# Instrumentation & Measurement Magazine 26-1 - 60

```Therefore, the loop current of the readout coil on the left side
of Fig. 2 is (5), where
Zʹ and Zʹ are the resistive parts of Z1
1
and Z2
.
I1 




ZZ
ʹʹ 

12 ∙
M2
s
2 
22
L
 00
I1
2

Z ∙

1
ʹʹZ M LR RM

2   2
2
1 000 2M 

2

2  2
2
URR L R 2
2 
2
SL 00
2
2 



2
2
2
(6)
4 4
2
To facilitate the simplification of the formula, the physical
parameters determined from the present experimental material
are taken to be L1
k12=0.5, ω=413.5kHz, RL
 L R RM M  .
Therefore, (6) can be simplified to:
22 2
00 0
2 2
2
I1 
UR R sL L
22


22 2
10
MR

2

∙0 


1
4 4
2
1/2
(7)
Generally, conductivity is used to express the hindrance to
seawater. The reciprocal of resistivity ρ is called conductivity σ.
Its calculation is shown in (8), where M is the length of the conductor
(unit: m), A is the cross-sectional area of the conductor
(in m2
), and ρ is the resistivity of the conductor (in Ω m):
R 
M
A
proportional to the seawater conductivity:

I1 
UR R LA
22
ss L
2 2
 1
MM



2 22
1
(8)
Equation (9) is derived from (7) and (8). The input current I1
 
∙

1/2
(9)
Conductivity Curve Fitting Algorithm
L0
is
=L2=14.8μH, C1
=10Ω, L0
=C2
=10nF, R1
=R2
=0.15Ω,
is the unknown inductance
of the μH level, and R0 is taken a value about 1kΩ. Its physical
parameter law only needs to be satisfied: 22MZZ ∙ʹʹ1 12
,
Experimental System Construction
At present, wireless systems used in seawater magnetic coupling
generally use two coil structures that can be divided into
planar spiral coils [11] and PCB coils, as shown in Fig. 3. Compared
with PCB coils, planar spiral coils wound by Litz wire
have a better quality factor and higher coupling coefficient k12
.
changes with the change in the seawater conductivity σ.
There is no way to measure the actual value of L0
multiple data of I1
and conductivity σ through experimental
measurement. Through data fitting, the nonlinear curve
between I1
and conductivity is fitted. Then only the output
current I1 needs to be measured later, and the seawater conductivity
σ at this time can be obtained. Here, the least squares
method is used for polynomial nonlinear curve fitting. The
least squares method (also known as the least square method)
is a mathematical optimization technique. It finds the best
function that matches the data by minimizing the sum of the
squares of errors:
 a aI a I a I 01 2

The sum of the squares is calculated as:
n
Q   a a I a I a I
   


t tt t
01 2
t1
60
3
23
3
(10)
. We obtain
PCB coils are easier to manufacture and copy in batches.
This planar spiral coil making process starts by setting the
inner diameter size and then coiling the Leeds wire tightly together.
When the required outer diameter size is wound, the
second layer of coils is wound. Finally, the two end coils are led
out and the wire ends are tinned through a solder pot.
In the seawater conductivity measurement system, we
choose planar spiral coils with a better coupling effect, increasing
the influence of seawater on the system. Thus, the
conductivity is measured more accurately. The measuring
coil is a double-layer circular coil with 10 turns. The specific
parameters are an inner diameter of 20 mm and an outer diameter
of 43 mm. Litz wires of 0.07 mm (147 strands) are used. The
actual inductance is 14.8 μH; the resistance is approximately
0.15 Ω. A 10 nF capacitor is connected in series, and the resonant
frequency is approximately 413.5 kHz.
Measuring the conductivity of seawater is of great significance
to marine scientific research, marine development and
utilization, and military defense. The measurement of seawater
conductivity is of great importance to marine scientific
research, marine exploration and military defense. Seawater
salinity is one of the fundamental variables in current physical
oceanography research. Seawater density can be described
through seawater temperature and salinity, which contributes
to the scientific understanding of seawater activities such as
water mass mixing, turbulence and eddies, as well as being an
important analytical indicator for other basic oceanographic

jL R
 M1
22
(5)
2
In the formula, (σt
,It) is the measured data, and t= 1, 2, ..., n.
The least squares method has the smallest square error and
Q value principle. In addition, it can solve the undetermined
coefficient in the expression. According to the rule that the
partial derivative is 0, the extreme value of function Q can be
obtained. Finally, the system of equations satisfied and the
undetermined coefficient ai
is obtained. Therefore, the fitting
expression of the seawater conductivity curve can be obtained.
Experiment and Simulation Verification
23 

2
(11)
Fig. 3. Coil types. (a) Planar spiral coils; (b) PCB coils.
IEEE Instrumentation & Measurement Magazine
February 2023
```

# Instrumentation & Measurement Magazine 26-1

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