AC Electric Circuits

Impedance Matching With Transformers

19 questions By Tony R. Kuphaldt

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Question 16 of 19

Calculate the primary winding current (magnitude and phase angle) for this unloaded isolation transformer, with primary and secondary inductances of 18 Henrys each:

Assume the winding inductances are “pure” (no resistive components).

Reveal answer

I_primary = 17.68 mA ∠−90^o

Challenge question: what changes, if any, would result in the primary current value is this were not an isolation transformer, but rather a transformer where the secondary inductance was something other than 18 H?

Notes:
Students should realize from the answer that an unloaded transformer simply appears as an inductor to the source.
Question 17 of 19

Calculate the primary winding current (magnitude and phase angle) for this resistively loaded isolation transformer, with primary and secondary inductances of 18 Henrys each:

Also, draw an equivalent schematic diagram (with no transformer in it) illustrating the impedance “seen” by the AC power source. Assume no winding resistance in either transformer winding, and a magnetic coupling coefficient between the two windings of exactly 1.

Reveal answer

I_primary = 1.2001 A ∠−0.84^o

Follow-up question: what kind of impedance (predominantly resistive, inductive, or capacitive) does the AC source “see” in this circuit? Contrast this against a situation with no load connected to the transformer at all.

Notes:
This question illustrates how reflected load impedance is “seen” by the source, and how it interacts with the transformer’s intrinsic winding impedance.
Question 18 of 19

Calculate the primary winding current (magnitude and phase angle) for this resistively loaded transformer, with a primary inductance of 18 Henrys and a secondary inductance of 36 Henrys:

Also, draw an equivalent schematic diagram (with no transformer in it) illustrating the impedance “seen” by the AC power source. Assume no winding resistance in either transformer winding, and a magnetic coupling coefficient between the two windings of exactly 1.

Reveal answer

I_primary = 2.4001 A ∠−0.42^o

Follow-up question: what is the “step” ratio of this transformer, and is it step-up or step-down?

Notes:
This question illustrates how reflected load impedance is “seen” by the source, and how it interacts with the transformer’s intrinsic winding impedance.