To maximize t , t should be close to zero. In addition,
because of the short distance between two claw-type poles, the
magnetic field around the coil is assumed as uniform, so the
maximum value of induced voltage of coil in the receiver can
be written as:
2 m E N B S f (6)
where, B is the magnetic induction intensity, S is the area
of coil, and f is the changing frequency of magnet field.
Based on the principle of wireless power transfer in HPWC as
mentioned above, the output voltage of HPWC changes
periodically, which is analogous to a single-phase alternator.
Therefore, when the magnet rotates at a frequency, the output
voltage of the receiver coil in HPWC can also be
mathematically expressed as:
0 sin(2 ) m u U ft (7)
where, u is the output voltage of coil in the receiver, m U is
the maximum value of output voltage of the coil, t is time,
0
is the starting phase angle of u . Changing m U into
2 m E N B S f , then (7) can be transformed as:
0
0
sin(2 )
2 sin(2 )
m u E ft
N B S f ft
(8)
For HPWC, f depends on the revolving speed of magnet and
the number of the magnet poles, which can be expressed as:
4 f n p (9)
where, 4 n is the revolving speed of the magnet, p is the
number of magnet pole. So (8) can be changed as:
0
4 4 0
2 sin(2 )
2 sin(2 )
u N B S f ft
N B S n p n pt
(10)
Combining (4) and (10), the output voltage of the receiver coil
in HPWC can be defined as:
1 2 1 3 2 4 3
1 2 1 3 2 4 3 0
2 [( )( )( )]
sin (2 ) [( ) ( ) ( )]
u N B S n z z z z z z p
n pt z z z z z z
(11)
From (11) one can see that the maximum value of output
voltage depends on the number of coil turns, the magnetic
induction of magnetic field, area of the coil, the revolving speed
of hand crank, transmission ratios of the gear train and the pole
number of magnet. When the magnet and the transmission
mechanism are fixed, dimensions of coil in the receiver and the
revolving speed of hand crank are two important factors to
influence the performance of HPWC. Therefore, in the
following experiment, the influences on HPWC by these two
elements will be presented respectively.