UNIVERSITY of PENNSYLVANIA DEPARTMENT of ELECTRICAL and SYSTEMS ENGINEERING ESE206  Electrical Circuits and Systems II Laboratory.


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1 UNIVERSITY of PENNSYLVANIA DEPARTMENT of ELECTRICAL and SYSTEMS ENGINEERING ESE06  Electrical Circuits and Systems II Laboratory. Objectives: Transformer Lab. Comparison of the ideal transformer versus the physical transformer. Measure some of the circuit parameters of a physical transformer to determine how they affect transformer performance..3 Investigate the ideal transformer and calculate the power delivered and absorbed.. Introduction By now we should all be familiar with the wall power transformers used to power PC peripherals, calculators, radios, and other electronic devices. These transformers convert the 0V 60Hz line voltage to low voltage DC using a diode bridge rectifier. In addition to power supplies, transformers find use in circuits as power line isolators, impedance matchers, pulse transformers, voltage amplifiers, and as speaker drivers in radio circuits. A transformer is a specific form of a coupled circuit in which the coupling mechanism is the mutual inductances between two coils. The common magnetic flux path is provided by an iron core. A transformer can be represented as shown in Figure a. A physical implementation is given in Figure b. (a) Figure (a) An iron core transformer showing magnetic paths. (b) Figure (b) Construction of an iron core transformer. For clarity the coils are shown separated, Physically, one coil is usually wound around the second coil to maximize the magnetic coupling
2 N, N are the number of turns at the primary and secondary windings; φ is the flux produced by I and φ is the flux produced by I. In Figure a, it is seen by using the righthand rule method that with the currents as shown the magnetic flux produced by the coils is additive; if the secondary current direction is reversed, the flux would be subtractive. When coil is supplied with an alternating current, the magnetic field is coupled into coil which induces a voltage V across the coil. The resultant current in coil creates its own magnetic field which, in turn, is coupled to coil. This mutual coupling results in a term called mutual inductance, M. The mutual inductance M is related to the self inductances through the coupling factor k (k ): M = k L / L where L and L are the selfinductances of coils and, respectively. The symbol for mutually coupled coils is shown in Figure. For sinusoidal steadystate the relationship between the voltage and currents (phasors) is given below: V V = jωl I = ± jωmi ± jωmi + jωl I () Figure : Schematic symbol for mutually coupled coils The dots shown in the drawing will indicate the sign of M. By convention, if both currents are leaving the dots or entering the dots, the sign of M is positive (i.e. the fluxes are additive). A consequence of a subtractive M is a 80 deg phase reversal between the input and output voltages measured from a reference point. An equivalent circuit model of a lossless transformer is shown in Figure 3 (Tmodel). The equivalent inductances are La, Lb and Lm and have the following expressions. Notice the sign reversal for M in the expressions for La and Lb. La = L m M Lb = L Lm = ± M m M () Figure 3: Equivalent circuit of a lossless linear transformer.
3 3. Ideal iron core transformer In the ideal transformer the core flux φ links both coils (i.e. the leakage flux is zero) so that the coupling coefficient k=. We also assume that the winding resistance is zero and the hysteresis and eddy current losses in the iron core are zero. The symbol for the ideal transformer is shown in Figure 4. The relations that describe the ideal transformer are given below. Z is the impedance seen at the primary when the load impedance is Z L (impedance reflection in the primary). V V I I N = N N = N = n = n (3) Z = Z L / n Figure 4 Symbol for the ideal transformer' ZL is the load impedance. 4. The Nonideal iron core transformer The transformer to be used in this lab session is pictured in Figure 5 a. It is normally used in the audio frequency band (00 Hz to 5 khz). Either coil can be energized. If the.5x coil is energized, we have a.5: stepdown transformer; if the x coil is used as the primary (energized coil) we have a stepup transformer. By convention, the energized coil is considered to be the primary, the load side the secondary. While any welldesigned transformer is highly efficient, practical transformers do have losses, magnetic leakage, and winding capacitance that will have an effect on the behavior of the transformer. In welldesigned transformers these losses are low, but they do exist. (b) (a) Figure 5: (a) Audio transformer used in the lab (P side is the x.5 coil); (b) schematic representation of the audio transformer with center taps. For the lab, we won't use the center taps. 3
4 IV While properly designed transformers are assumed to be essentially ideal over the frequency range for which they were designed, it would be interesting to note the parameters of a physical transformer and their high frequency effect on transformer performance. Figure 6 shows the equivalent circuit that takes into account the nonidealities of an iron core transformer. We have added the effects of the resistances of the windings, Ra and Rb. The losses in the core is represented by the resistor Rm. The capacitors Ca and Cb represent the winding capacitances that are very small so that their impedance can usually be neglected in the midfrequency range of operation. Since the circuit contains both capacitive and inductive components (RLC circuit) a condition for resonance exists at high frequency. In this lab you will measure and investigate the effects of these physical parameters on transformer performance. Figure 6 Equivalent circuit for a nonideal iron core transformer Ra = primary winding resistance Rb = secondary winding resistance La = primary leakage inductance Lb = secondary leakage inductance Ca = primary winding capacitance Cb = secondary windig capacitance Rm represents core losses (hysteresis and eddy current losses) n =N/N Lm = mutual inductance The mutual inductance Lm is much greater than La, the leakage inductance. Since the impedance seen at the primary terminals Z = Z L /n (Z L is the load impedance in the secondary circuit) we can simplify the circuit by reflecting the secondary impedance to the primary side as shown in Figure 7a. The circuit can be simplified a shown in Figure 7b. The approximation is valid since the current in Lm and Rm is very small as compare to I. We have also neglected the effect of the capacitances. (a) 4
5 (b) Figure 7 (a) Equivalent circuit for the nonideal transformer in which Lb and Rb have been reflected into the primary; (b) Approximate transformer equivalent circuit where Lw = La + Lb/n, Rw = Ra + Rb/n. The capacitance has been ignored which is a valid assumption at low and midfrequencies. 5. Prelab Assignment 5. Consider the following circuit with an ideal transformer. Figure 8 Circuit schematic with ideal transformer Find: a. The currents in the primary and secondary loops (I and I). b. The voltages V and V over the primary and secondary terminals. c. Power supplied by the source and power dissipated by the KOhm resistance and the 8. Ohm load resistance. Compare the total power supplied to the total power dissipated. d. The value of the impedance Z seen at the input of the primary coil. 5. Equivalent Circuit of the linear transformer. Prove that the values of La, Lb and Lm in the equivalent circuit of Figure 3 are equal to: La = L m M Lb = L m M Lm = ± M Hint: You can prove this relationship by comparing the expressions () of the mutual inductances with those of the equivalent circuit: find the expressions of V and V as a function of I and I for the circuit of Figure 3. These expressions should be the same as those if Figure. 5
6 6. Experimental Procedure A. Parts and instruments: Audio transformer (.5:): Mouser Electronics, No. 4TM03 x scope probe Function generator Oscilloscope Power supply Multimeter Components: 8. Ohm, KOhm resistors, and a 68nF capacitor. B. Experiments: B. Measurement of the transformer parameters with the Philips PM6303 RLC Meter To measure the parameters of a real (nonideal) transformer you will use the Philips RLC meter. This meter provides a khz, Vrms test voltage and displays the dominant reactive component and associated resistive values (serial and parallel resistances, Rs and Rp, respectively) of the device under test. You will be using the transformer as a stepdown transformer with a.5: ratio. Use the x.5 coil as the primary. The parameters Lw, Rw, Lm and Rm (see Figure 7b) can be determined from shortcircuit test and opencircuit tests: a. Short the x secondary coil. This will reflect as a short across the x.5 primary coil so that the RLC meter will measure the leakage reactance Lw and winding resistance Rw. Obtain the values corresponding to the series connections (see Figure 7b). Record these values. b. Open circuit the secondary coil. Since the value of Lm and Rm are much larger than those of Lw and Rw, respectively, you can ignore Lw and Rw, compared to Lm and Rm. Measure the values of the inductance and resistor seen at the primary coil. Obtain the values corresponding to the parallel circuit. Write down the values. Compare the values of Lw and Rw to those measured here and verify that Lm and Rm are much larger than Lw and Rw. B. Measurements of current and voltages in the transformer circuit The goal of this experiment is to experimentally verify the operation of the transformer. a. Build the circuit of Figure 9 (same as the one in the prelab). Use as 8. Ω load resistance R L (this is similar to the load of a speaker). For source resistance Rs use a KΩ resistor. Adjust the output of the function generator for a sinusoid of 5 Vrms and khz (check on the oscilloscope). Measure the actual values of the resistors. Figure 9: Circuit with a.5: audio transformer and a load of 8. Ω. 6
7 b. Measure the voltage V and V (in V rms) over the primary and secondary coils using the oscilloscope. Calculate the turn ratio n (V/V) and /n. Observe the phase of V in reference to V. Place the dots on the transformer of Figure 9. Compare the measured values of V and V with those calculated in the prelab. c. Measure the voltage over the KOhm resistor and calculate the corresponding current I in the primary coil. You can use the multimeter for this measurement (remember that the multimeter gives rms values). Find also the current I in the secondary loop. Calculate the current ratio and compare it to the voltage ratio. Also compare the measured current values with those calculated in the prelab. [Note: when you use the amp meter to measure the current I, use the Fluke Multimeter and use the current range of 00mA]. d. Based on the measurement of V and I what is the resistance seen at the input of the primary coil? How does it compare to the one calculated in the prelab? e. Use the measured values of current and voltage to calculate the power delivered by the function generator and the power absorbed by the two resistors. Compare the generated and dissipated power. Explain the difference (hint: the transformer is not ideal). Note: for the calculations you can use RMS or amplitude values. Be consistent in your calculations. B3. Transformer frequency response The audio transformer should have a constant voltage ratio over it specified frequency range. The manufacturer gives a frequency response of kHz with a variation of ±3dB (note: db corresponds to 0xLog 0 A). As discussed earlier, at very high frequencies the effect of the capacitors will be seen as a resonance that will cause the ratio n=v/v to increase considerably above the nominal value n (=/.5). The goal of this experiment is to measure the frequency response over a large frequency range and verify that the response is within the specification of the manufacturer. You will also measure the response at very high frequencies and measure the resonant frequency. This will allow you to find the parasitic capacitance. B3. Frequency response of the stepdown (x.5 coil as primary) transformer a. Connect a function generator to the x.5 coil and leave the secondary open. Set the generator frequency to khz sine waveform and adjust the output of the function generator to 0 Vpp. Use a : scope probe to measure the secondary voltage (don t not use the white scope probes (they cannot be switched to the x setting). The x0 probe contains circuits causing multiple resonances to appear. b. Starting at f = 00 Hz increase the frequency to 5 MHz (on a log scale) to obtain a frequency response curve of V/V. Also measure the phase of V in reference to V. You will notice that at high frequencies (MHz range) the output voltage starts to increase quickly. This is a result of the resonance due to the inductance Lw and the capacitance. Increase the number of measurements around this resonant frequency f o so that you can plot the frequency response accurately around this peak. Plot 0Log V/V (in db) vs frequency. c. As mentioned, at high frequencies the capacitances of the windings cannot be ignored and will determine the value of the resonant frequency. The equivalent model of the transformer can now be written as shown in Figure 0. 7
8 Figure 0 Simplified equivalent model of the transformer at high frequencies The expression of the radial resonant frequency can be written as follows: f o (5) π L C w r Cr includes the primary and reflected secondary capacitance: C r = C a + n C b. Use this expression to find the value of C r. Assume that C a << n C b, and calculate the value of the capacitance C b of the secondary coil. Does the input capacitance of the oscilloscope contribute a significant amount to C b? (You can read the input capacitance on the oscilloscope or on the probe, in case you use a probe). NOTE: It is possible that you will observe multiple resonant frequencies if you go high enough in frequency. Use the first peak for f o to calculate the capacitance. B3.. Transformer resonance with capacitive loads Now you will add a capacitor of 68nF over the secondary terminals and measure the frequency response of V/V, similarly as you did in the previous section. Since you add a larger capacitor than the parasitic winding capacitances, you can expect that the resonant frequency will be smaller. a. Select the x.5 winding as the primary side of the transformer and set V = 0 V pp at a frequency of khz. b. Load the secondary with the 68 nf capacitor. Vary the frequency from 00 Hz to about 5MHz and record V and V. Increase the number of measurements around the resonant frequency. c. Plot the frequency response of 0Log V/V (in db) vs. frequency (log scale) This plot can be drawn on the same graph as the previous one. Compare the location of the resonant frequency. References. Engineering Circuit Analysis, D. Irwin, J. Wiley&Sons, 7th ed The Analysis and Design of Linear Circuits Thomas & Rosa, Prentice Hall Electronics Engineer's Reference Book Edited by F.F. Mazda 5th ed Electronic Designers Handbook, Landee, et al, McGrawHill 957 Written by G. Hunka. Updated and revised by J. Van der Spiegel, January
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