3.10.3 Experimental principles
1)The principle of measuring magnetic field by using Hall effect method
Hall effect is an electromotive effect caused by the interactions between the current and the magnetic field in a conductive material.Hall,a graduate student of Hopkins University,discovered this electromagnetic phenomenon in 1879 when studying the mechanism of the metal conduction,therefore,it is called Hall effect.Scientists tried to make magnetic sensors to measure the magnetic field using Hall effect,but the Hall effect of metal is too weak to be applied in practice.With the development of semiconductor materials and manufacturing technology,Hall elements made up from semiconductor materials have been applied and developed due to the remarkable Hall effect.Now the Hall elements are widely used in non-electric measurement,electric control,electromagnetic measurement and computing devices.
The Hall effect,in its nature,is a deflection caused by movable charged particles acted by Lorentz force in a magnetic field.
When charged particles(hole or electron)are bound in solid materials,the deflection causes the accumulation of positive and negative charges perpendicular to the direction of the current and magnetic field in different sides,and thus forms an additional cross electric field.For the semiconductor material shown in Figure 3.10.3,if operating current IS flows in X direction and magnetic field B is added in Y direction,contrary sign charges start to accumulate in Z direction(on the sides of A and B)to form a corresponding additional electric field.The electric field stops the carriers from displacing continuously to the sides.When the electric field force fE received by carriers is equal to Lorentz force fL,the accumulation of charges on both sides of the semiconductor will balance,and at the time it can be expressed as:
Where e is charge electric quantity;EH is Hall electric field intensity;v is drift velocity of carriers in current direction;B is magnetic strength of applied magnetic field;VH is the Hall voltage,and l is the width of Hall materials.
Figure 3.10.3 The schematic diagram of Hall effect
Supposing that the width of the Hall element is l,and its thickness is d.The carrier concentration is n,and the average speed is
Then the operating current IS could be written as
It can be obtained from Equation(3.10.1)and Equation(3.10.2)that
So Hall voltage VH is proportional to the products of B and IS,and is inversely proportional to the thickness of Hall element d.The proportional coefficient
is called Hall coefficient,which is an important parameter to reflect the capability of material to generate Hall effect.
According to the electrical conductivity of a material:
We can also obtain the following relationship:
Where μ is the carrier mobility,which is the velocity of the carrier per unit electric field.Generally,the mobility of electrons is higher than that of holes,so most Hall elements are made of n-type semiconductor materials.
Hall device is the electric-magnetic transition element made by using the Hall effect mentioned above.As for finished Hall device,RH and d are known,therefore,in actual application,Equation(3.10.3)can be expressed as:
Where KH=RH/d,called the sensitivity of Hall device,indicates the Hall voltage output of the device under unit operating current and unit operating magnetic strength.By measuring the Hall voltage VH,magnetic field strength B can be found out,i.e.
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For metal material,its high electron concentration n can lead to the low value of RH and KH,thus it is not suitable for making Hall element.In addition,the thinner the Hall element is,the higher VH of the Hall element is.So the sensitivity of the Hall element can be increased by reducing the thickness d.However,it should not be considered that the thinner is the better,because the input and output resistances of the element will increase,which is undesirable for Hall elements.Attention:when the magnetic intensity B and the panel normal of the Hall element are in a certain angle,effective magnetic intensity on the Hall element is the component of the normal direction B cos θ,which can be expressed as:
According to Equation(3.10.8),it can be inferred that the Hall voltage direction will change if the direction of the operating current or the magnetic field intensity changes.If both directions change at the same time,Hall voltage direction will remain unchanged.
Figure 3.10.4 Direction of effective magnetic field on Hall element
2)The measurement of Hall voltage VH
The circuit diagram for measuring the magnetic field with a Hall element is shown in Figure 3.10.5.The Hall element is placed in the corresponding position of the magnetic field to be measured so that the plane of the element perpendicular to the magnetic induction intensity B.Constant operating current is applied at the control terminal,and the Hall voltage output terminal of the Hall element is connected to a millivoltmeter to measure the Hall voltage value.
Figure 3.10.5 Circuit diagram for measuring magnetic field with a Hall element
When Hall effect is generated,many secondary effects appear simultaneously.The measured voltage is not strictly equal to Hall voltage VH,and it includes additional voltage resulted from many secondary effects;therefore,we must try to eliminate them.Based on the mechanism generated by secondary effects,with the symmetric measurement method of current and magnetic field reversal,the influence of secondary effects can be basically eliminated.The practical method is:keep the values of IS and B,and change the directions of the working current IS and magnetic field B,and measure the voltage of four groups V1,V2,V3,and V4 in turn,i.e.
And then find out the algebraic average value of the four groups voltages above,i.e.
3)The magnetic strength in long straight carrier solenoid
Based on the Biot-Savard law,for a spiral tube of length 2L,number of turns for N and radius R,the magnetic induction intensity B away from the center axis x is:
Where μ0=4π×10-7 N/A2,n=N/2L,is the number of turns per unit length.
For an“infinite”solenoid,L≫R,so Equation(3.10.10)can be simplified into:
For a“semi-infinite”solenoid,there is x=L at the endpoints,and L≫R,formula(3.10.10)can be simplified into:
