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Audio Transformers-Page2
Handbook for Sound Engineers, 3rd Edition

Bill Whitlock Audio Transformers Page 2

Handbook for Sound Engineers, 3rd Edition

1 Audio Transformer Basics

Since the birth of audio electronics, the audio transformer has played an important role. When compared to modern miniaturized
electronics, a transformer seems large, heavy, and expensive but it continues to be the most effective solution in many audio
applications. The usefulness of a transformer lies in the fact that electrical energy can be transferred from one circuit to another
without direct connection, and in the process the energy can be readily changed from one voltage level to another. Although a
transformer is not a complex device, considerable explanation is required to properly understand how it operates. This chapter is
intended to help the audio system engineer properly select and apply transformers. In the interest of simplicity, only basic concepts
of their design and manufacture will be discussed.

1.1 Basic Principles and Terminology
1.1.1 Magnetic Fields and Induction
As shown in Figure 1, a magnetic field is created around any

conductor (wire) in which current flows. The strength of the

field is directly proportional to current. These invisible magnetic

lines of force, collectively called flux, are set up at right angles to the wire and have a direction, or magnetic polarity,
which depends on the direction of current flow. Note that although the flux around the upper and lower wires have different directions,
the lines inside the loop aid because they point in the same direction. If an alternating current flows in the loop, the instantaneous
intensity and polarity of the flux will vary at the same frequency and in direct proportion to the instantaneous current.
We can visualize this flux, represented by the concentric circles in Figure 2, as expanding, contracting, and reversing in polarity
with each cycle of the ac current. The law of induction states that a voltage will be induced in a conductor exposed to changing
flux and that the induced voltage will be proportional to the rate of the flux change. This voltage has an instantaneous polarity
which opposes the original current flow in the wire, creating an apparent resistance called inductive reactance. Inductive
reactance is calculated according to the formula XL = 2dfL, where XL is inductive reactance in ohms, fis frequency in Hz,
and L is inductance in Henries. An inductor generally consists of many turns or loops of wire called a coil, as shown in Figure 3,
which links and concentrates magnetic flux lines, increasing the flux density. The inductance of any given coil is determined
by factors such as the number of turns, the physical dimensions and nature of the winding, and the properties of materials in
the path of the magnetic flux.

According to the law of induction, a voltage will be induced in any conductor (wire) that cuts flux lines. Therefore,
if we place two coils near each other as shown in Figure 4, an ac current in one coil will induce an ac voltage in the second coil.
This is the essential principle of energy transfer in a transformer. Because they require a changing magnetic field to operate,
transformers will not work at dc. In an ideal transformer, the magnetic coupling between the two coils is total and complete,
i.e., all the flux lines from one cut across all the turns of the other. The coupling coefficient is said to be unity or 1.00.

1.1.2 Windings and Turns Ratio
The coil or winding that is driven by an electrical source is called the primary and the other is called the secondary. The ratio of
the number of turns on the primary to the number of turns on the secondary is called the turns ratio. Since essentially the same
voltage is induced in each turn of each winding, the primary to secondary voltage ratio is the same as the turns ratio. For example,
with 100 turns on the primary and 50 turns on the secondary, the turns ratio is 2:1. Therefore, if 20 volts were applied to the
primary, 10 volts would appear at the secondary. Since it reduces voltage, this transformer would be called a step-down
transformer. Conversely, a transformer with a turns ratio of 1:2 would be called a step-up transformer since its secondary voltage
would be twice that of the primary. Since a transformer does not create power, the power output from the secondary of an ideal
transformer can only equal (and in a real transformer only be less than) the power input to the primary. Consider an ideal 1:2 step-
up transformer. When 10 volts is applied to its primary, 20 volts appears at its secondary. Since no current is drawn by the

Figure 1 - Magnetic Field
Surrounding Conductor
Figure 2 - AC Magnetic Field
Figure 3 - Coil
Concentrates Flux
Figure 4 - Inductive Coupling

Bill Whitlock Audio Transformers Page 3

Handbook for Sound Engineers, 3rd Edition

primary, its impedance appears to be infinite or an open circuit. When a 20 U load is connected to the secondary, a current of 1
amp flows making output power equal 20 watts. At the same time, a current of 2 amps is drawn by the primary, making input
power equal 20 watts. Since the primary is now drawing 2 amps with 10 volts applied, its impedance appears to be 5 U. In other
words, the 20 U load impedance on the secondary has been reflected to the primary as 5 U. In this example, a transformer with a

1:2 turns ratio exhibited an impedance ratio of 1:4. Transformers always reflect impedances from one winding to another by the
square of the their turns ratio or, expressed as a formula: Zp/Zs = (Np/Ns)2 where Zp is primary impedance, Zs is secondary
impedance, and Np/Ns is turns ratio (which is the same as the voltage ratio).
The direction in which coils are wound, i.e., clockwise or counter-clockwise, and/or the connections to the start or finish of each
winding determines the instantaneous polarity of the ac voltages. All windings which are wound in the same direction will have
the same polarity between start and finish ends. Therefore, relative to the primary, polarity can be inverted by either (1) winding
the primary and secondary in opposite directions, or (2) reversing the start and finish connections to either winding. In schematic
symbols for transformers, dots are sometimes used to indicate which ends of windings have the same polarity. Observing polarity
is essential when making series or parallel connections to transformers with multiple windings. Taps are connections made at any
intermediate point in a winding. If 50 turns are wound, an electrical connection brought out, and another 50 turns completes the
winding for example, the 100-turn winding is said to be center-tapped.

1.1.3 Excitation Current
As shown in Figure 5, when there is no load on the secondary of a transformer and an ac voltage is applied to the primary,
an excitation current will flow in the primary creating magnetic excitation flux around the winding. In theory, the current is due only

Figure 5 - Excitation Current to the inductive reactance of the primary winding. In Figure 6 - Cancellation of Flux

accordance with Ohm’s law and the formula for Generated by Load Current inductive reactance, IE = EP ? 2dfLP
where IE is excitation current in amperes, EP is primary voltage in volts, f is frequency in Hz, and LP is primary
inductance in Henries. In an ideal transformer, primary inductance would be infinite, making excitation current zero.
As shown in Figure 6, when a load is connected, current will flow in the secondary winding.
Because secondary current flow is in the opposite direction, it creates magnetic flux which opposes the excitation flux.
This causes the impedance of the primary winding to drop, resulting in additional current being drawn from the driving source,
which creates additional flux just sufficient to completely cancel that created by the secondary. The result,
which may surprise some, is that flux density in a transformer is not increased by load current.
This also illustrates how load current on the secondary is reflected to the primary.

Figure 7 illustrates the relationships between voltage, excitation current, and flux in a transformer as frequency is changed.
The horizontal scale is time. The primary voltage Ep is held at a constant voltage as the frequency is tripled and then tripled again.
For example, the left waveform could represent one cycle at 100 Hz, the middle 300 Hz, and the right 900 Hz.
Because of the primary inductance, excitation current Ip will decrease linearly with frequency, i.e., halving for every doubling
in frequency or decreasing at 6 dB per octave. The magnitude of the magnetic flux will likewise decrease exactly the same way.
Note that the inductance causes a 90-degree phase lag as well. Since the slew rate of a constant amplitude sine wave increases
linearly with frequency, i.e., doubling for every doubling in frequency or increasing at 6 dB per octave, the resultant flux
rate of change remains constant. Note that the slope of the Ip and flux waveforms stays constant as frequency is changed.
Since, according to the law of induction, the voltage induced in the secondary is proportional to this slope or rate of change,
frequency response will be uniform or "flat."

Figure 7 - Excitation Current and Flux
Vary Inversely with Frequency

Bill Whitlock Audio Transformers Page 4

Figure 8 - Transformer Low-Frequency Parasitic Elements
Handbook for Sound Engineers, 3rd Edition

1.2 Realities of Practical Transformers
Thus far, we have not considered the unavoidable parasitic elements which exist in any practical transformer. Even the design of a
relatively simple 60 Hz power transformer must take them into account. The design of an audio transformer operating over a 20
Hz to 20 kHz frequency range is much more difficult because these elements often interact in complex ways. For example,
materials and techniques which improve low-frequency performance are often detrimental to high-frequency performance and
vice-versa. Good transformer designs must consider both the surrounding electronic circuitry and the performance ramifications of
internal design tradeoffs.

A schematic representation of the major low-frequency parasitic elements in a generalized transformer is shown in Figure 8.
The "IDEAL XFMR" represents a perfect transformer having a turns ratio of 1:N and no parasitic elements of any kind.
The actual transformer is connected at the "PRI" terminals to the driving voltage source, through its source impedance RG,
and at the "SEC" terminals to the load RL.

One of the main goals in the design of any transformer is to reduce the excitation current in the primary winding to negligible
levels so as not to become a significant load on the driving source. At a given source voltage and frequency, primary excitation
current can be reduced only by increasing inductance LP. In the context of normal electronic circuit impedances, very large values
of inductance are required for satisfactory operation at the lowest audio frequencies. Of course, inductance can be raised by using
a very large number of coil turns but, for reasons discussed later, there are practical limits due to other considerations. Another
way to increase inductance by a factor of 10,000 or more is to wind the coil around certain highly magnetic materials.

1.2.1 Core Materials and Construction
Magnetic circuits are quite similar to electric circuits. As shown in Figure 11, magnetic flux always takes a closed path from one
magnetic pole to the other and, like an electric current, always favors the paths of highest conductivity or least resistance. The
equivalent of applied voltage in magnetic circuits is magnetizing force, symbolized H. It is directly proportional to "ampere-turns"

(coil current I times its number of turns N) and inversely proportional to the flux path length R in the magnetic circuit. The
equivalent of electric current flow is flux density, symbolized B. It is measured as the number of magnetic flux lines per square
unit of area. A graphic plot of the relationship between field intensity and flux density is shown in Figure 9 and is referred to a the
"B-H loop" or "hysteresis loop" for a given material. In the United States, the most commonly used units for magnetizing force
and flux density are the Oersted and Gauss, respectively, which are CGS (centimeter, gram, second) units. In Europe, the SI
(Systeme International) units amperes per meter and Tesla, respectively, are more common. The slope of the B-H loop indicates
how an incremental increase in applied magnetizing force changes the resulting flux density. This slope is effectively a measure of
conductivity in the magnetic circuit and is called permeability, symbolized i. Any material inside a coil, which can also serve as a
form to support it, is called a core. By definition, the permeability of air is 1.00 and common "non-magnetic" materials such as
aluminum, brass, copper, paper, glass, and plastic also have a permeability of 1 for practical purposes. The permeability of some
common "ferro-magnetic" materials is about 300 for ordinary steel, about 5,000 for 4% silicon transformer steel, and up to about
100,000 for some nickel-iron-molybdenum alloys. Because such materials concentrate magnetic flux, they greatly increase the
inductance of a coil. Audio transformers must utilize both high-permeability cores and the largest practical number of coil turns to
create high primary inductance. Coil inductance increases as the square of the number of turns and in direct proportion to the
permeability of the core and can be approximated using the formula: L = 3.2 N 2 i A / 10 8 R where L = inductance in Henries, N =

number of coil turns, i = permeability of core, A = cross-section area of core in square inches, and R = mean flux path length in
inches.

Bill Whitlock Audio Transformers Page 5

Figure 9 - B-H Loop for Magnetic Core Material Handbook for Sound Engineers, 3rd Edition

The permeability of magnetic materials varies with flux density. As shown in Figure 9, when magnetic field intensity becomes high,
the material can saturate, essentially losing its ability to conduct any additional flux. As a material saturates, its permeability
decreases until, at complete saturation, its permeability becomes that of air or 1. In audio transformer applications,
magnetic saturation causes low-frequency harmonic distortion to increase steadily for low-frequency signals as they increase
in level beyond a threshold. In general, materials with a higher permeability tend to saturate at a lower flux density. In general,
permeability also varies inversely with frequency.

Magnetic hysteresis can be thought of as a magnetic memory effect. When a magnetizing force saturates material that has high
-hysteresis, it remains strongly magnetized even after the force is removed. High- hysteresis materials have wide or "square"
B-H loops and are used to make magnetic memory devices and permanent magnets. However, if we magnetically saturate
zero-hysteresis material, it will have no residual magnetism (flux density) when the magnetizing force is removed.
However, virtually all high-permeability core materials have some hysteresis, retaining a small memory of their previous magnetic state.
Hysteresis can be greatly reduced by using certain metal alloys which have been annealed or heat-treated using special processes.
In audio transformers, the nonlinearity due to magnetic hysteresis causes increased harmonic distortion for low-frequency signals at
relatively low signal levels. Resistor RC in Figure 8 is a non-linear resistance which represents the combined effects of magnetic
saturation, magnetic hysteresis, and eddy-current losses.

The magnetic operating point (or zero signal point) for most transformers is the center of the B-H loop shown in Figure 9, where
the net magnetizing force is zero. Small ac signals cause a small portion of the loop to be traversed in the direction of the arrows.
Large ac signals traverse portions farther from the operating point and may approach the saturation end points. For this normal
operating point at the center, signal distortions (discussed in detail later) caused by the curvature of the loop are symmetrical, i.e.,
they affect the positive excursion and negative excursion equally. Symmetrical distortions produce odd-order harmonics such as
third and fifth. If dc current flows in a winding, the operating point will shift to a point on the loop away from the center. This
causes the distortion of a superimposed ac signal to become non-symmetrical. Non-symmetrical distortions produce even-order
harmonics such as second and fourth. When a small dc current flows in a winding, under say 1% of the saturation value, the effect
is to add even-order harmonics to the normal odd-order content of the hysteresis distortion, which affects mostly low-level signals.
The same effects occur when the core becomes weakly magnetized, as could happen via the brief accidental application of dc to a
winding for example. However, the narrow B-H loop indicates that only a weak residual field would remain even if a magnetizing
force strong enough to saturate the core were applied and then removed.

When a larger dc current flows in a winding, the symmetry of saturation distortion is also affected in a similar way. For example,
enough dc current might flow in a winding to move the operating point to 50% of the core saturation value. Only half as much ac
signal could then be handled before the core would saturate and, when it did, it would occur only for one direction of the signal
swing. This would produce strong second-harmonic distortion. To avoid such saturation effects, air gaps are sometimes
intentionally built into the magnetic circuit. This can be done, for example, by placing a thin paper spacer between the center leg
of the E and I cores of Figure 10. The magnetic permeability of such a gap is so low . even though it may be only a few
thousandths of an inch . compared to the core material, that it effectively controls the flux density in the entire magnetic circuit.
Although it drastically reduces the inductance of the coil, gapping is done to prevent flux density from reaching levels which
would otherwise saturate the core, especially when substantial dc is present in a winding.

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Handbook for Sound Engineers, 3rd Edition

Because high-permeability materials are usually electrical conductors as well, small voltages are also induced in the cross-section
of the core material itself giving rise to eddy currents. Eddy currents are greatly reduced when the core consists of a "stack"
of thin sheets called laminations, as shown in Figure 10. Because the laminations are effectively insulated from each other,
eddy currents are generally insignificant. The E and I shaped laminations shown form the widely used "shell" or "double-window"
core construction. Its parallel magnetic paths are illustrated in Figure 11. When cores are made of laminations, care must be taken
that they are flat and straight to avoid tiny air gaps between them which could significantly reduce inductance.

A toroidal core is made by rolling a long thin strip of core material into a coiled ring shape that looks something like a donut.
It is insulated with a conformal coating or tape and windings are wound around the core through the center hole using special machines.
With a toroidal core, there are no unintended air gaps which can degrade magnetic properties. Audio transformers don’t often use
toroidal cores because, especially in high- bandwidth designs where multiple sections or Faraday shields are

necessary, physical construction becomes very complex. Other core configurations include the ring core, sometimes called
"semitoroidal." It is similar to core of Figure 11 but without the center section and windings are placed on the sides.
Sometimes a solid (not laminations) metal version of a ring core is cut into two pieces having polished mating faces.
These two C-cores are then held together with clamps after the windings are installed.

1.2.2 Winding Resistances and Auto-Transformers
If zero-resistance wire existed, some truly amazing transformers could be built. In a 60 Hz power transformer, for example,
we could wind a primary with tiny wire on a tiny core to create enough inductance to make excitation current reasonable.
Then we could wind a secondary with equally tiny wire. Because the wire has no resistance and the flux density in the core doesn’t
change with load current, this postage-stamp sized transformer could handle unlimited kilo-watts of power . and it wouldn’t
even get warm! But, at least until practical superconducting wire is available, real wire has resistance. As primary and secondary
currents flow in the winding resistances, the resulting voltage drops cause signal loss in audio transformers and significant heating
in power transformers. This resistance can be reduced by using larger (lower gauge) wire or fewer turns, but the required number
of turns and the tolerable power loss (or resulting heat) all conspire to force transformers to become physically larger and heavier
as their rated power increases. Sometimes silver wire is suggested to replace copper, but since its resistance is only about 6% less,
its effect is minimal and certainly not cost-effective.
However, there is an alternative configuration of transformer windings, called an autotransformer, which can reduce the size and
cost in certain applications. Because an autotransformer electrically connects primary and secondary windings, it can’t be used
where electrical isolation is required! In addition, the size and cost advantage is maximum when the required turns ratio is very close
to 1:1 and diminishes at higher ratios, becoming minimal in practical designs at about 3:1 or 1:3.

For example, in a hypothetical transformer to convert 100 volts to 140 volts, the primary could have 100 turns and the secondary
140 turns of wire. This transformer, with its 1:1.4 turns ratio, is represented in the upper diagram of Figure 12. If 1 amp of secondary
(load) current IS flows, transformer output power is 140 watts and 1.4 amp of primary

Figure 10 - Core Laminations are Stacked and Interleaved around Bobbin which Holds Windings
Figure 11 - Magnetic
Circuits in Shell Core
Figure 12 - Auto-Transformers
Employ a Buck/Boost Principle

Bill Whitlock Audio Transformers Page 7

Handbook for Sound Engineers, 3rd Edition

current IP will flow since input and output power must be equal in the ideal case. In a practical transformer, the wire size for each
winding would be chosen to limit voltage losses and/or heating.

An auto-transformer essentially puts the windings in series so that the secondary voltage adds to (boosting) or subtracts from
(bucking) the primary input voltage. A step-up auto-transformer is shown in the middle diagram of Figure 12. Note that the dots
indicate ends of the windings with the same instantaneous polarity. A 40-volt secondary (the upper winding), series connected as
shown with the 100-volt primary, would result in an output of 140 volts. Now, if 1 amp of secondary (load) current IS flows,
transformer output power is only 40 watts and only 0.4 amp of primary current IP will flow. Although the total power delivered to
the load is still 140 watts, 100 watts have come directly from the driving source and only 40 watts have been transformed and
added by the auto-transformer. In the auto-transformer, 100 turns of smaller wire can be used for the primary and only 40 turns of
heavier wire is needed for the secondary. Compare this to the total of 240 turns of heavier wire required in the transformer.

A step-down auto-transformer is shown in the bottom diagram of Figure 12. Operation is similar except that the secondary is
connected so that its instantaneous polarity subtracts from or bucks the input voltage. For example, we could step down US 120volt
ac power to Japanese 100-volt ac power by configuring a 100-volt to 20-volt step-down transformer as an auto-transformer.
Thus, a 100-watt load can be driven using only a 20-watt rated transformer.

The windings of low-level audio transformers may consist of hundreds or even many thousands of turns of wire, sometimes as
small as #46 gauge, whose 0.0015 inch diameter is comparable to a human hair. As a result, each winding may have a dc
resistance as high as several thousand ohms. Transformer primary and secondary winding resistances are represented by RP and
RS, respectively, in Figure 8.

1.2.3 Leakage Inductance and Winding Techniques In an ideal transformer, since all flux generated by the primary is linked to
the secondary, a short-circuit on the secondary would be reflected to the primary as a short circuit. In real transformers,
the unlinked flux causes a residual or leakage inductance which can be measured at either winding. Therefore, the secondary
would appear to have residual inductance if the primary were shorted and vice-versa. The leakage inductance is shown as LL
in the model of Figure 13. Note that leakage inductance is reflected from one winding to another as the square of turns ratio,
just as other impedances are.

The degree of flux coupling between primary and secondary windings depends on the physical spacing between them and how
they are placed with respect to each other. The lowest leakage inductance is achieved by winding the coils on a common axis and
as close as possible to each other. The ultimate form of this technique is called multi-filar winding where multiple wires are wound
simultaneously as if they were a single strand. For example, if two windings (say primary and secondary) are wound as one, the
transformer is said to be bi-filar wound. Note in the cross-section view of Figure 14 how the primary and secondary windings are
side-by-side throughout the entire winding. Another technique to reduce leakage inductance is to use layering, a technique in
which portions or sections of the primary and/or secondary are wound in sequence over each other to interleave them. For

example, Figure 15 shows the cross-section of a 3-layer transformer where half the primary is wound, then the secondary,
followed by the other half of the primary. This results in considerably less leakage inductance than just a secondary over
primary 2-layer design. Leakage inductance decreases rapidly as the number of layers is increased.

Figure 13 - Transformer High-Frequency Parasitic Elements
Figure 14 - Bi-Filar Windings Figure 15 - Layered Windings

Bill Whitlock Audio Transformers Page 8

Figure 16 - High-Frequency Equivalent Circuit of Transformer with Faraday Shield and Driven by a Balanced Source
Handbook for Sound Engineers, 3rd Edition

1.2.4 Winding Capacitances and Faraday Shields
To allow the maximum number of turns in a given space, the insulation on the wire used to wind transformers is very thin. Called
"magnet wire," it is most commonly insulated by a thin film of polyurethane enamel. A transformer winding is made, in general,
by spinning the bobbin shown in Figure 10 on a machine similar to a lathe and guiding the wire to form a layer one wire thick
across the length of the bobbin. The wire is guided to traverse back and forth across the bobbin to form a coil of many layers as
shown in Figure 15, where the bobbin cross-section is the solid line on three sides of the winding. This simple side-to-side, back-
and-forth winding results in considerable layer-to-layer capacitance within a winding or winding section. More complex
techniques such as "universal" winding are sometimes used to substantially reduce winding capacitances. These capacitances
within the windings are represented by CP and CS in the circuit model of Figure 13. Additional capacitances will exist between
the primary and secondary windings and are represented by capacitors CW in the model. Sometimes layers of insulating tape are
added to increase the spacing, therefore reducing capacitance, between primary and secondary windings. In the bi-filar windings
of Figure 14, since the wires of primary and secondary windings are side by side throughout, the inter-winding capacitances CW
can be quite high.

In some applications, inter-winding capacitances are very undesirable. Their effects can be almost completely eliminated by the use
of a Faraday shield between the windings. Sometimes called an electrostatic shield, it generally takes the form of a thin sheet of
copper foil placed between the windings. Obviously, transformers that utilize multiple layers to reduce leakage inductance will require
Faraday shields between all adjacent layers. In Figure 15 the dark lines between the winding layers are the Faraday shields. Normally,
all the shields surrounding a winding are tied together and treated as a single electrical connection. When connected to circuit ground,
as shown in Figure 16, a Faraday shield intercepts the capacitive current which would otherwise flow between transformer windings.

Faraday shields are nearly always used in transformers designed to eliminate "ground noise." In these applications, the transformer
is intended to respond only to the voltage difference or signal across its primary and have no response to the noise that exists
equally (or common-mode) at the terminals of its primary. A Faraday shield is used to prevent capacitive coupling (via CW in
Figure 13) of this noise to the secondary. For any winding connected to a balanced line, the matching of capacitances to ground is
critical to the rejection of common-mode noise or CMRR, as discussed in Chapter 37. In Figure 16, if the primary is driven by a
balanced line, C1 and C2 must be very accurately matched to achieve high CMRR. In most applications, such as microphone or
line input transformers, the secondary is operated unbalanced, i.e., one side is grounded. This relaxes the matching requirements
for capacitances C3 and C4. Although capacitances CC1 and CC2 are generally quite small (a few pF), they have the effect of
diminishing CMRR at high audio frequencies and limiting rejection of RF interference.

1.2.5 Magnetic Shielding
A magnetic shield has a completely different purpose. Devices such as power transformers, electric motors, and television or
computer monitor cathode-ray tubes generate powerful ac magnetic fields. If such a field takes a path through the core of an audio
transformer, it can induce an undesired voltage in its windings . most often heard as hum. If the offending source and the victim
transformer have fixed locations, orientation of one or both can sometimes nullify the pick-up. In Figure 11 note that an external
field which flows vertically through the core will cause a flux gradient across the length of the coil, inducing a voltage in it, but a
field which flows horizontally through the core will not. Such magnetic pick-up is usually worse in "input" transformers (discussed
later) because they generally have more turns. It should also be noted that higher permeability core materials are more immune to
external fields. Therefore, an unshielded "output" transformer with a high-nickel core will be more immune than one with a steel
core.

Another way to prevent such pick-up is to surround the core with a closed (no air gap) magnetic path. This magnetic shield most
often takes the form of a can or box with tight-fitting lid and is made of high-permeability material. While the permeability of
ordinary steel, such as that in electrical conduit, is only about 300, special-purpose nickel alloys can have permeability as high as
100,000. Commercial products include MumetalR, PermalloyR, HyMuR and Co-NeticR.[1][2] Since the shield completely
surrounds the transformer, the offending external field will now flow through it instead of the transformer core. Generally

Bill Whitlock Audio Transformers Page 9

Handbook for Sound Engineers, 3rd Edition

speaking, care must be taken not to mechanically stress these metals because doing so will significantly decrease their
permeability. For this reason, most magnetic shield materials must be re-annealed after they are fabricated.

The effectiveness of magnetic shielding is generally rated in dB. The transformer is placed in an external magnetic field of known
strength, generally at 60 Hz. Its output without and with the shield is then compared. For example, a housing of 1/8” thick cast-
iron reduces pickup by about 12 dB and a Mumetal can by about 30 dB. Where low-level transformers operate near strong
magnetic fields, several progressively smaller shield cans can be nested around the transformer. Two or three Mumetal cans can
provide 60 dB and 90 dB of shielding respectively. In very strong fields, because high-permeability materials might saturate, an
iron or steel outer can is sometimes used.

Toroidal power transformers can have a weaker radiated magnetic field than other types. Using them can be an advantage if audio
transformers must be located near them. However, a toroidal transformer must be otherwise well designed to produce a low
external field. For example, every winding must completely cover the full periphery of the core. The attachment points of the
transformer lead wires are frequently a problem in this regard. To gain size and cost advantages, most commercial power
transformers of any kind are designed to operate on the verge of magnetic saturation of the core. When saturation occurs in any
transformer, magnetic field essentially squirts out of the core. Power transformers designed to operate at low flux density will
prevent this. Often a standard commercial transformer, when operated at reduced primary voltage, will have a very low external
field.

1.3 General Application Considerations
For any given application, a number of parameters must be considered when selecting or designing an appropriate audio
transformer. We will discuss how the performance of a transformer can be profoundly affected by its interaction with surrounding
circuitry.

1.3.1 Maximum Signal Level, Distortion, and Source Impedance
Because these parameters are inextricably inter-dependent, they must be discussed as a group. Although transformer operating
level is often specified in terms of power such as dBm or watts, the only thing that affects distortion is the equivalent driving
voltage. Distortion is caused by excitation current in the primary winding which is proportional to primary voltage, not power.
Referring to Figure 8, recall that RC represents the distortion producing mechanisms of the core material. Consider that, if both
RG (driving source impedance) and RP (internal winding resistance) were zero, the voltage source (by definition, zero impedance)
would effectively "short out" RC resulting in zero distortion! But in a real transformer design there is a fixed relationship between
signal level, distortion, and source impedance. Since distortion is also a function of magnetic flux density, which increases as
frequency decreases, a maximum operating level specification must also specify a frequency. The specified maximum operating
level, maximum distortion at a specified low frequency, and maximum allowable source impedance will usually dictate the type of
core material which must be used and its physical size. And, of course, cost plays a role, too.

The most commonly used audio transformer core materials are M6 steel (a steel alloy containing 6% silicon) and 49% nickel or 84%
nickel (alloys containing 49% or 84% nickel plus iron and molybdenum). Nickel alloys are substantially more expensive than steel.
Figure 17 shows how the choice of core material affects low-frequency distortion as signal level changes. The increased distortion
at low levels is due to magnetic hysteresis and at high levels is due to magnetic saturation. Figure 18 shows how distortion decreases
rapidly with increasing frequency. Because of differences in their hysteresis distortion, the fall-off is most rapid for the 84% nickel
and least rapid for the steel. Figure 19 shows how distortion is strongly affected by the impedance of the driving source
(the plots begin at 40 U because that is the resistance of the primary winding). Therefore, maximum operating levels predicated on
higher frequencies, higher distortion, and lower source impedance will always be higher than those predicated on lower frequencies,
lower distortion, and lower source impedance.

Figure 17 - Measured THD at 20 Hz and 40 U Source vs Signal Level for Three Types of Core Material

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As background, it should be said that THD or total harmonic distortion is a remarkably inadequate way to describe the perceived
awfulness of distortion. Distortion consisting of low-order harmonics, 2nd or 3rd for example, is dramatically less audible than that
consisting of high-order harmonics, 7th or 13th for example. Consider that, at very low frequencies, even the finest loudspeakers
routinely exhibit harmonic distortion in the range of several percent at normal listening levels. Simple distortion tests whose results
correlate well with the human auditory experience simply don’t exist. Clearly, such perceptions are far too complex to quantify
with a single figure.

One type of distortion which is particularly audible is inter- modulation or IM distortion. Tests frequently use a large low-frequency
signal and a smaller high-frequency signal and measure how much the amplitude of the high frequency is modulated by the lower
frequency. Such inter-modulation creates tones at new, non-harmonic frequencies. The classic SMPTE (Society of Motion Picture
and Television Engineers) IM distortion test mixes 60 Hz and 7 kHz signals in a 4:1 amplitude ratio. For virtually all electronic amplifier
circuits, there is an approximate relationship between harmonic distortion and SMPTE IM distortion. For example, if an amplifier
measured 0.1% THD at 60 Hz at a given operating level, its SMPTE IM distortion would measure about three or four times that,
or 0.3% to 0.4% at an equivalent operating level. This correlation is due to the fact that electronic non-linearities generally distort
audio signals without regard to frequency. Actually, because of negative feedback and limited gain-bandwidth, most electronic
distortions become worse as frequency increases.

Distortion in audio transformers is different in a way which makes it unusually benign. It is caused by the smooth symmetrical
curvature of the magnetic transfer characteristic or B-H loop of the core material shown in Figure 9. The non-linearity is related
to flux density which, for a constant voltage input, is inversely proportional to frequency. The resulting harmonic distortion
products are nearly pure third harmonic. In Figure 18, note that distortion for 84% nickel cores roughly quarters for every doubling
of frequency, dropping to less than 0.001% above about 50 Hz. Unlike that in amplifiers, the distortion mechanism in a transformer
is frequency selective. This makes its IM distortion much less than might be expected. For example, the Jensen JT-10KB-D line
input transformer has a THD of about 0.03% for a +26 dBu input at 60 Hz. But, at an equivalent level, its SMPTE IM distortion is
only about 0.01% . about a tenth of what it would be for an amplifier having the same THD.

1.3.2 Frequency Response
The simplified equivalent circuit of Figure 20 shows the high-pass RL filter formed by the circuit resistances and transformer
primary inductance LP. The effective source impedance is the parallel equivalent of RG + RP and RS + RL. When the inductive
reactance of LP equals the effective source impedance, low-frequency response will fall to 3 dB below its mid-band value. For
example, consider a transformer having an LP of 10 Henries and winding resistances RP and RS of 50 U each. The generator
impedance RG is 600 U and the load RL is 10 kU. The effective source impedance is then (600 U + 50 U ) in parallel with (10 kU

+ 50 U) which computes to about 610 U. A 10 Henry inductor will have 610 U of reactance at about 10 Hz, making response 3 dB
down at that frequency. If the generator impedance RG were made 50 U instead, response would be !3 dB at 1.6 Hz. Lower
source impedance will always extend low-frequency bandwidth. Since the filter is single-pole, response falls at 6 dB per octave.
As discussed earlier, the permeability of most core material steadily increases as frequency is lowered and typically reaches its
Figure 18 - Measured THD at 0 dBu and 40 U Source vs Frequency for the Cores of Figure 16
Figure 19 - Measured THD at 0 dBu and 20 Hz vs Source Impedance for the Cores of Figures 16 and 17

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maximum somewhere under 1 Hz. This results in an actual roll-off rate less than 6 dB per octave and a corresponding
improvement in phase distortion (deviation from linear phase). Although a transformer cannot have response to 0 Hz or dc, it can
have much less phase distortion than a coupling capacitor chosen for the same cutoff frequency. Or, as a salesperson might say
"it’s not a defect, it’s a feature."

Figure 20 - Simplified Low Frequency
Transformer Equivalent Circuit
Figure 21 - Simplified High-Frequency
Transformer Equivalent Circuit
The simplified equivalent schematic of Figure 21 shows the parasitic elements which limit and control high-frequency response.
Except in bi-filar wound types discussed below, leakage inductance LL and load capacitance are the major limiting factors. This is
especially true when Faraday shields because of the increase in leakage inductance. Note that a low-pass filter is formed by series
leakage inductance LL with shunt winding capacitance CS plus external load capacitance CL. Since this filter has two reactive
elements, it is a two-pole filter subject to response variations caused by damping. Resistive elements in a filter provide damping,
dissipating energy when the inductive and capacitive elements resonate. As shown in the figure, if damping resistance RD is too
high, response will rise before it falls and if damping resistance is too low, response falls too early. Optimum damping results in

the widest bandwidth with no response peak. It should be noted that placing capacitive loads CL on transformers with high leakage
inductance not only lowers their bandwidth but changes the resistance required for optimum damping. For most transformers,
RL controls damping. In the time domain, under- damping manifests itself as ringing on square-waves as shown in Figure 22.
When loaded by its specified load resistance, the same transformer responds as shown in Figure 23. In some transformers,
source impedance also provides significant damping.

Figure 22 - Undamped Response Figure 23 - Proper Damping
In bi-filar wound transformers, leakage inductance LL is very low but inter-winding capacitance CW and winding capacitances
CP and CS are quite high. Leakage inductance must be kept very small in applications such as line drivers because large cable
capacitances CL would otherwise be disastrous to high- frequency response. Also note that a low-pass filter is formed by series
RG and shunt CP plus CS. Therefore, driving sources may limit high-frequency response if their source impedance RG is too high.
In normal 1:1 bi-filar output transformer designs, CW actually works to capacitively couple very high frequencies between windings.
Depending on the application, this can be either a defect or a feature.

1.3.3 Insertion Loss
The power output from a transformer will always be slightly less than power input to it. As current flows in its windings, their dc
resistance causes additional voltage drops and power loss as heat. Broadly defined, insertion loss (or gain) is that caused by
inserting a device into the signal path. But, because even an ideal lossless transformer can increase or decrease signal level by
virtue of its turns ratio, the term insertion loss is usually defined as the difference in output signal level between the real
transformer and an ideal one with the same turns ratio.

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The circuit models, Thevenin equivalent circuits, and equations for both ideal and real transformers are shown in Figure 24. For example,
consider an ideal 1:1 turns ratio transformer and RG =

RL = 600 U. Since N/N is 1, the equivalent circuit

sp

becomes simply E in series with RG or 600 U. When RL is connected, a simple voltage divider is formed

i

making E = 0.5 E (or a

oi
6.02 dB loss). For a real
transformer having RP = RS
= 50 U, the equivalent
circuit becomes E in series
with RG + RP + RS or 700 U. Figure 24 - Insertion Loss Compares the Outputs of Real and Ideal Transformers

i

Now, the output E = 0.462 E (or a 6.72 dB loss). Therefore, the insertion loss of the transformer is 0.70 dB.

oi
Calculations are similar for transformers with turns ratios other than 1:1, except that voltage is multiplied by the turns ratio and
reflected impedances are multiplied by the turns ratio squared as shown in the equations. For example, consider a 2:1 turns ratio

transformer, RG = 600 U, and RL = 150 U. The ideal transformer output appears as 0.5 E in series with RG/4 or 150 U. When RL

i

is connected, a simple voltage divider is formed making E = 0.25 E (or a 12.04 dB loss). For a real transformer having RP = 50

oi
U and RS = 25 U, the equivalent circuit becomes 0.5 E in series with (RG + RP)/4 + RS or 187.5 U. Now, the output E = 0.222

io

E (or a 13.07 dB loss). Therefore, the insertion loss of this transformer is 1.03 dB.

i

1.3.4 Sources with Zero Impedance
One effect of using negative feedback around a high-gain amplifier is to reduce output impedance. Output impedance is reduced
by the feedback factor which is open-loop gain in dB minus closed-loop gain in dB. A typical op-amp with an open-loop gain of
80 dB, set for closed-loop gain of 20 dB (feedback factor is 80 dB ! 20 dB = 60 dB or 1000) will have its open-loop output
impedance of 50 U reduced by the feedback factor to about 0.05 U. Within the limits of linear operation, i.e., no current limiting
or voltage clipping, the feedback around the amplifier forces the output to remain constant regardless of loading. For all practical
purposes this can be considered a true voltage source.

As seen in Figure 19, the distortion performance of ANY transformer is significantly improved when the driving source
impedance is less than the dc resistance of the primary. However, little is gained below about 10% of the winding dc resistance.
For example, consider a typical line output transformer with a primary dc resistance of 40 U. A driving source impedance well
under 4 U will result in lowest distortion. The line drivers shown in Figure 28 and Figure 29 use a paralleled inductor and resistor
to isolate or decouple the amplifier from the destabilizing effects of load (cable) capacitance at very high frequencies. Because its
impedance is well under an ohm at all audio frequencies, it is much preferred to the relatively large series or "build-out" resistor
often used for the purpose. It is even possible for an amplifier to generate negative output resistance to cancel the winding
resistance of the output transformer. Audio Precision uses such a patented circuit in their System 1 audio generator to reduce
transformer-related distortion to extremely low levels.

1.3.5 Bi-Directional Reflection of Impedances
The impedances associated with audio transformers seems to confuse many. Much of the confusion probably stems from the fact
that transformers can simultaneously reflect two different impedances. One is the impedance of the driving source, as seen from
the secondary, and the other is the impedance of the load, as seen from the primary. Transformers simply reflect impedances,
modified by the square of their turns ratio, from one winding to another. However, because of their internal parasitic elements,
transformers tend to produce optimum results when used within a specified range of external impedances.

There is essentially no intrinsic impedance associated with the transformer itself. With no load on its secondary, the primary of a
transformer is just an inductor and its impedance will vary linearly with frequency. For example, a 5 H primary winding would

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have an input impedance of about 3 kU at 100 Hz, 30 kU at 1 kHz, and 300 kU at 10 kHz. In a proper transformer design, this
self-impedance, as well as those of other internal parasitics, should have negligible effects on circuit operation.
The following applications will illustrate the point.

A 1:1 output transformer application is shown in Figure 25. It has a winding inductance of about 25 H and negligible leakage
inductance. The open circuit impedance, at 1 kHz, of either winding is about 150 kU. Since the DC resistance is about 40 U
per winding, if the primary is short circuited, the secondary impedance will be 80 U. If we place the transformer between a
zero-impedance amplifier (more on that later) and a load, the amplifier will “see” the load through the transformer and the
load will “see” the amplifier through the transformer. In our example, the amplifier would “look like” 80 U to the output line
or load and the 600 U load would “look like” 680 U to the amplifier. If the load were 20 kU, it would “look like” slightly less
than 20 kU because the open circuit transformer impedance (150 kU at 1 kHz) is effectively in parallel with it. For most loads,
this effect is negligible.

A 4:1 input transformer example is shown in Figure 26. It has a primary inductance of about 300 H and negligible winding
capacitance. The open circuit impedance, at 1 kHz, of the primary is about 2 MU. Because this transformer has a 4:1 turns ratio,
therefore

16:1 impedance ratio, the secondary open circuit impedance is about 125 kU. The DC resistances are about 2.5 kU for the primary and
92 U for the secondary. Since this is an input transformer, it must be used with the specified secondary load resistance of 2.43 kU for
proper damping (flat frequency response). This load on the secondary will be transformed by the turns ratio to “look like” about
42 kU at the primary. To minimize the noise contribution of the amplifier stage, we need to know what the transformer secondary
“looks like,” impedance wise, to the amplifier. If we assume that the primary is driven from the line in our previous output transformer
example with its 80 U source impedance, we can calculate that the secondary will “look like” about 225 U to the amplifier input.
Actually, any source impedance less than 1 kU would have little effect on the impedance seen at the secondary.
Transformers are not “intelligent” . they can’t isolate, in the loading sense, outputs from one another or magically couple signals in
one direction only. Magnetic coupling is truly bi-directional. For example, Figure 27 shows a three-winding 1:1:1 transformer
connected to drive two 600 U loads. The driver "sees" the loads in parallel or, neglecting winding resistances, 300 U. Likewise,
a short on either output will be reflected to the driver as a short. Of course, turns ratios and winding resistances must be
taken into account to calculate actual driver loading. For the same reason, stereo L and R outputs driving two windings on the same
transformer are effectively driving each other, possibly causing distortion or damage.

1.3.6 Transformer Noise Figure
Although the step-up turns ratio of a transformer may provide "noise-free" voltage gain, some 20 dB for a 1:10 turns ratio, it’s
important to understand that improvements in signal-to-noise ratio are not solely due to this gain. Because most amplifying
devices generate current noise as well as voltage noise, their noise performance will suffer when turns ratio is above the optimum
(see Chapter 21 on mic preamps). Noise figure measures, in dB, how much the output signal-to-noise ratio of a system is degraded
by a given system component. All resistances, including the winding resistances of transformers, generate thermal noise.
Therefore, the noise figure of a transformer indicates the increase in thermal noise or hiss when it replaces an ideal noiseless
transformer having the same turns ratio, i.e., voltage gain. The noise figure of a transformer is calculated as follows:

Figure 25 - Impedance Reflection in a 1:1 Transformer
Figure 26 - Impedance Reflection in a 4:1 Transformer
Figure 27 - Multiple Loads
are Effectively Paralleled

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1.3.7 Basic Classification by Application
Many aspects of transformer performance, such as level-handling, distortion, and bandwidth, depend critically on the impedance
of the driving source and, in some cases, the resistance and capacitance of the load. These impedances play such an important role
that they essentially classify audio transformers into two basic types. Most simply stated, output transformers are used when load
impedances are low, as in line drivers, while input transformers are used when load impedances are high, as in line receivers. The
conflicting technical requirements for output and input types make their design and physical construction very different. Of course,
some audio transformer applications need features of both input and output transformers and are not so easily classified.

Output transformers must have very low leakage inductance in order to maintain high-frequency bandwidth with capacitive loads.
Because of this, they rarely use Faraday shields and are often multi-filar wound. For low insertion loss, they use relatively few
turns of large wire to decrease winding resistances. Since they use fewer turns and operate at relatively high signal levels, output
transformers seldom use magnetic shielding. On the other hand, input transformers directly drive the usually high-resistance, low-
capacitance input of amplifier circuitry. Many input transformers operate at relatively low signal levels, frequently have a Faraday
shield, and are usually enclosed in at least one magnetic shield.