Signal Transformer Application

In the simplest sense, a transformer is two or more windings coupled by a common magnetic field. This magnetic field provides the means to pass voltages and currents from one winding (primary) to the other winding (secondary). Magnetic flux is created when an alternating current flows through a winding (see Figure 1).
 
The magnetic field (represented by magnetic flux lines) follows the path of least magnetic resistance (reluctance). Not all of the flux created by the first winding flows through the second winding. Leakage flux is the flux that does not connect the two windings and results in lost energy. There are other forms of energy losses such as core and winding losses that also reduce the efficiency of the transformer but they will not be discussed in detail here. One way of reducing the amount of leakage flux is to shorten the path between the two windings or to place the windings on top of each other. Properly configuring the windings allows more of the flux to link both windings and limits losses. Lowering leakage flux (leakage inductance) is a primary goal of the signal transformer designer since fewer losses means that a greater amount of the signal will be transferred in an undistorted manner.

Transformer have many uses, such as isolation of DC currents, voltage and current transformations, and impedance matching. The type of signals to be transferred from the primary to secondary windings dictate the type of transformer that should be used in an application. For instance, a transformer needed to provide DC isolation between two windings carrying large amounts of currents would be designed differently from a transformer that needs to provide an impedance match to a small signal communications network. In this article, the emphasis will be on two types of signal transformers that are designed specifically for the transmission of data at low power levels with DC isolation (the wideband transformer) and those designed to be non-isolating (the auto transformer). These types of transformers are not limited to low power capabilities, but the emphasis here is for use in communication and small signal applications.

The Wideband Transformer

Many transformers are efficient in their ability to carry large amounts of voltage and current over a narrow range of frequencies. However, transformers are inefficient in transferring energy if they distort the signal. A wideband transformer can transmit a clean, undistorted low-power signal over a wide range of frequencies. This is important when transmitting signals such as square waves because each individual pulse is made up of a wide range of harmonics. These harmonics give the square wave its shape and are necessary to preserving the original wave shape.

Wideband transformers can be used for many different applications including: DC isolation between circuits, impedance matching, phase shifting, coupling, balanced to unbalanced transitions, and current and voltage conversion. The significance of a wideband transformer is that it can transmit small signal information over a wide range of frequencies. Wide bandwidths are possible through tight coupling between the primary and secondary windings.

The operable range of frequencies for a wideband transformer is referred to as the bandwidth. The bandwidth is the range of frequencies that is allowed to pass while still maintaining at least half of the signal power. The half power point is specified as being 3 dB down from the insertion loss (see Figure 2).

Other parameters also need to be considered when evaluating a wideband transformer. Depending on the application, the maximum or minimum inductance of the primary or secondary winding, DC resistance of the windings, rise time, or a number of other factors might be considered. One primary parameter that needs to be determined is the turns or inductance ratio. The ratio is used for matching the primary and secondary impedance of the transformer to the circuit into which it is inserted. This ratio is also crucial for “stepping up” or “stepping down” a voltage or current from one side of the transformer to the other.
 

Design Equations

Wideband transformers are often used to step-up or stepdown voltages or currents. The same techniques can be applied to matching impedances between unbalanced circuits.
 
For the purpose of design simplicity, a lossless transformer will be used to derive the equations (see Figure 3). For a lossless transformer, the following equations are true:
  Where:
N₁ = number of turns on primary
N₂ = number of turns on secondary
V₁ = voltage across primary
V₂ = voltage across secondary
I₁ = current through primary
I₂ = current through secondary
a = turns ratio

The inductance of a winding can be approximated by using the following relation: where A_L is the equivalent inductance (per turns squared) of the core material. This is generally specified by the core manufacturer.

To find the required turns ratio necessary to match two impedances Z₁ and Z₂, the following relations are used:
 
Note that the impedance is proportional to the square of the turns. For example, if a 100 Ohm source Z₁ is to be connected to a 150 Ohm load Z₂, the resulting turns ratio necessary would be:

The Autotransformer

Design Equations

    Where:
N₁ = number of turns common to primary
N₂ = number of turns common to secondary
N_T = N₁ + N₂ = total number of turns
V₁ = voltage across primary
V₂ = voltage across secondary
I₁ = current in tap
I₂ = current in N₂ winding
I₃ = current in N₁ winding
a = turns ratio = N₁/ N_T

The inductance of a winding can be approximated by using the following relation: where A_L is the equivalent inductance (per turns squared) of the core material. This is generally specified by the core manufacturer.

To use the autotransformer as a voltage divider network, use the following equation:
To use the autotransformer as an impedance matching network, use the following equations:    

Conclusion

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