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Estimate maximum range, SNR, transmission loss and source level of a sonar system

The **Sonar Equation Calculator** app solves the basic sonar equation
for monostatic sonar systems. The sonar equation relates transmission loss (or target
range), source level, directivity, noise level, target strength, and signal SNR. You can
solve for one of these quantities in terms of the others. Using this app, you
can:

Calculate the received SNR value from transmission loss (or equivalently, target range), source level, and noise level.

Solve for transmission loss from sonar source level of the sonar, specified received SNR, and array directivity.

Solve for target range from sonar source level of the sonar, specified received SNR, and array directivity.

Calculate required source level from target range, source level, and received SNR.

MATLAB

^{®}Toolstrip: On the**Apps**tab, under**Signal Processing and Communications**, click the app icon.MATLAB command line: Enter

`sonarEquationCalculator`

.

Compute the maximum detection range of an active monostatic sonar designed to achieve an SNR of at least 10 dB. The operating frequency is 5 kHz, and the source level is 180 dB. Assume that the noise level is 73 dB, the receiver directivity is 20 dB, and the target strength is 10 dB.

Set

**Calculation**to`Target Range`

.Set

**Mode**to`Active`

.Set

**Noise Level**to`73`

dB//1μPa.Set receiver

**Directivity index**to`20`

dB.Set

**Target Strength**to`10`

dB.Set

**Frequency**to`5`

kHz.Set channel

**Depth**to`100`

m.Set

**Source Level**to`180`

dB//1μPa.Set required

**SNR**to`10`

dB.

The maximum target range is 14.61 km.

Use multiple pulses to reduce the source level while maintaining the same maximum target range.

Start with the values set in the Maximum Detection Range of Active Sonar example.

Click the arrows to the right of the

**SNR**label to access the**Detection Specifications for SNR**options.Set

**Probability of Detection**to`0.95`

.Set

**Probability of False Alarm**to`1e-6`

.Set

**Number of Pulses**to`10`

.Reduce

**Source Level**to`175`

.Set the

**Swerling Case Number**to`0`

assuming a nonfluctuating target.

The maximum detection range is 14.81 km, approximately the same as in the previous example, but the source level is reduced by 5 dB.

Compute the source level for an active monostatic sonar with a received SNR of 15 dB. The target range is 5 km and the target strength is 25 dB. Assume a 5-kHz sonar frequency.

Set

**Calculation**to`Source Level`

.Set

**Mode**to`Active`

.Set

**Noise Level**to`75`

.Set receiver

**Directivity index**to`20`

dB.Set

**Target Strength**to`25`

.Click the arrows to the right of the

**Transmission Loss**label to access the**Calculation of Transmission Loss**options.Set the

**Range**to`10.0`

km.Set the

**Frequency**to`5`

kHz.Set the

**Depth**to`200`

m.Set

**SNR**to`15`

dB.

The required source level is 171.6 dB//1 μPa.

Compute the received SNR for a passive sonar with a source level of 140 db//1 μPa for a source 10.0 km away. Assume a 3-kHz sonar frequency.

Set

**Calculation**to`SNR`

.Set

**Mode**to`Passive`

.Set

**Noise Level**to`75`

.Set receiver

**Directivity index**to`20`

dB.Click the arrows to the right of the

**Transmission Loss**label to access the**Calculation of Transmission Loss**options.Set

**Range**to`10.0`

km.Set

**Frequency**to`3`

kHz.Set

**Depth**to`200`

m.Set

**Source Level**to`140`

dB//1 μPa.

The received SNR is 23.16 dB.

Compute the transmission loss for an active sonar that results in an SNR of 15 dB. The source level is 215 dB//1 μPa. Assume that the noise level is 75 dB//1 μPa, the receiver directivity is 20 dB, and the target strength is 10 dB.

Set

**Calculation**to`Transmission Loss`

.Set

**Mode**to`Active`

.Set

**Noise Level**to`75`

dB.Set receiver

**Directivity index**to`20`

dB.Set

**Target Strength**to`25`

dB.Set

**Source Level**to`215`

dB.Set required

**SNR**to`15`

dB.

The transmission loss is 85 dB.

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