# EK80 Power, Power to Sv and TS

Echoview derives power (dB re 1 W) raw variables from EK80 data files. Power variables on the Filesets window represent the received power which is calculated from the raw power, number of transducer segments and transceiver impedance read from the data file.

Continuous wave (CW) data

Frequency modulated (FM) data

EK80 EC150-3C data

## Continuous wave (CW) data

The CW instrument configuration records data returned under a single frequency transmit pulse.

Echoview derives two raw variables from power data from each transducer segment (T1, T2,... T*t*):

- Sv raw pings T
*t* - TS raw pings T
*t*

### Calculation of Sv and TS

The Sv and TS values are calculated from the raw power data according to:

where:

R= the corrected range (m) - see TVG Range CorrectionPr = received power (dB re 1 W)

Pt = transmitted power (W)

α= absorption coefficient (dB/m). CW variables can use a calculated value for AbsorptionCoefficient. The calculated value can be overridden by the AbsorptionCoefficient specified in an ECS file.G0 = transducer peak gain (non-dimensional)

Echoview calculates G0 = 10^(G'0/10) where:

G'0=G''0 + 20 log (f/fNominal)where:

G''0 is theTransducerGain(dB) on the Calibration page of the Variable Properties dialog box. This value should be the same for TS and Sv variables and equal to the Transducer gain specified underPing (from file)of the Details dialog box.f is the center frequency (Hz). For CW data, this is the

Frequencyon the Calibration page of the Variable Properties dialog box.fNominal is the nominal frequency (Hz) represented by the

Frequencyon the Calibration page of the Variable Properties dialog box.λ =

c/f= wavelength (m) atfc = sound speed (m/s) entered on the Calibration Page of the Variable Properties dialog box.

τ = pulse duration (s). For CW data, this is calculated using EffectivePulseDuration. CW data recorded as non-complex data may use the TransceiverSamplingFrequency to calculate the EffectivePulseDuration.

ψ = equivalent two-way beam angle (steradian) defined as the beam width at f.

Echoview calculates ψ = 10^[(Ψ'+ 20 log(fNominal/f))/10], where:

Ψ' is the

Two-way beam angle(dB re 1 steradian) on the Calibration Page of the Variable Properties dialog box.fNominal is the nominal frequency (Hz) represented by

Frequencyon the Calibration page of the Variable Properties dialog box.f is the center frequency (Hz). For CW data, this is the

Frequencyon the Calibration page of the Variable Properties dialog box.

Sacorrection = Simrad correction factor (dB re 1m-1) determined during calibration of the EK80. Its value represents the correction between the ideal pulse the system is trying to generate, and the actual pulse. It is specified as the SaCorrectionFactor on the Calibration page of the Variable Properties dialog box.

**Notes:**

- EK80 TVG range correction is only applied to Sv data.
- Sv TVG range correction is calculated using TransmittedPulseDuration.
- CW Sv calculations for the -10 log [cτψ/2] term support Soundspeed-Depth data. See also: Using sound speed profile data.
- CalibrationOffset is added to the Sv equation when it is read from an ECS file or included in a data file.
- CalibrationOffset is added to the TS equation when it is read from an ECS file or included in a data file.

## Frequency Modulated (FM) data

The FM instrument configuration records data returned under a frequency modulated transmit pulse (chirp).

Echoview derives these raw variables from power data from each transducer segment (T1, T2,... T*t*):

- Sv wideband pings T
*t* - TS wideband pings T
*t* - Sv pulse compressed wideband pings T
*t* - TS pulse compressed wideband pings T
*t*

### Calculation of Sv and TS

Echoview can read frequency dependent information from the data file and interpolates values for transducer gain, beam width, frequency and Simrad LOBE beam compensation as required. See also Simrad EK80: Frequency dependent limitations. When frequency dependent data is unavailable, equations that use relationships based on a nominal frequency are used.

#### Wideband variables

The transmitted pulse characteristics of the chirp are used to calculate transducer constants. Echoview reads temperature, acidity and salinity from the Simrad EK80 data file and uses the Francois & Garrison (1982) equation to calculate absorption coefficients for TVG. The Simrad EK80 'Ramping' for the chirp is included in calculations. For further details about the EK80 wideband power to Sv and TS equations contact Simrad.

The Sv and TS values are calculated from the raw power data using these equations:

where:

*R* = the corrected range (m) - see TVG Range Correction

Pr = received power (dB re 1 W)

Pt = transmitted power (W)

*α* = absorption coefficient (dB/m)

fc = center frequency (Hz)

Echoview calculates fc = (fS +fE)/2, where fS is the

FrequencyStart(kHz) and fE is theFrequencyEnd(kHz) on the Calibration page of the Variable Properties dialog box.

λfc = *c*/*fc* = wavelength (m) at *fc*

τeff = the EffectivePulseDuration on the Calibration page of the Variable Properties dialog box. It is calculated using the auto correlation function of the matched filter signal and the decimated sampling frequency.

Gfc = the transducer gain at the center frequency, where

fc is the center frequency (Hz)

fnominal is the nominal frequency (Hz) represented by the

Frequencyon the Calibration page of the Variable Properties dialog box.G(fnominal) is calculated by looking up the value from

GainTableWidebandat the center frequency (Hz). When available,GainTableWidebandmay be viewed on the Calibration page of the Variable Properties dialog box. When GainTableWideband is unavailable, G(fnominal) is theTransducerGain(dB) on the Calibration page of the Variable Properties dialog box. This value should be the same for TS and Sv variables and equal to the Transducer gain specified underPing (from file)of the Details dialog box.

ψfc = Two-way beam angle (steradian) evaluated at fc, where

Ψnominal is the

Two-way beam angle(dB re 1 steradian) on the Calibration Page of the Variable Properties dialog box.fc is the center frequency (Hz)

fnominal is the nominal frequency represented by

Frequencyin Hz on the Calibration page of the Variable Properties dialog box.The Sv equation uses the linear form of two-way beam angle:

**Notes**

- Sv calculations for the wideband -10 log (cτeffψfc/2) term support Soundspeed-Depth data. See also: Using sound speed profile data.
- Echoview doesn't use a term for Sa correction in the Sv equation.
- TSOffsetTableWideband is added to the TS equation when it is read from an ECS file or included in a data file.

#### Pulse compressed wideband variables

Wideband data is pulse compressed by a matched filter convolution. The matched filter is based on the transmitted pulse. Pulse compressed wideband Sv is calculated using PulseCompressedEffectivePulseDuration. For further details about the EK80 wideband power to Sv and TS equations contact Simrad.

EK80 pulse compressed Sv represents the pulse compressed Sv for the chirp. EK80 pulse compressed TS represents the pulse compressed TS for the chirp.

**Note:** Pulse compressed wideband Sv is calculated using PulseCompressedEffectivePulseDuration.

To extract useful single frequency information from pulse compressed data it is advised to analyze the TS data of a single target. To do this, Echoview offers:

- a Single target detection – wideband operator to detect single targets from pulse compressed data
- a Wideband Frequency Response graph that displays the TS frequency spectrum associated with single targets

## EK80 EC150-3C data

Echoview uses EK80 CW and FM equations to calculate EC150-3C Sv and TS from *.raw data. There are several unique EC150-3C handling differences:

- power calculations differ from standard EK80 power
- stage 1 matched filtering is different from standard EK80 matched filtering
- Echoview doesn't apply a SaCorrection to Sv wideband variables

### EC150-3C power calculations

Where:

Pr(linear) = 10^[Pr(dB)/10] is the received power in linear units, read from the data file.

irms= the RMS value ofi:

iis the magnitude of the real and imaginary components of the complex power read from the data file:

Realis read from the data file.

Imagis read from the data file.

Gtrd= 0.0265

#### See also

Simrad EK80 file format

Raw variables derived from Simrad EK80 data

Calibration settings for Simrad EK80 data

About transmitted pulses