PHYS1520 Hall Effect Derivation Assignment Sample

Subject Code : PHYS1520
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Subject Name : Engineering

Physics for Electrical and Electronic Engineering

a) It is given that sensor is made up of copper

Dimensions of hall sensor=120 micrometers (thin copper film of thickness (d) 120 micrometers is used for Hall probe).

Current needed =20 Amperes

Working

External magnetic field activates the Hall Effect sensors. There are two major features of magnetic field

1) Polarity

2) Flux density

The Hall Effect sensor output signal depends on magnetic field density surrounding the device. The sensor will detect and generate an output voltage when the magnetic flux density surrounding the sensor is more than a certain pre-set threshold.

Hall Effect Sensor is composed of a thin piece of p-type semiconductor (gallium arsenide (GaAs), indium antimonide (InSb) or indium arsenide (InAs)) rectangular in shape. Placing a Hall Effect sensor in a magnetic field results in magnetic flux lines that exert force on the semiconductor material. As a result, the charge carriers (electrons or holes) are deflected to either side of semiconductor slab. Charge carriers movement is due to magnetic force they are experiencing while passing through semiconductor material.

Movement of electron and holes leads to potential difference. External magnetic field impacts the electron movement through semiconductor. This impact is more in flat rectangular shape material.

b) Hall Effect Derivation

The Hall Effect derivation is as follows

A metal with charge carrier (only electrons)
Steady-state condition
Charges do not move in the y-axis direction

The downward magnetic field is equal to upward electric force at equilibrium

Where,

V_H is Hall voltage
E_H is Hall field
v is the drift velocity
d is the width of the metal slab
B is the magnetic field
Bev is a force acting on an electron

I=−nevA

Where,

I is an electric current
n is no.of electrons per unit volume
A is the cross-sectional area of the conductor

Where,

R is Hall resistance

c) It is given that Hall Voltage must be 1V. Thus, the selected parameters are

n=8.47x10²⁸ electrons/m³

I=20 amperes

B=0.087 Tesla (given)

D=120×10^-6 meters

Sensitivity of Hall probe= = 10^-6/87× 10^-3 = 0.00001149 V/T or 0.01149 Mv/T

d) Design Evaluation

The range of sensitivity for modern Hall probes is between 50 mV/T and 1 V/T at the nominal biasing current. The sensitivity drifts with time which necessitates periodic calibration, VH = f (B), of the Hall probe.

Another research shows that range of sensitivity for Hall Effect sensors goes around -0.07 to + 0.07T but it is too sensitive.

It is practical to construct our designed Hall sensor as our sensitivity is close sensitivity of commercial hall probes available.

The sensitivity of Hall sensors can be improve by implementing them into an especially tailored magnetic concentrator. In this way Noise Equivalent Magnetic Induction (NEMI) can be reduced.

References for Hall Effect Derivation

[online] Available at: <https://www.electronics-tutorials.ws/electromagnetism/hall-effect.html> [Accessed 17 October 2020].

Ausserlechner, U., 2016. Hall Effect Devices with Three Terminals: Their Magnetic Sensitivity and Offset Cancellation Scheme. Journal of Sensors, 2016, pp.1-16.

BYJUS. 2020. Hall Effect Derivation With Simple Steps And Applications Hall Effect. [online] Available at: <https://byjus.com/physics/derivation-of-hall-effect/> [Accessed 17 October 2020].

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