Lesson 29 – Transformers
and Reflected Impedance
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.
REVIEW
Winding direction

The polarity of ac voltages can easily be changed
by changing the direction of the windings.
0º phase
shift
180º phase
shift
Transformation ratio

The transformation ratio (or turns ratio) is given by the
symbol a.
a

REVIEW
E pri
Esec
I sec N pri


I pri Nsec
Because we are considering an ideal transformer,
power in equals power out.
Sin  Sout
E pri I pri  Esec I sec
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 a2Zsec is referred to as the load’s
reflected impedance.
 pri reflected 
E pri
I pri
aEsec
2 E sec

a
 a 2 Zsec
I sec
 I sec 


 a 
Reflected Impedance
Example Problem 1
a
E pri
Esec
I sec N pri


I pri Nsec
 pri reflected  a 2 Zsec
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!
Power Supply Transformers

Power supply transformers are used to convert
incoming 120 Vac to dc voltages of various levels
necessary for different circuits.
Impedance Matching

Transformers are used to raise or lower the
apparent impedance in order to achieve
maximum power transfer.
Example Problem 2
An amplifier is modeled with a Thèvenin equivalent impedance of 36-54j .
a.
b.
What load impedance must be chosen to ensure maximum power
transfer occurs?
What is the transformer load (VA) for this value of ZLD?
Example Problem 3
An amplifier is modeled with a Thèvenin equivalent impedance of 320-160j
. A transformer is used to impedance match the load to the source
to ensure max power transfer.
a.
b.
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?