3.3 Transformers and Magnetic Circuits
Key Takeaways
- Transformer operational principles rely on mutual induction across primary and secondary windings governed by turns ratio (Np/Ns = Ep/Es = Is/Ip = √(Zp/Zs)).
- Step-up transformers increase secondary voltage while decreasing secondary current; step-down transformers decrease secondary voltage while increasing secondary current to conserve power (Pin = Pout assuming 100% efficiency).
- Autotransformers utilize a single tapped winding for voltage transformation providing high efficiency and small size, whereas isolation transformers feature physically separate windings to eliminate direct DC ground loops.
- Core losses consist of eddy current losses (minimized by thin, insulated lamination sheets) and hysteresis losses (minimized by high-permeability silicon steel core materials).
- A shorted transformer primary typically opens the upstream fuse or CB; open or shorted secondary coils yield zero useful load voltage or overload heating.
Transformers and Magnetic Circuits
Transformers are electromagnetic devices that transfer electrical energy between two or more AC circuits through mutual induction. They allow aircraft power distribution systems to step up or step down AC voltages with exceptionally high efficiency. In modern aircraft equipped with 115 VAC, 400 Hz electrical systems, transformers are essential for stepping down voltage to 28 VAC for flight deck instruments or supplying isolated power to sensitive navigation sensors.
Fundamentals of Mutual Induction and Transformer Operation
A transformer consists of two separate wire coils—the primary winding and secondary winding—wound around a common ferromagnetic core.
Principle of Operation
- An alternating voltage ($E_p$) applied to the primary winding drives an alternating primary current ($I_p$).
- This current generates an alternating magnetic flux ($\Phi$) in the iron core.
- The core concentrates and channels the magnetic flux into the secondary winding.
- According to Faraday's Law of Electromagnetic Induction, the changing magnetic flux induces an alternating electromotive force ($E_s$) across the secondary winding.
Fundamental Ideal Transformer Equations
For an ideal transformer (assuming 100% efficiency with zero flux leakage and zero resistive losses):
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Turns and Voltage Ratio: Where $E_p$ is primary voltage, $E_s$ is secondary voltage, $N_p$ is primary turns, and $N_s$ is secondary turns.
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Turns and Current Ratio: Since power in equals power out ($P_{\text{in}} = P_{\text{out}} \implies E_p \cdot I_p = E_s \cdot I_s$), secondary current varies inversely with turns ratio:
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Impedance Transformation Ratio: Transformers transform load impedance ($Z_s$) reflected back into the primary circuit ($Z_p$):
Step-Up vs. Step-Down Classifications
- Step-Up Transformer: $N_s > N_p \implies E_s > E_p$ and $I_s < I_p$. Used in weather radar magnetron power supplies to generate kilovolt pulses.
- Step-Down Transformer: $N_s < N_p \implies E_s < E_p$ and $I_s > I_p$. Used in Transformer-Rectifier Units (TRUs) converting 115 VAC to 28 VDC.
Special Transformer Configurations in Avionics
Autotransformers
An autotransformer utilizes a single continuous tapped winding wound on an iron core, serving as both primary and secondary.
- Advantages: Requires significantly less copper wire and core steel, resulting in smaller physical dimensions, reduced weight, lower cost, and superior efficiency compared to standard two-winding transformers.
- Disadvantages: Provides no galvanic (DC) isolation between primary and secondary circuits because they share a common physical conductor.
- Avionics Application: Cockpit panel lighting auto-dimming circuits and windshield anti-ice power adjustment.
Isolation Transformers
An isolation transformer features completely separate primary and secondary windings with a $1:1$ turns ratio ($N_p = N_s \implies E_p = E_s$).
- Purpose: Electrically isolates secondary equipment from the aircraft primary electrical ground, preventing ground loop noise currents from interfering with sensitive synchro/resolver angle sensors and audio distribution panels.
Instrument Transformers
- Current Transformers (CT): Used to sample high AC bus currents without opening heavy power cables. A single-turn primary power cable passes through a toroidal core wrapped with many turns of secondary wire, driving an AC ammeter or protective relay.
- Potential Transformers (PT): Step down high bus voltages to standardized low voltages for precision voltmeter monitoring.
Core Losses and Efficiency Optimization
Although practical aircraft transformers achieve efficiencies exceeding $95%$, internal power losses convert electrical energy into waste heat. Transformer losses fall into two main categories: Copper Losses and Core (Iron) Losses.
Transformer Loss Breakdown
| Loss Type | Physical Cause | Mitigation Technique in Avionics |
|---|---|---|
| Copper ($I^2R$) Losses | Ohmic resistance of primary and secondary wire windings dissipating heat when current flows. | Use larger gauge copper wire or silver-plated oxygen-free copper conductors. |
| Eddy Current Losses | Alternating magnetic flux induces circulating electrical currents (eddy currents) inside the conductive iron core, generating $I^2R$ heating. | Construct the core from thin, varnish-insulated silicon steel lamination sheets stacked parallel to flux lines. |
| Hysteresis Losses | Energy expended continuously re-orienting magnetic domains within the ferromagnetic core material during each AC cycle. | Use high-permeability, soft magnetic silicon steel or powdered ferrite core alloys with narrow hysteresis loops. |
Why Aircraft Electrical Systems Use 400 Hz AC
Standard commercial power distribution operates at 50 Hz or 60 Hz, whereas aircraft AC electrical systems (Boeing 737, Airbus A320, Gulfstream G650) operate at 400 Hz.
- Induced EMF Equation: $E_{\text{rms}} = 4.44 \cdot f \cdot N \cdot \Phi_{\text{max}}$
- Increasing frequency ($f$) by a factor of nearly 7 (from 60 Hz to 400 Hz) allows a 400 Hz transformer or motor to require far less magnetic flux ($\Phi_{\text{max}}$) and core cross-sectional area for the same voltage and power rating. Consequently, 400 Hz transformers weigh approximately $10%$ to $12%$ of equivalent 60 Hz transformers—yielding tremendous aircraft weight savings.
Worked Calculation Examples & Avionics Traps
Worked Example 1: Avionics Step-Down TRU Transformer
An aircraft Transformer-Rectifier Unit (TRU) steps down 115 VAC primary power to 28 VAC secondary power to feed a diode rectifier bridge. The primary winding contains 1,150 turns, and the secondary load draws 20 A.
- Find Secondary Turns ($N_s$):
- Find Primary Current ($I_p$) assuming 100% Efficiency:
Worked Example 2: Audio Matching Transformer
An aircraft intercom amplifier with an output impedance of $600\ \Omega$ must drive a $150\ \Omega$ flight deck headset.
- Required Turns Ratio ($N_p/N_s$):
Avionics Maintenance Hazard: Open Current Transformer Secondary
DANGER: Never open-circuit the secondary terminals of an energized Current Transformer (CT). With no secondary current to create opposing magnetic flux, the primary current forces the core into extreme magnetic saturation, inducing dangerous voltage spikes ($>1,000\text{ V}$) across the secondary terminals that can cause fatal electric shock and arc-flash fires.
Transformer Fault Isolation (NCATT Standard)
In addition to CT secondary hazards, NCATT AET candidates must isolate general transformer faults: improper installation, open/shorted primary, open/shorted secondary, and resistance/insulation breakdown.
Improperly Installed Transformers
Incorrect primary/secondary connections, wrong tap selection, missing grounding of electrostatic shields, or mounting that violates industry installation standards produce wrong voltages, hum, overheating, and EMI. Verify nameplate ratios and schematic terminal IDs before energizing.
Open or Shorted Primary Coil
An open primary stops all transformer action—secondary voltage is zero and primary current is zero. A shorted primary draws excess current and typically opens the upstream fuse or circuit breaker (CB). Always treat a tripped CB protecting a transformer primary as a short/overload clue until proven otherwise.
Open or Shorted Secondary Coil
An open secondary yields zero load voltage because coupling cannot deliver power to the load (imperfect coupling to the load path). A shorted secondary overloads the magnetic circuit, overheats the transformer, and often reflects as excess primary current and another CB trip.
Resistance Testing
Use an ohmmeter (power removed, capacitors discharged) to compare primary and secondary winding resistances to manufacturer data. Sudden low resistance suggests shorted turns; infinite resistance indicates an open winding. Insulation breakdown between primary and secondary (or to core) requires insulation-resistance testing with an approved megohmmeter per the maintenance manual—not a casual DMM continuity check alone.
| Fault | Typical Observation | Isolation Tip |
|---|---|---|
| Open primary | No secondary voltage; no primary current | Ω test primary winding |
| Shorted primary | Fuse/CB opens on apply power | Inspect for burned smell; Ω very low |
| Open secondary | Zero volts at load; primary may still draw magnetizing current | Ω test secondary |
| Shorted secondary | Overheat; CB trip; low secondary Ω | Compare to nameplate resistance |
| Insulation breakdown | Leakage to core/chassis | Megger per AMM limits |
Avionics Trap: Measuring secondary voltage with the wrong tap selected looks like a "faulty transformer" when the install is simply non-compliant.
An aircraft transformer steps down 115 VAC primary power to 28 VAC to power avionics instruments. If the primary winding has 1,150 turns and the secondary delivers a load current of 10 A, what is the secondary turn count and primary current (assuming 100% efficiency)?
How are eddy current losses minimized in aircraft 400 Hz power transformer cores?
What is a major advantage and a key limitation of an autotransformer compared to a standard two-winding isolation transformer in aircraft applications?