When 2 coils are placed in close proximity to each other and a sinusoidal current is applied to one coil…
A second sinusoidal voltage ( and current ) will be induced in the second coil. This is caused by a changing magnetic field
Mutual inductance definition
Defined as the amount of voltage induced in the second coil when voltage is applied to
the first coil
The coefficient of coupling (k) is…
The ratio of flux lines produced by coil 1 linking coil 2, to the total flux produced by coil 1
K = (ϕL_1-2)/(ϕL_1)
K is dependent on…
The physical closeness of the coils and the type of core material
Basic Transformer Construction
- Both primary and secondary windings are would around a core material.
- The purpose of the core material is to provide a body to place the windings and to also
provide a magnetic path for the flux lines. - There are 3 general types of core materials a) Air b) Ferrite, and c) Iron.
- Air and Ferrite cores are typically used in high frequency applications whereas Iron cores
are used in power applications. ( Power Supply )
The formula to determine the turns ratio is…
n = N_s/N_p
Direction of windings
- The primary and secondary voltages are in phase when the windings of both the primary and secondary are
wound in the same direction. - If the windings are wound in the opposite direction, the primary and secondary voltages are out of phase.
- Phase dots on schematic diagrams indicate this phase relationship.
Step up transformers
- A Step-up transformer has a larger secondary voltage than the primary.
- Formula to determine the secondary voltage of a Step-Up transformer is:
VS = ( NS ) / ( NP ) * VP
Step down transformers
A Step-Down transformer has a smaller secondary voltage than the primary.
* Formula to determine the secondary voltage of a Step-Down transformer is:
VS = ( NS ) / ( NP ) * VP
Loading the secondary of a transformer
- When a load resistor is connected to the secondary, the current thru the load is described as follows:
IS = ( NP ) / ( NS ) x IP - Note: ( NP ) / ( NS ) is the reciprocal of the turns ratio formula
Primary Power Equals…
- Secondary power
- The power delivered to a load in the secondary can never be greater than the power put into the primary of a
transformer. - Some of the power in the secondary is lost because of non-ideal conditions .
- This loss of power is given up as heat.
- Power is dependent on voltage and current. P= E X I
- If voltage is stepped up in a transformer, the current is stepped down, and visa-versa.
- An ideal transformer will always have Pin = Pout
Reflected Load in a Transformer
- The load ( in ohms ) in the secondary is not the actual ohms as ‘seen’ by the transformer’s primary winding,
but is based on the turns ratio, the primary current, and the value of the load resistor.
RP = ( 1 )2 x RL
( n ) - Where: RP = Reflected resistance as seen by the source
- n = Turns ratio of the transformer
- RL = Actual resistance of load ( in ohms )
Matching the Load Resistance to a Source Resistance
- One application of transformers is to use it for impedance matching to provide maximum power transfer in a
circuit. - Maximum power transfer occurs when both the source and load impedances ( AC resistance ) are equal.
- Perfect power transfer is never achievable but the higher the better as any differences in ideal power transfer
are typically given up as heat in a circuit. ( Heat is inefficient )
Transformers
When a source is connected to a load, the maximum power is delivered to the load when…
The load
resistance is equal to the source resistance
Transformer as an Isolation Device
- A transformer is an AC device.
- DC Current cannot pass through a transformer.
- A transformer is often used to isolate and filter DC voltage but allow AC to pass to next circuit.
- A transformer is also used to isolate circuits for electrical shock. Remember: A transformer is a coupling of electromagnetism and does not provide a direct coupling of line voltage to a circuit. Ie: Unity transformer
Transformer power rating
Volt-Amperes (VA)
Non-Ideal Transformer Characteristics
Winding Resistance – Primary and Secondary winding resistances cause small voltage drops, thus less voltage to load.
* Losses in the Core – Heating of the ferrite and iron cores. It is caused by continuous changing of magnetic field. It is
commonly called hysteresis loss.
* Magnetic Flux Leakage – Magnetic flux produced in primary does not all pass thru the core to the secondary. Typically
99% passes.
* Winding Capacitance – Stray capacitance between adjacent turns of a winding. Affects higher frequency operation ( Xc
drops ) resulting in bypass effect across primary winding and across the secondary load.
Transformers
Transformer efficiency
Pout/Pin*100%
Other Types of Transformers (List)
- Tapped
- Multiple winding
- Auto
- Three-phase
Other types of transformers (specifics)
Tapped Transformers (Pg. 656 ) – Center Tapped Secondary. Voltages in secondary are now ½ with reference to CT.
Also out of phase. Used in power supplies. Also used in residential wiring.
* Multiple Winding Transformers (Pg. 657 ) – Multiple primary windings allowing operation of 120VAC or 240VAC.
* Autotransformers ( Pg. 658 )– Have adjustable tap using sliding contact which is moved to vary the output ( called a
variac )
* Three- Phase Transformers ( Pg. 659 ) Delta and Wye configurations
Troubleshooting Transformers
- Most problems encountered with defective transformers are that of open primary and secondary windings ( excessive
current burns wiring ). - Check with ohmmeter – POWER OFF
- Other but less frequent problems are shorted or partially shorted windings. Check with ohmmeter versus a good unit
Mutual Inductance
When two coils are placed close to each other, a
changing flux in one coil will cause an induced voltage
in the second coil. The coils are said to have mutual
inductance (LM), which can either add or subtract
from the total inductance depending on if the fields are aiding or opposing
Mutul Inductance Formula
L_M=Ksqrt(L_1L_2)
