### TRANSFORMER FUNDAMENTALS

TRANSFORMER EFFICIENCY
All transformer windings and transformer cores produce copper and magnetic losses that appear as heat:
VAin = VAout + Wloss
where VA = volts x amperes
Wloss = Wcu + Wfe
Wcu = watts dissipated through copper losses in the windings
Wfe = watts dissipated through magnetic losses in the core

A toroidal transformer typically requires only 10% of the magne­tizing current required by laminated transformers. Higher flux den­sities are permitted because the direction of the magnetic flux is the same as the steel core grain. High flux densities allow fewer turns of copper wire, reducing the DCR of the winding. See Figure 5 for the efficiency that can be expected in terms of VA power ratio.

HIGH PACKING DENSITY
Toroidal power transformer cores are the ideal shape; minimizing the amount of core material and allowing symmetrical distribution of the winding around the entire core. Along with higher operat­ing flux densities, this allows for fewer copper wire turns than required on an equivalent laminated core. These inherent characteristics result in considerable weight and volume savings, as well as other advantages.

Referring to Faraday's equation for induced voltage in a transformer winding:
ERMS = 4.44 x N x AC x F x B x 10-8
where:
F = frequency
N = number of turns
8 = flux density (gauss)
AC = core cross section area (cm2)

Toroidal power transformers can operate at flux densities up to 16.5 kilo-gauss, approximately 40% higher than the conventional laminated power transformer. Operation of any core beyond its maximum rated flux density will result in increased Wfe losses in addition to waveform distortion.

The weight of a toroidal power transformer is comprised of the following items:
Copper (windings) + Steel (core) + Insulation materials + Mounting hardware or potting material

The physical dimensions (volume) of a transformer can be varied for any given design. The core of the toroidal transformer is made of a strip of grain oriented silicon steel. The strip width determines the height of the core while the inside and outside diameters determine the physical dimensions and the core's cross-section area. The cost to produce a custom vs. standard toroid core is rela­tively low. Most toroidal transformers have a diameter to height ratio of 3:1, but ratios of 2:1 (high profile) and 7:1 (low profile) are possible. See Fig. 2 for a comparison of standard Toroid vs. Laminated volumes.

The obvious trade-off for weight reduction is between the amount of copper wire and the size of the core. A well-designed transformer will be a balance of copper and steel needed to obtain reasonable AC regulation, temperature rise, and minimum physical size. See Fig. 3 for a comparison of Toroidal vs. Laminated weights.

OTHER ADVANTAGES OF HIGH PACKING DENSITY
EMI fields are very low because of the unique construction of the Toroidal Power Transformer. These transformers are wound on a ring-shaped core, a configuration that provides maximum containment of mag­netic fields. Unlike laminated transformers, toroidal transformers are not typically designed with air gaps within the core. Air gaps can cause a discontinuity in the magnetic path giving rise to increased radiated fields. Additionally, the even distribution of the primary winding over the secondary winding, uniformly around the entire core, ensures that the magnetic fields generated in the windings can be cancelled. Reductions of up to eight times, relative to the laminated transformer, can be expected. Further reduction is possible with a metal bellyband around the outside of the transformer, or full con­tainment of the transformer within a steel enclosure.  See Figure 9, TPT with Metal Belly Band.

Audible noise generated by a Toroidal Transformer is inherently low. The single strip of steel wound into a ring and welded at both ends is very solid and stable. The copper windings and insulation system completely envelop the core, further stabilizing the transformer and dampening the acoustical noise caused by magnetostriction phenomena.

Transformer noise can also be minimized by increasing DC ripple requirements in linear power supply applications. Low DC ripple require the transformer to deliver very large pulses of current in short periods of time. The high energy pulses further increase the magnetostriction action.

### TOROIDAL POWER APPLICATION GUIDE

LINE FREQUENCY
The majority of toroidal power transformers are designed to operate in 50/60Hz, 60Hz or 400Hz applications. As the frequency increases the thickness of the strip steel is decreased to improve efficiency. The core size and/or the winding also decreases, making for a smaller transformer. This reduction in the physical size of the transformer, as a function of frequency, should be considered when packaging a transformer into an application. A 60Hz transformer will be 20% smaller than a 50/60Hz transformer.

A transformer operates using magnetic induction. The basic transformer con­sists of two coils of wire wound on a steel core. When a voltage is applied to one of the coils, it magnetizes the core and a voltage is induced in the second coil. The ratio of the primary voltage to the secondary voltage depends on the turns ratio of the two coils:
Vp  / Vs = Tp / Ts
where V = voltage and T = turns
Taps may be provided on the transformer to compensate for different country requirements. See Fig. 6 for typical primary voltage configurations.
Note: Multiple primary windings must be connected in parallel or series to main­tain rated power.

SECONDARY VOLTAGE
The secondary voltage(s) of the transformer is specified with rated primary volt­age and full load secondary current.

SECONDARY VOLTAGE REGULATION
The voltage regulation of the transformer is the relationship of the open circuit (no load condition) to the rated voltage (full load condition). This condition can be expressed as:
Reg = (VNL – VFL) / VFL
where VNL = no load AC voltage and VFL = full load AC voltage
Regulation can be improved by decreasing the Wcu losses or by specifying a transformer with a larger VA rating.

SECONDARY DUTY CYCLE
The secondary VA requirements can be reduced if the load is intermittent and the "on" time is shorter than the transformer thermal time constant. Thermal time constants for transformers are typically a few minutes to fifteen minutes, depending on physical mass of the transformer.
Duty Cycle = (TON / (TON +TOFF )1/2
where TON = time transformer is powering load and
TOFF = time transformer is not powering load

SECONDARY VA REQUIREMENTS
The secondary winding capacity is defined in terms of voltage, current and duty cycle:
VA = VFL x IFL x (Duty Cycle)
where:
VFL = AC secondary voltage at specified current requirements and
IFL = AC secondary current at specified maximum requirement

ELECTROSTATIC SHIELDS
There are two distinct types of transients present on the power grid; Common Mode and Transverse. Transverse noise are transients pre­sent, but not referenced to ground. Typical examples are switching power supplies, universal motors, etc. This noise is usually extin­guished at its source with line filters. Common mode noise are tran­sients present on the power grid but referenced to ground. Typical examples are lighting strikes, switching, electromagnetic pulses, etc. To decrease common mode noise, transformers can be modified by incorporating an electrostatic shield between the primary and secondary windings. The capacitance between the primary and the shield channels most of the common mode noise to ground.

THERMAL PROTECTION
Bicron offers two types of thermal protection for transform­ers; non-reset and auto-reset. The purpose of these devices is to shut down the transformer in the event of overheating. The non-reset is used primarily for protection from internal transformer faults, tripping at a preset temperature. The auto-reset provides intermittent protection from internal transformer faults and exter­nal overloads. This device will open at a preset high temperature and close at a preset lower temperature. These devices are mount­ed internal to the transformer and wired in series with the winding.

MOUNTING PRECAUTIONS
The inadvertent design of a shorted turn by providing a conduc­tive loop (turn) through the center of a toroidal transformer must be avoided. This typically occurs when designing special mounting hardware for the transformer. A shorted turn results in high circulating currents, excessive heat, and poor performance. (Fig.7)

INRUSH PRECAUTIONS
Because the core does not have air gaps, toroidal transformers have the advantage over traditional E-I transformers of low stand­by power consumption (magnetization current). However, this results in a higher residual flux (remanence) when power is removed. When power is applied again the core may go into satura­tion, causing a current inrush which may be 15 times higher than the steady state current. The condition rarely lasts for more than two cycles.

There are several approaches for addressing inrush:
1. Adding a resistor in series with the primary winding of the trans­former, which is removed from the circuit after power is applied.
2. Utilizing delayed action fuses for the protection devices.
3. Reduce the residual flux (Remanence) which will increase the mag­netization current in the core. Methods used to reduce residual flux include introducing a gap, or utilizing alternate materials, and/or annealing methods.
Bicron is successful at designing transformers with low inrush. We can help you determine the best approach for your application.

A Lean Sigma Company