Hysteresis curve of transformer coreAim : Apparatus : To plot the B-H curve of transformer core and find the energy loss of core material from the curve Step down transformer, test transformer core, Bread board, Dual Trace Oscilloscope, discrete components like Resistors and capacitors, connecting Wires

Theory :

Hysteresis refers to systems that may exhibit path dependence in which the final state of the system depends not only on the initial state of the system, but also on the internal state of the system When an external magnetic field is applied to a ferromagnet (Ferrite in this case), the atomic dipoles align themselves with the external field. Even when the external field is removed, part of the alignment will be retained. To demagnetize, it would be necessary to apply a magnetic field in the opposite direction. The relationship between magnetic field strength (H) and magnetic flux density (B) - Fig. 2, is not linear in such materials. When a graph is plotted with B Vs H in increasing magnetic fields, magnetic saturation occurs where there is no further change in B. When the applied field is reduced to zero, the plot traces a different curve backward to reach a point where there is a remanent or reminiscent flux density BR, corresponding to zero applied field. By reversing the field direction the flux density is made zero for a value of H known as coercive field Hc. When the field is further decreased, the ferrite core gets magnetized in the reverse direction. A curve of B Vs H for acomplete cycle of increasing and decreasing current is known as a hysteresis curve and the phenomenon in which B lags behind H so that the magnetization curve for increasing and decreasing fields is not the same is called Hysteresis.

Fig. 1. Hysteresis loop of transformer core

Circuit :

Fig. 2. Measurement of energy loss from B-H curve Circuit theory: When an input transformer or a high power oscillator is used to produce alternating current in the primary winding of the test transformer, the field produced is given by Amperes Law as (1) (2) The magnetic Flux induced in the secondary windings is time varying and gives rise to a voltage (3) As it is desirable to measure B and not dB/dT, The output of secondary is integrated using a passive integrating circuit to produce an output voltage proportional to B (4) (5)The area of the hysteresis curve is important since it represents the work done in one hysteresis cycle per unit volume of the transformer core material. It is known from Eqn. 2, that the current in the primary coil is given by

(6) And the voltage across the primary coil is and the power used are given by ; (7) The total work done per complete cycle is given by

(8) Where V=Al is the volume of the ferrite core and is the area enclosed by the Hysteresis curve (in H X B units). Thus power dissipated is given by Power = (Area of curve) X (Volume of core) X frequency

Formula : (9) Where N1 = No# of turns in the primary N2 = No# of turns in the secondary R1 = Resistance connected to primary R2 = Resistance in the integrating circuit L = length of the specimen A = Area of cross of the ferrite core SH = Horizontal voltage sensitivity in (volts/m) SV = Vertical voltage sensitivity in(volts/m)

Area of ferrite sample in Sq. Meter A = (d2-d1) X thickness of the sample Length of the ferrite sample L = 2 X X (d1 + d2)/2 Where d1 is the external diameter and d2 the internal diameter

Procedure :

(1) Connect the circuit as in the fig.2 (2) Adjust the CRO to work in the X-Y mode (time base switched off) (3) Connect the y- channel of the CRO to integrator output (4) Connect the X- channel of the CRO across R1 (5) Adjust the horizontal and vertical gains (voltage knobs) so that maximum area is observed on the screen (6) Note the position of the Horizontal knob giving horizontal sensitivity SH (7) Note the position of the vertical knob giving vertical sensitivity SV (8) Trace the loop on a transparency and reproduce the same on a graph sheet

Precautions : (1) If the Hysteresis curve appear backwards, reverse the leads connecting the X-channel of the CRO, to the resistor in the primary circuit. (2) Set the coupling for each channel on the oscilloscope to DC. Set the point Observed to be on the origin by adjusting the X and Y controls of each Channel Observations : N1= R1 = C2 = SH = Area under the loop = A= (volts/cm) SV = Sq. M N2 = R2 = L= (volts/cm)

Result :

Energy Loss E. L =

(Joules/cycle/unit volume)