ELEC 226, Spring 2012
Prof. Rich Kozick

Laboratory 4: Transformers

Objective: We will make measurements with the transformers and compare results with the equations for the linear transformer in Figure 13-8 and Section 13-2.2, and also the ideal transformer in Section 13-4. Notes are provided that summarize the formulas for linear and ideal transformers as well as the conditions required for ideal transformer approximation.

Please keep your circuits assembled until you discuss the results with the instructor, and bring your results to class on March 29.

Lab Activities:

1. Please study the analysis of the linear transformer and make sure you understand equations (13.23)-(13.25) and the notes.
   
   
2. We will use the outer terminals on the transformer box as the primary and the AC cord terminals as the secondary, so the turns ratio is expected to be approximately n = N₂ / N₁ = 10 (as defined in equations 13.35 and 13.36). Apply a 1 volt sinusoidal voltage source at 200 Hz to the primary side of your transformer. Make measurements at the secondary terminals to determine the turns ratio (n) and the “dots” on the primary and secondary sides of your transformer. Do a quick check to see if n remains the same if you change the frequency. Also, apply a 10 V sinusoid at 200 Hz to the secondary, and measure the voltage at the primary. See if the ratio is close to 1/n.
   
   
3. Use a frequency of 200 Hz and characterize your transformer at this frequency. That is, estimate the internal resistances of the primary and secondary coils (R₁ and R₂) and the self-inductances (L₁ and L₂). In addition, devise a procedure to estimate the mutual inductance, M, and the coefficient of coupling, k (defined via ). You should use a larger input voltage when applying the source to the AC cord terminals.
   Discuss your planned procedure with the instructor before making measurements.
   
   
4. Examine your results and consider how well your transformer satisfies the conditions required for ideal transformer approximation.
   
   
5. Next add a load resistor of about R_L = 5,000 ohms across the secondary terminals, so current will flow in both the primary and the secondary. Measure the voltage phasors V_T, V₁, V₂, and use these to calculate the current phasors I₁ and I₂ (use a 10 ohm helper resistor). Compare the measured results with the linear transformer equations as well as the ideal transformer equations, which are as follows:
   
   
   
   
   
   Determine how closely your measured results match with the linear and ideal transformer equations. In particular, calculate the “reflected impedance” of the load using the linear and ideal transformer models, and see which one agrees with your measured results.
   
   
6. Repeat step 5 at 20 kHz instead of 200 Hz. Are the results closer to the ideal transformer model?

Each lab group should prepare a summary of your analysis and measured results and discuss it with the instructor before leaving. Then each student is asked to explain all analysis and measurements for submission in class on Tuesday, April 3, 2012.

In the work that you submit, you should include for each case (1) a diagram of the circuit that you constructed, showing the component values and the voltages and currents; (2) your measured values of voltage and/or current; and (3) the computations that you performed. Your work will be evaluated based on the correctness of the approach rather than the degree of agreement between measurement and analysis. (The real transformers contain some features that are not modeled by the analysis.)