THE HALL EFFECT AND CURRENT SENSORS. Experiment 3

Transcription

1 THE HALL EFFECT AND CURRENT SENSORS Experiment 3 Equipment Electromagnet Electromagnet power supply Gaussmeter kit Germanium wafer PCB Hall effect current supply 3 x multimeters ACS712 current sensor PCB Dual DC bench power supply 3A AC power supply 3x 12v stop/tail bulbs Time : 3 hours Preliminary Read up on Hall effect so you understand what you are seeing in part 1 of the experiment. Answer the first 3 questions. Read the data sheet for the ACS712 current sensor. Introduction The motion of a charged particle moving in an electric and magnetic field is governed by the Lorentz force which is given by F = q( E + v B) (1) In the first part of this experiment the effect of an external, constant magnetic field, on a current moving through a semiconductor will be investigated. In the second half of the experiment a commercial Hall effect current sensing IC will be used to monitor both AC and DC currents. Theory The movement of a charged particle in a conductor or semiconductor, under the influence of an electric field, can be considered as a random motion with a net drift. The average drift velocity v in the direction of the current flow is proportional to the applied electric field such that v = µe (2) where µ is called the mobility of the charged particles, which for a semiconductor, can either be negatively charged (electrons) or positively charged (holes). If there are n charged particles per unit volume, then the current density, J is defined as J = nq v (3) 1

2 It follows from equation (2) that J = nqµe σe (4) where σ is the conductivity of the semiconductor. If the semiconductor is placed in a transverse magnetic field, then from equation (1), the magnetic force component will act to shift the charged particles to the surface. This drift of the charged particles, transversely to their direction of motion, sets up an electric field, the Hall field, to counteract the deflection. At equilibrium, the force due to the Hall field cancels the magnetic force. Q1 Show that the Hall field can be written as where R is the Hall coefficient. E H = R( J B) (5) R = 1 nq (6) The geometry of the hall sensor is shown in figure 1. y x z B V H t J w Figure 1. J = Ji and B = Bk (7) Q2 Show that R = E H JB where E H is the amplitude of the Hall field. (8) Q3 Hence show that V H = R W IB (9) 2

3 where VH is the Hall voltage across the semiconductor established by the Hall field, and I is the external current supplied to the semiconductor. Experiment - part 1 The Hall effect will be investigated in samples of Germanium semiconductor. The magnetic field will be generated by an electromagnet. (a) Identify the equipment Figure 2. The electromagnet with the semiconductor sample in place. Figure 3. The magnet power supply and the Hall sensor power supply. 3

4 Figure 4. The gaussmeter with sensor attached. Figure 5. The PCB containing the germanium wafer. Note the current path through the wafer and the output terminals for the Hall voltage. A potentiometer is placed on the pcb to null the output with no magnet field applied. 4

5 (b) The test circuit Hall Effect Current Supply Supply. Pole pieces Magnet Power Supply Figure 6. The Hall effect test circuit. NOTE: The gaussmeter is a delicate instrument. Please take care with it. Connect the electromagnet to the magnet power supply as shown in figure 6. Calibrate the magnetic field by measuring the field centrally between the pole pieces with the gauss meter. (Note: The magnetic field sensor must be oriented for maximum output.) The field should be measured for 1 Amp increments in the magnet current. The magnet current should then be reversed and the measurements repeated. Plot and comment on this relationship. Connect up the Hall effect sensor board as shown in figure 6. With the magnet current turned OFF insert the PCB into the board holder on the magnet. Turn on the Hall effect current supply and adjust the current through the wafer to be 5mA. Observe the Hall voltage and set it to be zero by adjusting the potentiometer. This adjustment offsets any inaccuracies in the placement of the wafer and therefore gives a zero volt output to correspond with no magnetic field. 5

6 (c) Hall voltage measurements Turn on the electromagnet power supply and measure the Hall voltage for 1 Amp increments in magnet current. Repeat for the magnet current in the other direction. Now repeat the above measurements with the wafer current set to 10mA, 15mA and 20mA. Plot the curves for the 4 sets of Hall voltage data taken above. These should be plotted against magnetic flux density. Fit these curves and determine the magnitude and sign of R. Q4 What is the sign and density of the charge carriers in your sample? Experiment - part 2 Figure 7. The Hall effect current sensor test board.. Current in Output PSU (12v) GND Current out Vcc (8-12v) PSU Figure 8. Current sensor test circuit. (d) DC current and power measurement Connect 3 stoplight bulbs in parallel to form a dummy load which should be placed in series with the current sensor and an ammeter as shown in figure 8 (If the power supply has a digital ammeter, this may be used). This circuit should be connected to the DC bench power supply set initially to 0V. A voltmeter should be placed across the bulb load. 6

7 Another voltmeter should monitor the output voltage from the current sensor. A power supply should be used to supply approx 8V to the current sensor PCB. Record (i)voltage across the load, (ii)current measured by the ammeter and (iii)the voltage output of the current sensor. Increase the voltage of the power supply connected to the dummy load until a current of 0.1A flows in the load. Repeat the measurements and continue to increase the current in steps of 0.1A until 3.0A is reached. Tabulate your results. Plot the sensor voltage versus load current and comment on the relationship. Refer to the data sheet to back your findings. Calculate and plot the power in the load versus supply voltage. Q5 Comment on the relationship between the power in the load versus the supply voltage. (e) AC current and power measurement Repeat part (d) using the 12VAC transformer connected to the mains via a variac. The variac can then be used to allow voltages of approx 1 to 12V to be delivered to the dummy load. The dummy load should be reduced to one bulb. Examine the current sensor output on a CRO. A similar analysis to part (d) should be undertaken except the sensor output should be measured on the CRO. Record both maximum and minimum values from the screen. Calculate the RMS value for each measurement (Your CRO may be able to do this). Q6 If the load were inductive explain what you would observe when measuring this circuit with an AC voltage applied. 7