# Frequently Asked Questions

There are two general considerations for determining the maximum pressure at which a hydrophone can be used: (1) the linearity of its preamplifier, and (2) hydrophone damage

**1. Linearity of Preamplifier**

Amplifiers have a voltage limit, beyond which they become non-linear and saturate. This is a reversible problem. That is, if it happens it does not damage the hydrophone or preamp. Although the data is invalid, the hydrophone can still be re-used within the amplifier’s specified voltage range. For Onda’s modular amplifiers (i.e., AH-20x0, AG-20x0, and AH-1100), a maximum voltage output is provided as a specification. The formulas to calculate loaded sensitivity can be used to determine the expected acoustic pressure level of the signal to verify they will be within the linear range of the amplifier. For high-sensitivity hydrophone models, Onda also offers a signal attenuator (i.e., ATH-1000) to prevent preamplifier saturation. For membrane hydrophone models which have an integral preamplifier, the maximum linear pressure range is also provided as a specification.

**2. Hydrophone Damage**

Unlike preamp linearity, damage thresholds are much more difficult to provide. Hydrophones are intrinsically fragile, particularly near the sensing element, because they are designed to have high sensitivity to detect transient pressures. Different models have varying degrees of protection depending on the construction. To add to the complexity, the robustness of each hydrophone depends on several factors in the test environment. For instance, it is particularly important to minimize the dissolved oxygen content in water to limit bubble formation which increases the likelihood of cavitation damage. Other factors that contribute to the likelihood of damage include drive frequency, duty cycle, and temperature.

The Pressure Range plot should be used as a guideline but not taken in a strict sense given these dependencies. The following plot estimates the pressure range that can be measured with each hydrophone model. However, it should be noted these are only guidelines. It is important that the user considers the details of other factors that contribute to the actual pressure thresholds (e.g., aperture size, preamplifier noise, water quality, drive conditions, etc.).

As can be seen from the plot, the only pressures that are clearly acceptable for all circumstances are below approximately 100 kPa. This is particularly true for continuous or quasi-continuous waves, which at pressures higher than 100 kPa make the hydrophone more susceptible to cavitation damage. So from a conservative point of view, the only clearly safe conditions are below 100 kPa peak negative pressure.

For more information please Contact UsOnda’s hydrophones are calibrated with respect to a plane-wave. The hydrophone is positioned so that its active surface is parallel with the planar wavefront, i.e., the direction of propagation of the wave is normal to the active surface of the hydrophone. For example, in the case of needle or capsule hydrophones, the active surface is at the tip, so the normal is the major axis of the needle or capsule.

The hydrophone’s sensitivity decreases as it is rotated with respect to the normal position. For needle and capsule hydrophones the sensitivity approximately follows formula 1:

D(theta,f) = [((1+cos(theta))/2] (2J1(k a sin(theta)) / [k a sin(theta)] (1)

**Where:**

- theta = the angle relative to the normal
- D = directivity function (voltage out of the hydrophone relative to voltage when an incoming wave is normal to the tip)
- f = frequency
- J1 = Bessell function of the first kind
- k = wave number (2 pi / wavelength) = 2 pi f /c where c is the wavespeed = 1500 m/s in water
- a = radius of the hydrophone (0.75 mm approximately for an HNC1500, for example)

For high frequencies and small angles the (1+cos(theta)) term becomes negligible and the formula becomes:

D(theta,f) = (2J1(k a sin(theta)) / [k a sin(theta)] (1b)

Furthermore, for small angles as well as low frequency Eq. (1b) may be approximated as:

D(theta,f) = 2J1(2 pi f a theta/c)/[2 pi f a theta /c] (1c)

From (1c) it can be seen that for small angles and low frequency the directivity will scale with theta*f where f is the frequency. That means that under such conditions you can take the directivity pattern acquired at one frequency f1, and estimate the directivity pattern at another frequency f2 from the same curve, replacing theta with theta * f1/ f2. For example, if at 5 MHz the directivity is 0.9 at 10 degrees, at 2.5 MHz it will be 0.9 at 20 degrees. Onda provides typical directivity patterns measured at 5 MHz for this purpose.

The user should be aware, however, that Eq. (1c) loses accuracy at very low frequencies, as can be seen from Eq (1), which is the more exact formula.

An End-of-Cable Open Circuit (EOC) sensitivity represents the sensitivity measured at the hydrophone connector without the preamplifier. An EOC hydrophone calibration can be mathematically converted to a preamplifier-loaded calibration. See the Resources section for the white paper. Onda also can supply a software utility to combine the standalone calibration data sets. An EOC calibration offers more flexibility because it can be paired with different preamplifiers. However, the user can avoid the conversion by having hydrophones calibrated in a preamplifier-loaded configuration.

Please note, however, that as the frequency goes up, the mathematical conversion becomes invalid because cable transmission line effects become more important. In particular, cable resonance effects become more prevalent at high frequencies. In some cases for fairly non-linear pulsed waveforms, there may be significant waveform distortion because the pressure signal contains very high frequency harmonics which excite cable resonances. In general, we recommend that the cable length be less than a tenth of the electrical wavelength in the cable for any relevant frequency. The cable electrical wavelength is given by the cable phase velocity divided by the frequency. The phase velocity can be assumed to be 2 x 108 m/s, so for example, at 20 MHz the cable electrical wavelength will be 1 meter. So, results above 20 MHz for a 1m cable. Just bear in mind that in many practical applications non-linear harmonics go to much higher frequencies than 20 MHz.

Note that frequencies above 20 MHz require the calibration to be preamplifier-loaded to ensure sufficient sensitivity.