EECE 310L Lab 9, Fall 2011

EECE 310L : Electric Circuits Laboratory Experiment 9 1 A m e r i c a n U n i v e r s i t y o f B e i r u t Fall 2011 Experiment 9 Transformers EECE 310L : Electric Circuits Laboratory Experiment 9 2 Table of Contents I. Objectives .................................................................................................................................. 3 II. Theory ......................................................................................................................................... 3 A. Ideal Transformer .............................................................................................................. 3 B. Real Transformer ............................................................................................................... 3 B1. Effect of finite magnetizing current ................................................................................ 3 B2. Effect of core losses ............................................................................................................... 4 B3. Effect of leakage flux ............................................................................................................. 4 B4. Effect of winding resistance ............................................................................................... 4 B5. High frequency effects .......................................................................................................... 5 III. Material and Procedure ........................................................................................................ 5 A1. DC resistance ............................................................................................................................ 5 A2. Polarity ....................................................................................................................................... 5 A3. Magnetizing current .............................................................................................................. 5 A4. Transformer Ratio ................................................................................................................. 6 A5. Square wave input ................................................................................................................. 6 A6. Open circuit test ...................................................................................................................... 6 A7. Short circuit test ..................................................................................................................... 6 A8. Transformer Bandwidth ...................................................................................................... 7 IV. Outcomes ................................................................................................................................... 8 EECE 310L : Electric Circuits Laboratory Experiment 9 3 I. OBJECTIVES In this experiment you will investigate the following:  Transformer operating characteristics  Transformer equivalent circuit II. THEORY A. IDEAL TRANSFORMER The primary and secondary AC voltages and currents in an ideal transformer are related by (Figure A-1): where N1 is the number of turns of the primary winding, and N2 is the number of turns of the secondary winding. It follows that an impedance Z2 connected across the secondary terminals will be reflected as an impedance equal to ( ) connected across the primary. B. REAL TRANSFORMER B1. EFFECT OF FINITE MAGNETIZING CURRENT Since the permeability of the magnetic material in the core is not infinite, a certain magnetizing current is required to establish a magnetic flux in the core. The effect of the finite magnetizing current can be modeled by an inductance LM connected across the primary winding of the ideal transformer, as shown in Figure B-1. Figure ‎A-1: Ideal Transformer EECE 310L : Electric Circuits Laboratory Experiment 9 4 Figure ‎B-1: Real Transformer B2. EFFECT OF CORE LOSSES The effect of core losses may be accounted for by adding a resistance RC in parallel with LM such that = core losses . See the equivalent circuit of a real transformer shown in Figure B-1. B3. EFFECT OF LEAKAGE FLUX A primary leakage flux links the primary winding but not the secondary; a leakage flux also exists only at the secondary. Leakage fluxes can be modeled using two inductors LL1 and LL2 as shown in Figure B-2. B4. EFFECT OF WINDING RESISTANCE The wire resistance of the windings may be accounted for by adding two resistances R1 and R2, in series with LL1 and LL2, respectively, as shown in Figure B-2. At low frequencies, these resistances are equal to their values at DC. Figure ‎B-2: Real Transformer EECE 310L : Electric Circuits Laboratory Experiment 9 5 B5. HIGH FREQUENCY EFFECTS At high frequencies, the capacitance of the windings should be included in the equivalent circuit. Refer to the equivalent circuit of a real transformer shown in Figure B-2. III. MATERIAL AND PROCEDURE A1. DC RESISTANCE Using the DMM, measure the DC resistances of the transformer primary and secondary. A2. POLARITY Using the oscilloscope, establish the polarity markings of the windings of the transformer. A3. MAGNETIZING CURRENT Connect the circuit shown in Figure C, with RS = 10 Ohms. Apply a sinusoidal voltage of 100 Hz frequency, and observe V1, V2, and the voltage drop across RS. Note that as the voltage is increased, or the frequency is decreased, the waveform of the magnetizing current becomes markedly non-sinusoidal. • Refer to in-lab 9 exercise A-1 Exercise • Refer to in-lab 9 exercise A-2 Exercise Figure C: Transformer Circuit EECE 310L : Electric Circuits Laboratory Experiment 9 6 A4. TRANSFORMER RATIO Using a voltage level that gives a nearly sinusoidal magnetizing current, accurately measure V1 and V2, and determine the turns ratio N1/N2. A5. SQUARE WAVE INPUT Apply a square wave of 100 Hz frequency, and observe V1 and V2. Use first a square wave without a DC component, then a square wave with a DC component. Explain the behavior of the transformer. A6. OPEN CIRCUIT TEST Increase the value of RS to 100 Ohms. Apply a sinusoidal voltage of 100 Hz, adjusting the voltage so that the magnetizing current is nearly sinusoidal. Measure the magnitude and phase shift of this current with respect to V1. From these measurements, calculate the values of LM and RC in Figure B-2. You may neglect the value of LL1 compared to LM. A7. SHORT CIRCUIT TEST Reduce the magnitude of the applied voltage to about a fifth of its original value, and with the help of the Lab Instructor short circuit the secondary terminals. Measure the magnitude and phase shift of the primary current with respect to V1, and from these measurements, calculate the values of R = R1 + R2( ) and L = LL1 + LL2( ) . To calculate LL1 and LL2, you may assume that LL1 = L/2. • Refer to in-lab 9 exercise A-3 Exercise • Refer to in-lab 9 exercise A-4 Exercise • Refer to in-lab 9 exercise A-5 Exercise Exercise • Refer to in-lab 9 exercise A-6 EECE 310L : Electric Circuits Laboratory Experiment 9 7 A8. TRANSFORMER BANDWIDTH Connect a 100 Ohm resistor at the secondary of the transformer. Determine the bandwidth of the transformer with the load connected: find the lower cutoff frequency f1 and the upper cutoff frequency f2. The cutoff frequencies are the frequencies at which the output voltage is 0.7071 times its value at mid frequencies. Make sure that the magnetizing current remains sinusoidal at all frequencies. • Refer to in-lab 9 exercise A-7 Exercise • Refer to in-lab 9 exercise A-8 Exercise Discussion on Part A • What are the values of the circuit elements R1, LL1, RC, LM, R2, and LL2 in the transformer model of Fig. 3? • What causes the distortion in the current waveform in part 3? • How can you explain the behavior of the transformer in part 5? • How does the measured value of R in part 7 compare with the calculated value from R1, R2, and the turns ratio N1/N2? • Calculate the transfer function V2(s)/V1(s) of the transformer with a load RL connected at the secondary. Using the transformer model of Fig. 3 and with RL = 100 Ohm, find the the value of the total winding capacitance C = C1 + (N2 / N1)2 from the measured upper cutoff frequency f2. EECE 310L : Electric Circuits Laboratory Experiment 9 8 IV. OUTCOMES By the end of Experiment IX, students:  Are familiar with ideal and real transformer characteristics  Are able to compute (experimentally and theoretically) the real transformer characteristics