1. Lesson 26: Transformers and Reflected Impedance

2. Learning Objectives
Predict the reflected impedance and derive an equivalent circuit using the reflected impedance.
Calculate the transformation ratio to deliver maximum power to a load.
Determine safe operation parameters from power transformer ratings.
Explain how the transformer acts as an isolation device.
List and explain several practical applications of transformers.

3. Winding Direction
Recall that the polarity of ac voltages can be changed by changing the direction of the windings.
0º phase shift
180º phase shift

4. Transformation Ratio
Recall that the transformation ratio (a) is the ratio of the primary voltage to secondary voltage, which is equal to the ratio of primary turns to secondary turns, which is equal to the ratio of the secondary current to the primary current or otherwise stated:

5. Current Ratio and Power
Because we are considering an ideal transformer, power in equals power out (Pin = Pout).
The above shows that if the voltage is stepped up, then the current is stepped down, and vice versa.

6. Reflected Impedance
Transformers make load impedances “look” bigger or smaller depending on their turns ratio (a).
Zpri-reflected is the impedance that “appears” at the primary windings.
The term a2*Zsec is referred to as the load’s reflected impedance.

7. Reflected Impedance

8. Example Problem 1
Use the reflected impedance concept to solve for the total impedance ZT. Determine Ig and ILD.
NOTE: You must use the “reflected impedance” method any time there are line impedances in the primary circuit!
Redraw the circuit:

9. Power Supply Transformers
Power supply transformers are used to convert incoming 120 Vac to dc voltages of various levels necessary for different circuits.

10. Impedance Matching
Transformers are used to raise or lower the apparent impedance in order to achieve maximum power transfer.
Recall that Pmax is transferred to a load when it’s impedance is a match with the internal resistance of the supply.

11. Example (Chapter 23, pg. 1045) a)
The source impedance (Zpri) for the supply is 500Ω, which is a poor match with the 8Ω impedance of the speaker. Is is given as 236.2mA. You can expect that the power delivered to the speaker will be less than the maximum power possible.
Determine the power to the speaker under the original conditions shown in figure (a) below.
Next, in figure (b), a commercially available 500Ω to 8Ω impedance matching transformer is introduced between the speaker and the source.
Determine the input impedance of the transformer and the power delivered to the speaker. a)
b) Now that the transformer input impedance matches the source impedance the source current can now be determined as:

12. Example Problem 2
An amplifier is modeled with a Thèvenin equivalent impedance of 36-54j .
What load impedance must be chosen to ensure maximum power transfer occurs?
What is the transformer load (VA) for this value of ZLD?
Now find the xfmr load impedance:
=>Vpri is not the same as Eg

13. Example Problem 3
An amplifier is modeled with a Thèvenin equivalent impedance of j . A transformer is used to impedance match the load to the source to ensure max power transfer.
What turns ratio should be chosen for the transformer, and what value of load resistance should be chosen to ensure max power transfer?
What is the real and reactive power of the load? What is the real and reactive power delivered by the source?
NOTE: we only need to look at the reactance for max power to the turns ratio (a). 2
80Ω
Now we know (a) we can find the real (R) resistive portion:

14. Example Problem 3 cont.
An amplifier is modeled with a Thèvenin equivalent impedance of j . A transformer is used to impedance match the load to the source to ensure max power transfer.
What turns ratio should be chosen for the transformer, and what value of load resistance should be chosen to ensure max power transfer?
What is the real and reactive power of the load? What is the real and reactive power delivered by the source?
2:1
80Ω
Remember, Zpri = a2 ZLD
=>This implies xfmr Pin = 7.8W, which = Pout of 7.8W
Remember that Xpri = XLD are matched therefore cancel each other out (-j160=j160)

15. QUESTIONS?