circuit

Z_SC  is the complex impedance of the extension cable alone measured with the free ends short-circuit

References

• IEC 60565:2006, The calibration of hydrophones, International Electrotechnical Commission, Geneva, 2006.
• G Hayman, P N Gélat, G R Moore, G O Wells and S P Robinson, A method for correcting the complex electrical impedance and open-circuit sensitivity of a hydrophone for the effect of added extension cable, Meas. Sci. Technol. 18 (2007) N47-N52.
• D. Stansfield, Underwater Electroacoustic Transducers, Bath University Press, Bath, UK, 1991, p.297.
• H A J Rijnja, Small Sensitive Hydrophones, Acustica, vol 27 pp.182-188, 1972.
• S P Robinson, G R Doré, Uncertainties in the calibration of hydrophones at NPL by the three-transducer spherical-wave reciprocity method in the frequency range 10 kHz to 500 kHz, NPL Report RSA(EXT) 54, November 1994.
• K Simonyi, Foundations of Electrical Engineering, Pergamon Press, London, UK, 1963, pp. 522-533.
• The Impedance Measurement Handbook: A Guide to Measurement Technology and Techniques Copyright® 2000-2003 Agilent Technologies Co Ltd
• K Beissner, Free-field reciprocity calibration in the transition range between near-field and far-field, Acustica, vol 46, p 162-166, 1980

For further information, contact Stephen Robinson