Piezoelectric receivers (e.g. hydrophones) generally have a much wider usable frequency range than acoustic / ultrasonic transmitters. This article explains why and looks at how different manufacturers specify the usable range of a hydrophone.
Origins of the Piezoelectric Receiver
The first practical application of piezoelectric materials was in underwater sonar. That system was designed during World War I and was deployed in 1917 in response to a new threat: the German U-boat.
The transducer was a simple design. A thin layer of quartz was sandwiched between two metal plates and that assembly was housed in a waterproof enclosure. The device was patented in 1917.
Since then, designs have changed and materials have improved. (Modern PZT vastly outperforms the quartz used in the original sonar.) Yet, this single-resonator echo sounder concept is still the foundation of many modern underwater designs. The transducer transmits at its resonance frequency, where it is most effective. When the echo returns, the same transducer is also an effective receiver. However, this familiar design overlooks one of the major advantages of piezoelectric receivers: wide bandwidth. In fact, this application may be largely responsible for the confusion surrounding the usable frequency range of transmitters versus that of receivers.
Broadband Hydrophone Response
The difference between transmitting bandwidth and receiving bandwidth can be explained succinctly. Transmitting is a resonant function: maximum output occurs at resonance and is generally poor off resonance. Receiving, on the other hand, is a non-resonant application: hydrophones work well over the entire band below their resonance point. This behavior is clearly illustrated in the 1979 U.S. Naval Research Laboratory (NRL) paper “NRL-USRD Series F42 Omnidirectional Standard Transducers”. The paper characterizes and compares the F42 series of reference spherical transducers, in both transmitting and receiving modes. It is available in its entirety here.
The F42 series of transducers are labeled in order of decreasing diameter from A, the largest diameter, to D. Fig. 2, below, shows the transmit voltage response (TVR) curves for the set of transducers. The performance of each unit peaks at the resonance frequency and drops off quickly as the transmit frequency moves away from resonance. Transmit performance is highly resonant; the usable frequency range is narrow. These curves are typical of a piezoelectric transmitter.
Transducer F42A is the largest, so it has the lowest resonance frequency. Its transmit peak occurs somewhere in the 30 – 40 kHz range. (Resonance frequency is primarily determined by size. Larger sensors have a lower frequency.) Transducers B through D have decreasing diameters and thus increasingly higher peak transmit frequencies. These higher frequencies shift the transmit curves horizontally, but do not change the shape of the curves. The transducers all display the same performance: peak transmission at resonance and a relatively narrow usable band.
The open circuit voltage response (OCV, also called free-field voltage sensitivity), shown in Fig. 3 below, has a very different shape. Like the TVR curve there is clearly a peak. This is the maximum receiving sensitivity which occurs, arguably (more on this below), at the resonant frequency. At frequencies below the resonance point, however, the performance does not decline as it does with transmitting response. Rather than having a steep slope, the receiving response curve below resonance is quite flat. The response of the transducers, when receiving, at frequencies below resonance, is both consistent and usable, all the way down to ~0 Hz.
Fig. 3 – Free-Field Voltage Sensitivity of the F42 series of spherical transducers
In fact, when a hydrophone is connected to a preamp, digital acquisition card, recording device or other electronics, the low end of the usable frequency range for the system is often limited by the electronics, not the hydrophone.
So, like transmitters, hydrophones can function in the region around their resonant frequency. Unlike transmitters however, hydrophones work not just in this small frequency band. They perform well over the entire frequency band below their first resonance point. Hydrophones are a non-resonant device. It is not uncommon for the usable frequency range of a hydrophone to span hundreds of thousands of Hertz.
(A general explanation of resonant and non-resonant piezoelectric sensors can be found here.)
The Dip Below the Peak
A typical OCV plot, such as Fig. 3, shows a decline in receiving sensitivity in the region just before the peak. This dip is caused by the diffraction effect.
At low frequencies the wavelength of an acoustic signal is long. It is much larger than the hydrophone itself, so the hydrophone creates a negligible disturbance in the pressure field.
At higher frequencies the wavelength gets shorter. As the wavelength approaches the size of the hydrophone, the hydrophone itself begins to have an impact on the pressure field. Specifically, it diffracts some of the incoming pressure waves. With a portion of the energy diffracted away, the output from the hydrophone decreases. This appears on the OCV plot as a drop in sensitivity.
Peak Receiving Response
There remains some disagreement about where the peak receiving sensitivity falls. Some text books and manufacturers state that it occurs at the resonance frequency of the hydrophone. Others claim that it occurs at anti-resonance. (Anti-resonance occurs at a slightly higher frequency than resonance.) Empirical evidence only complicates the issue; it often falls in between these two points.
However, the argument is unimportant from a practical perspective. Using the calibration data for a hydrophone you can adjust your measurements to account for the variation in receiving sensitivity that occurs around resonance. Better still, by using a hydrophone in the region well below resonance you can ensure a consistent response over the entire working frequency band.
Specifying Usable Frequency Range of a Hydrophone
The typical hydrophone receive response illustrated in Fig. 3 above helps provide an understanding of the different ways hydrophone manufacturers specify bandwidth.
Fig. 4 – Typical hydrophone OCV plot showing the -3 dB point
Some manufacturers define the usable frequency range of the hydrophone up to the point where the sensitivity drops 3 dB, commonly referred to as the -3 dB point. (Some manufactures cite a -6 dB point.) See Fig. 4 above. This approach states a wide bandwidth but suffers through the inconsistent receiving response that occurs around resonance. While the hydrophone is functional across this band it is not entirely consistent.
Other manufacturers avoid the region of inconsistent sensitivity response. They define the usable bandwidth of a hydrophone as the flat portion of the curve that occurs below resonance. “Flat portion” is typically constrained to a variation of 3 dB. See Fig. 5 below. This conservative approach provides a more consistent receiving response. However, it significantly reduces the defined bandwidth of the hydrophone.
Fig. 5 – Typical OCV plot showing the 3 dB usable band
You may also find hybrid versions of these two approaches. Some manufactures specify a usable frequency range by expressing the sensitivity range as an upper and a lower limit. For example, the 3 dB range illustrated in Fig. 5 above may be expressed as +1.5 /-1.5 dB. The upper and lower limits of the usable frequency range don’t necessarily need to be symmetrical. Some manufacturers define the usable range using the asymmetrical and more conservative limits +1/-1.5 dB. Or, in some cases it may be much looser, such as +3.5/−12.5 dB, which then includes the region of inconsistent response around Fr.
Finally, some manufactures avoid defining a usable frequency range altogether. Rather than using any of the methods described above, they simply state the resonant frequency of the hydrophone. In this case the user must determine if it will meet the needs of their application.
Generally, the hydrophone manufacturer will make it clear which method is being used to define the hydrophone’s usable range. As always, if you have questions, simply contact the manufacturer.