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TRANSFORMERS

- tutorial

This piezo tutorial provides a basic introduction to

piezoelectric transformers. Based on this, the tuto-

rial describes vital elements of the piezo trans-

former such as electrical equivalent circuit, soft

switching and the longitudinal mode transformer.

Index of the tutorial on piezo transformers:

Piezoelectric transformer fundamentals

Electrical equivalent circuit

Soft switching

The longitudinal mode transformer

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PIEZOELECTRIC TRANSFORMER FUNDAMENTALS

Piezoelectric Transformers (PT) or Solid State Transformers (SST) are made from hard piezoelectric ceram-

ics and can be made very small and light, while being at a comparable cost to conventional transformers,

when manufactured in large quantities.

Basic principle of the piezo transformer

PTs are based on piezoelectric ceramic materials, which has an electromechanical coupling, meaning that a mechanical

motion can be induced by applying an electric field over the material. A PT consists of two or more piezoelectric sections

in a joint structure, which enables the transfer of electrical energy through the mechanical domain. The primary side ele-

ment is then excited by an electrical AC voltage, which induces a deformation of the joined PT structure. The deformation

of the secondary element generates an output voltage and through proper PT design, a desired primary to secondary

voltage conversion can be obtained.

Electrically, PTs behave like a band pass filter, where high power throughput and high efficiency can be obtained when

operated close to the frequency of resonance. In many ways, this behavior is similar to traditional resonant converters,

and there are examples of the same types of converter topologies and control strategies being employed.

Operation in resonance mode

In order to transfer power at a high efficiency, the PT is operated in one of its resonance modes. In the top figure it is illus-

trated how an off resonance excitation only results in a deformation of the primary section itself. Resulting in no trans-

feral of mechanical energy to the secondary section.

The figure below illustrates the desired resonance operation, where the excitation of the primary section induces a

standing half wave (λ/2) sound wave in the joint structure, resulting in a transfer of mechanical energy. Furthermore, this

mode of resonance has a nodal line in the center of the structure, where there is no displacement of structure.

The PT resonates each time it is possible to generate a standing sound wave in the structure (half wave (λ/2), full wave (λ),

3/2 wave (3/2λ) etc.). However, in order to obtain the highest efficiency, the PT is usually optimized for one specific reso-

nance mode.

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ELECTRICAL EQUIVALENT CIRCUIT

The electromechanical characteristics of the PT structure resembles a distributed network, but can be ap-

proximated by a single linear circuit, which is valid around a chosen resonance mode of interest.

The lumped parameter model

For simplicity, normally only the resonance mode of interest is modeled. One of the most used PT models is the lumped

parameter model, which is illustrated in the figure below.

The model is basically an electrical LCC resonance tank. It consists of two terminal capacitors Cd1, Cd2, which are con-

nected by a resonant LCR branch. The LCR branch acts as a short circuit at resonance frequency and this gives the model

its band pass characteristic. Furthermore, the model includes an ideal transformer, which gives the model up and down

conversion capability. This resonance tank structure is known from traditional resonance converters and the behavior of

a PT based converter is quite similar to a traditional resonance converter.

Lumped parameter model, modeling a single mode of resonance.

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SOFT SWITCHING

Soft switching enables the usage of an inductor-less half-bridge topology.

Inductor-less half bridge topology

The inductor-less half-bridge consists of a MOSFET based half-bridge, the PT and possibly an output rectifier, depending

on the specific application. The inductor-less half bridge topology is illustrated in the figure below.

The topology has the advantage of being simple, as well as eliminating the bulky series inductor, and it only converts en-

ergy through the electromechanical PT resonance tank. Usually, a series inductor is required, in order to achieve zero

voltage switching (ZVS) operation of the half-bridge switches and avoid large hard switching losses, in connection to the

PT input capacitor Cd1. The power losses associated with hard switching of Cd1, can easily be as large as the output power

itself, giving the converter a very poor efficiency.

The inductor-less half-bridge topology, including the PT lumped parameter model

The key element in designing with soft switching

The core of the soft switching principle is to design the transformer in such a manner that there is sufficient resonating

energy in the PT, in order to charge and discharge the input capacitance Cd1 during each switching cycle. Furthermore,

some dead time in-between the switches is required, in order to allow the charging and discharging of Cd1 to occur, as

illustrated in the figure below (to the right).

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Non-soft switching (hard switching) input voltage (left) and soft switching input voltage (right)

Excitation frequency is key

However, ZVS operation is only obtainable in a narrow frequency band, located just above the resonance frequency.

Here the series resonance (L and C of the resonance tank) becomes inductive and possesses enough resonating energy to

charge and discharge input capacitance Cd1. Hence the excitation frequency is key, in order to achieve ZVS, consistent

and efficient operation. However, through a ZVS optimized PT design, soft switching can be obtained without auxiliary

components.

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THE LONGITUDINAL MODE TRANSFORMER

Longitudinal both refers to the vibration being in the length of the structure, as well as the vibration is in

the same direction as the polarization direction.

Furthermore as the structure is considerably longer than its other dimensions (L > 2*W), the PT utilizes the longitudinal

electro-mechanical coupling k33, which is considerably higher than the other modes and ensures optimal conditions for

energy transferal between the electrical and mechanical domain.

The top figure illustrates the stress and displacement of a longitudinal mode PT, operated in the first mode shape (half

wave (λ/2)). An animation of the first mode shape vibration can be found in the section Piezoelectric transformer funda-

mentals (Operation in resonance mode). The coloring of the deformed structure indicates the displacement, where blue

is no displacement and red is high displacement. As it can be seen, the first mode shape operation has a nodal line in the

center of the structure.

The figure below illustrates the stress and displacement of a longitudinal mode PT, operated in the second mode shape

(full wave (λ)). As it can be seen, the second mode shape operation has two nodal lines, where the PT is not moving.

Both figures illustrates high voltage PT’s, with a high step-up ratio, which is achieved by having a large amount of primary

layers and only one secondary layer. The conversion ratio of a PT is directly proportional to the primary to secondary

layer ratio (but is also affected by other factors, such as the electrical loading, placement of the sections and electro-me-

chanical coupling). This means that if the amount of primary layers is doubled (effectively halving the layer thickness), the

step-up ratio will double as well.

Stress and displacement of a longitudinal mode PT, operated in the first mode shape (half wave (λ/2))

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Stress and displacement of a longitudinal mode PT, operated in the second mode shape (full wave (λ))