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Physics-technical bases of work of measuring transducer of magnetic-field - sensor of Hall

The sensor of Hall is name a device by means of which measure the size of magnetic-field using the effect of Hall. The sensor of Hall consists of semiconductor rectangular plate which four electric conclusions are added to. Schematically the pickoff of sensor of Hall is shown on a fig. 1.
The effect of Hall consists in the following.  Let a standard have a form of rectangular plate long l,  breadthways d, in b (ñì.ðèñ. 1) thick.
The Hall effect and the physical basis of the Hall sensor. If along a standard to skip the electric current of I, and athwart to create the magnetic field of B the plane of plate, then on the lateral planes of plate in the direction of CD there will be the electric field which is named the field of Hall. In practice, as a rule, the field of Hall is characterized by the difference of potentials, which is measured between symmetric points With and D on the side of standard. This difference of potentials is named Hall by the difference of potentials of Uhal  or E.M.F. Hall of εhal.
In the classic theory of conductivity the effect of Hall is explained by that in the magnetic field force of Lourenca operates on locomotive electric charges, size and direction of which determined by vector equation:
F = e [VB]             ( 1 ),

where   B  is a vector of induction of magnetic-field,
V is a rate of movement of charges,
å is a charge of transmitters of current taking into account a sign.

Electric field of Hall
Ehal = V B           ( 2 ),
is associated E.M.F. Hall of εhal, or hall potential difference as follows:
εhal = Uhal = Ehal d= VBd              ( 3 ).
Strength of current which flows through unit of area of cross-sectional of standard is equal to the closeness of current :
J = enV                  ( 4 ),
where ï is an amount of transmitters of current in unit of volume of standard (concentration of transmitters of current). From here strength of current:

I = jbd=enVbd             ( 5 ).

That enables to write down:

V = I / enbd              ( 6 ),

εhal  = IB/ enb       ( 7 ).
Thus, E.M.F. Hall (or Uhal) proportional to strength of current, induction of magnetic-field, and inversely proportional to the thickness of standard and concentration of transmitters of current in him.
The principle of operation of Hall sensor. On a fig. 2 characteristic dependence  of Uhal is shown on magnetic-field at the direct current of feed.
In default of magnetic-field E.M.F. Hall must equal a zero. But as a result of different by-effects (for example, symmetric not enough placing of measuring electrodes of sensor) a measuring device can show some difference of potentials of Uî even in default of magnetic-field. For the exception of the errors related to it, size of Uî  follow to subtract from the measured difference of potentials    in the magnetic field.
One of basic description of sensor of Hall is a sensitiveness:
g = ΔUhal/ ΔB.
Sensitiveness of sensor, indicated in his passport data, use for determination the sizes of induction of measured magnetic-field :
B =  Uhal / g.

It is necessary to mean that a sensor measures the perpendicular (to the plane of sensor) constituent  of vector of magnetic-field. Therefore if it is needed to measure the maximal value of magnetic-field, then it is necessary to orient a sensor properly.
For making of sensors of Hall mostly use the semiconductors of InP, InSb, GaAs, Ge, Si. The use of semiconductors is conditioned by that due to high mobility of transmitters of current they have a large sensitiveness to influence of magnetic-field. A pickoff can be made both from by volume material and on the basis of semiconductor tapes on insulating bases. Can have a different form, that influences on linearness of dependence of output signal from magnetic-field, sensitiveness. The sizes of modern sensors of Hall can not exceed 1õ1õ0.5 mm, currents of feed as a rule 1- 100 ìÀ (depends on the size of entrance resistance of sensor), a sensitiveness can arrive at 1000 ìÂ/Òë and more, working range of temperatures from - 270 °Ñ to 200 °Ñ. Except for a sensitiveness one of basic parameters of sensors of Hall it is been temperature dependence of sensitiveness of entrance resistance, initial output signal of Uî. At good sensors they must be insignificant.