Piezoelectric Converters for DC/DC and AC/DC applications A. Vazquez Carazo Face Electronics, LC – Department of R &D Engineering 427W. 35th Street, Norfolk, VA 23507

Abstract – This paper introduces a cutting-edge transformer technology – the piezoelectric transformer – currently considered as a potential candidate to replace magnetic transformers in resonant switching converters. Magnetic transformers are extensively used for providing step-up and step-down voltages while allowing input to output isolation in ac-dc and dc-dc converters. Even with the extensive use, this component is still the largest, heaviest, and magnetically noisiest component in the power conversion chain. The paper introduces the reader in the piezoelectric transformer technology and proposes a simplified dc/dc converter case scenario to illustrate the different steps involved in applying this technology.

Furthermore, the technology development was accelerated thanks to the market demand of alternative products to magnetic transformers to be use in the backlighting of CCFL (cold cathode fluorescent lamps) for color liquid crystal displays (LCD). Currently, PTs are used in the high voltage backlighting inverter of laptop computers and flat-panel TV displays [4,5]. This type of PTs are so-called, “Rosen-type” PTs, since their structure follow the design envisioned by C.A. Rosen back in the 50s. INPUT ELECTRODES

OUTPUT ELECTRODE

I. INTRODUCTION Resonant dc/dc and ac/dc converters have attracted a great deal of attention over the last decade. Their ability to operate efficiently at high frequencies allows for considerable miniaturization of power supplies. When considering isolated topologies, the use of high frequencies wire-wound magnetic transformers is the most extended technology to provide step down and isolation between the primary and the secondary circuits. Recently, planar magnetic transformers have been introduced to replace standard wire-wounded transformers and provide lower-profile converters. In spite of this technological advancement, the transformer continues to be the largest and bulkiest component in dc/dc and ac/dc isolated converters. From a component perspective, the use of higher power density piezoelectric transformers (PTs) may allow a breakthrough to the existing state of the art of transformer leading to a more compact, lower profile converter designs. The first studies [1] on PTs took place in the late 20s and early 30s with the use of single crystal materials. In the 1945, B. Jaffe announced the discovery of a high performance ceramic material, called lead zirconia titanate (hereafter PZT), which had exceptional properties. Soon after the development of the PZT, Charles A. Rosen et al. applied for the first patent on a PT using the new material [2,3]. Today, C.A. Rosen is considered the “father” of the PT technology. Multiple applications were targeted during the 70s and 80s for piezoelectric transformers. However, initially the technology suffered from serious challenges related to: i) immature materials fabrication technology ; (ii) mechanical reliability problems at the nodal point; (iii) under-developed driving circuits. These problems created a barrier for technological advancement till the early 90’s. The 90’s saw several Japanese companies amending a revision in the concept of PT taking advantage the improvements in novel piezoelectric materials, more reliable manufacturing technologies like multilayer co-fired processes, new concepts in integrated circuits and housing solutions for the PTs.

Figure 1. “Rosen-type” piezoelectric transformers used in the LCD screen of laptop computers In this LCD backlighting application, PTs offer several advantages compared to magnetic transformers, such as: • Inherent high gain at no load, that provides the lamp ignition voltage. • Load dependent gain that avoids the use of the ballast capacitor in series with the lamp. • Absence of leakage magnetic field. • High Q factor, that gives low distorted sinusoidal lamp current waveform. • Small size and weight. • High reliability due to the absence of a high voltage secondary winding. Recently, the interest on PT technology has been extended to ac/dc and dc/dc power converter applications typically requiring higher power requirements and step -down capability compared to backlighting inverters. It is difficult in using the Rosen-type PTs for step -down voltage applications by simply reversing the input and output terminal connections. When the terminal connections are reversed, the driving electrical field becomes very small

because the transducer input part (output part when used in LCD applications) is too long. In order to allow the use of piezoelectric transformer technology to dc/dc and ac/dc converters new transformer designs have been proposed in the last years. These transformers must provide higher power output along with low output impedance. Since 1996, Face Electronics, LC has developed and patented different types of piezoelectric transformers with input and output multilayer topology thus allowing the adaptation of the input and output impedance to the different requirements of step -down applications. Some of these designs have already demonstrated to reach 20-50W with power densities in the order of 25W/cc. This represents over 6 times increase in power capabilities as compared to its magnetic counter parts. With these properties, piezoelectric technology is currently being envisioned as a potential candidate to replace magnetic transformers in certain low and medium power level applications, meeting the technical demands required for OEMs across all application ac/dc and dc/dc groups, including a) lower profiles, b) smaller footprints, c) high efficiency, and d) higher power densities. The purpose of this paper is to introduce this family of new transformers and present a simplified design case analysis for the development of a 15W regulated dc/dc converter operated under input voltages of 25 to 42 V to familiarize the reader with some of the application-related aspects of this technology. II. TRANSONER. CONSTRUCTION AND OPERATION PRINCIPLE Piezoelectric transformers, like magnetic devices, are basically energy converters. A magnetic transformer operates by converting electrical input to magnetic energy and then reconverting the magnetic energy back to electrical output. A piezoelectric transformer has an analogous operating mechanism. It converts an electrical input into mechanical energy and subsequently reconverts this mechanical energy back to an electrical output. In the piezoelectric transformer, an input and an output section made of piezoelectric ceramic material are placed in perfect mechanical contact with each other (through bonding or by integrating both sections in the same mechanical body). When an alternating voltage is applied to the input section with a frequency equal to one of the mechanical resonances of the transformer, the input section – due to the inverse piezoelectric effect - will vibrate creating an ultrasonic standing wave on the body of the transformer. This standing wave excites mechanically the output section which, due to the direct piezoelectric effect, will generate an electrical output. In this way, the input section acts as an actuator while the output section acts as a transducer. The dimensions of input and output sections as well as certain parameters of the piezoelectric material determine the transformer ratio between the input and output voltage as well as the efficiency of the device. Piezoelectric transformers do not require winding electrodes and all the entire piece – made of non-magnetic ceramic material - is used in the acoustic transfer. This design

reduces weight and size and allows the achievement of higher power densities. A typical design of a piezoelectric transformer manufactured and patented by Face Electronics is shown in Figure 2, and is commercially know as “Transoner®”. Transoner refers to a radially-operated piezoelectric transformer having a multilayer structure for the input and output sections. Transoner operates in the first fundamental radialextensional vibration mode. Different configurations are available. Figure 2 shows a topology including an input and an output section. Other topologies having the input layers divided in two parts sandwiching the output section have been also suggested to provide a symmetric structure. This allows the suppression of the spurious bending modes which may occur in a non-symmetrical structure. In the design illustrated in Figure 2, the input section includes a single layer polarized in the thickness direction. In contrast, the output part consists of many stacked thin piezoelectric ceramic layers, and the layers have alternating inverse polarizations to each other in the thickness direction. This allows increasing the transformer output capacitance and thus allows its operation to low output loads and step -down applications. One insulation layers is set between the input and output parts to isolate them electrically. The insulation layer has a slightly larger diameter compared to the PT body to enlarge the creepage distance between the input and the output sections.

INPUT

OUTPUT

Figure 2. Configuration of the laminated radial-type piezoelectric transformer, Transoner. When an AC voltage is applied to the input parts of the transformer of Figure 1, at a frequency that generates the fundamental radial-extensional vibration mode, the input parts oscillate in fundamental radial-extensional vibration mode, which depends upon the electromechanical coupling factor kr. The vibrations are simultaneously transmitted to the output part, which converts them into electric energy by the direct piezoelectric effect, which depends on the electromechanical coupling factor k p. Generally, k p of a piezoelectric ceramic material is approximately twice as high as the electromechanical coupling factor k 31 of longitudinal vibrations, leading to higher energy conversion efficiency of the radial vibration mode than that of the longitudinal vibration mode. Therefore, the power transmission efficiency of the piezoelectric transformer is higher, so that the volume of the transformer can be further reduced. Piezoelectric transformers are narrow band devices. This means that the transformer have to be operated in a frequency range close to the resonance frequency. In this operation, the driving circuit design must take into account that PTs are frequency and load dependent devices. Under these conditions, the PT operates in a window having the higher efficiency condition. Practically, the selected driving frequency is

chosen slightly above the resonant frequency. There are two main reasons for this selection: (i) the maximum efficiency is achieved at a frequency slightly higher than the resonant frequency and (ii) the control of the transformer is easier in the inductive window (above resonance). The frequency and load dependence can be easily evaluated by plotting the voltage gain against frequency curves for different output loads, as shown in Figure 3. 0.6

0.5 100 Ω

Gain

0.4

0.3

0.2

characteristics of the device and allows the manufacturer to relate the required electrical specifications to the physical dimensions of the device. In this circuit, Cd1 and Cd2 are the input and output damped capacitances, A1 and A2 are the socalled force factors for the input and output parts, and Lm , cm and rm are the equivalent mass, equivalent compliance, and equivalent mechanical resistance. The force factor represents the electrical-to-mechanical transformation ratio for each section (input and output). The intensity im indicated in the circuit is also called motional current and in a piezoelectric transformer is equal to the vibration velocity of the sample. The vibration velocity is an essential parameter during the design of the transformer. The maximum vibration velocity we can drive our sample will allow the determination of the maximum power capabilities.

60 Ω

rm

1:A1

10 Ω

cm

A2 :1 i 2 V2,PT

im

V1,PT 20 Ω

Lm

Cd2

Cd1

0.1

(a) 0

R 120

130

140

150

160

L

C

170

Frequency [kHz]

i2 V2,PT

i

V1,PT

Figure 3. Frequency and load dependence of a step-down piezoelectric transformer

1:N

Cd2

Cd1 (b)

Due to this double dependence, transformer ratio and efficiency are strongly dependent on frequency control, load fluctuation and input voltage variations. Consequently, in order to ensure stable operation of the PT, the driving circuit has to correct the influences of these electrical variables. The implementation of a compact and reliable controlling circuit using discrete components is complex and, thus has discouraged many researchers from entering this field. Currently, different IC makers have developed integrated circuit solutions which include frequency tracking control to achieve for input voltage and load regulation, and internally built protection circuitry, among other features Although this ICs have been, so far, focusing in the high-voltage backlighting applications, some IC-makers, case of Infineon in collaboration with Face Electronics [6], are currently developing ICs for ac/dc and dc/dc power conversion applications. III. EQUIVALENT CIRCUIT The integration of a piezoelectric transformer in the design of a power converter can be made by considering its lumped equivalent circuit. For a given off-the-shelf transformer, the equivalent circuit is typically given by the manufactured or can be easily determined using an impedance analyzer. However, in general, the application engineer will require a specific customized PT design to be manufactured in order to meet the specifications of a given converter design. Figure 4 includes two typical equivalent circuit used in the process of designing and using a piezoelectric transformer. The circuit of Figure 4.a. is typically used by the PT manufacturer during the design of the piezoelectric transformer. The advantage of this transformer is that it separates the two electrical ports and the mechanical

Figure 4. Lumped constant equivalent circuits. The circuit of Figure 4.b is more often provided in publications and by the transformer manufacturer to be used by the dc/dc or ac/dc application engineer. This second circuit is useful to perform simulations and circuit analysis during the design process of the converter. Its use will be illustrated in the following case study. In the circuit of Figure 4.b, the components of the resonant part of Figure 4.a. have been referred to the primary side using the following relationships:

R=

rm L A ; C = cm ⋅ A12 ; L = m2 ; N = 1 2 A A A1 2 1

(1)

IV. CASE STUDY: 15W DC/DC HALF-BRIDGE PIEZOCONVERTER The design of a piezoelectric-based converter involves several steps, similar to those related to the design of a conventional magnetic-based isolated converter, including: i) defining the design specifications, ii) selection of the converter topology, iii) design of the transformer, iv) control strategy and regulation including close loop, v) prototype development, vi) evaluation of performances. Each of these steps may require a detailed evaluation of the specific application. In this case study, we consider a first approach to the steps associated to the components selection and transformer design for a specific converter design. Due to the limit of this paper, we will not be able to consider in detail the issues related to the driving strategy and the feedback control. Comments on these matters will be provided during the presentation of this paper.

Piezoelectric Transformer

VGS1 Ls

VinDC VGS2

VLr

R

C

Vout,DC

L Lo

C d1 V 1_PT

RESR1

Co

Cd 2 V 2_PT

RL

Figure 5. Circuit diagram for the design of a piezoelectric-based DC-DC converter For the proposed case study, we have selected a Class-D (half-bridge) topology using a full-bridge diode-based rectifier to meet the following specifications: Vin = 25 V – 48 V Vout = 6 V; Iout = 2.5 A (Pout = 15 W)

From the theoretical waveform of this circuit and as a first approach, the ZVS operation can be achieved naturally when the switching frequency fs is greater than the resonant frequency of Ls-Cd1, fo, where:

f 0,Ls − Cd 1 =

1 TON

VGS1

Figure 5 shows the basic circuit configuration of the halfbridge piezoelectric-based DC-DC converter.

t VGS2

First Step: AC equivalent circuit of the input. The input half-bridge inverter is composed of two bi-directional twoquadrant switches S1 and S2. The switches consist of transistors and internally built anti-parallel diodes (usually body diodes of metal-oxide-semiconductors field-effect transistors (MOSFET)) that can conduct current in either direction. The active power switches of the inverter are gated by two complementary signals, VGS1 and VGS2, with a short dead time. Neglecting the dead time, the duty-ratio of VGS1 is D when the VGS2 is (1-D). The asymmetrical square-wave voltage, V Lr, illustrated in Figure 6, can be represented by the following function: V , for 0 < ωt ≤ ωt ON (2) v Lr = in,DC 0 , for ωt ON < ωt ≤ 2π This voltage V Lr can be represented by the following Fourier series: 2V V Lr (t ) = D ⋅ V DC + ∑ DC sin(nπD ) ⋅ sin(nωt + π + θ n ) (3) n nπ where sin (2nπ D ) θ n = tan −1 1 − cos (2nπ D )

(4)

where D = TON T s is the duty cycle of the high-side switch of the half-bridge amplifier. The Ls-Cd1 resonant circuit converts the square-wave voltage VDS2 into a sinusoidal output voltage driving the piezoelectric transformer if the loaded quality factor QL is high. The low-pass filter created by Ls is needed to prevent the harmonic contents from entering into the PTs and is regarded as an input matching network. The inductor Ls works not only as a low-pass filter of the voltage VLr but also as an important element which affects on the resonant characteristics and the ZVS operation of the converter. Therefore, the value of Ls must be selected to be an optimum value. Some guidelines will be given later in this paper.

(5)

2 ⋅ π ⋅ L s ⋅ C d1

0

TON

T 0

t VDS = VLr t iLs

t

V1,PT t

Figure 6. Typical waveforms for the input half-bridge inverter With a high quality factor of the load resonant circuit (intrinsically characteristic in piezoelectric transformers), almost all the harmonic contents, as well as the DC term, will be filtered out by the resonant circuit. Thus, only the fundamental current of the switching frequency is present in the load resonant inverter. Therefore, an approximate analysis can be made using phasor representation of the fundamental harmonic on the switching voltage, V Lr, which is at the inverter switching frequency, fs. The equivalent circuit of the load resonant inverter for the fundamental approximation is shown in Figure 7. V Lr (1) (t )

Ls V1 ,PT VLr(1)

R

C

L

RL

Cd1 R ESR1

Cd2

V2,PT

Figure 7. Equivalent circuit of the converter with the inverter reduced to an equivalent AC power supply VLr(1) is the RMS value of the fundamental component of VLr and can be expressed as follows:

VLr (1) = RMS

2 ⋅ sin (πD ) ⋅ Vin, DC = 0 .4502 ⋅ sin (πD )⋅ Vin ,DC π

(6)

In order to provide enough dead time between the two gate drives and to enhance transient response performance, typically the maximum duty cycle is chosen around 0.45. The voltage transfer ratio, MSW, for the switching ClassD (half-bridge) inverter can then be expressed as: V Lr( 1), RMS 2 ⋅ sin(π D ) (7) M SW = = ≈ 0.4502 ⋅ sin(π D ) Vin, DC π Second Step: AC equivalent resistance of the output rectifier. The output voltage required to design the piezoelectric transformer, V2,PT, can be determined once the output rectifier topology is chosen. Once the rectifier-type is decided, an equivalent AC resistance can be applied to the output of the piezoelectric transformer to compute the effect of the output rectifier. The method of calculating the AC equivalent resistance is shown here for the diode-bridge rectifier circuit, which is the suggested topology for this example. Figure 7 shows the full-bridge rectifier circuit with a constant current load (having a large enough filtering inductance connected in series at the DC output of the rectifier) and the associated waveforms. IDC

Lo

V out,DC

I2 ,PT Co

V2 ,PT

V 2,PT

RL

V 2, PT

I2,PT

ID C

Pout,REC

PDC 1 (10) = 2 ⋅ V 2 ⋅ RF Pin,REC P2,PT 1 + F + V out,DC RL where VF is the forward voltage drop of a rectifying diode and RF is the conduction resistance of the diode. Reorganizing the terms and using I DC = VDC R L we obtain: 2 Vout,DC = ⋅V 2, PT − 2 ⋅ VF − 2 ⋅ RF ⋅ I DC = π (11) V out,DC 2⋅ 2 = ⋅V 2 ,PT − 2 ⋅V F − 2 ⋅ R F ⋅ π RL ( RMS ) This equation can be also written in terms of the voltage transfer function of the rectifier: V out , DC (12) 2⋅ 2 η REC =

M REC =

V2

2 , PT ( RMS )

REQ

=

S

2π 1 π ⋅ ∫ I DC ⋅ V2, PT ⋅ sin ω s t + ∫ − I DC ⋅ V2 , PT ⋅ sin ω s t = 2 ⋅ π 0 π 2 ⋅ V2 , PT ⋅ I DC

(8)

π

Considering the forward voltage drop of the diodes, VF, and the losses for conduction in the forward resistance of the diodes, RF, and taking ?REC as the efficiency of the rectifier, the balance of input to output power is: P2,PT = PD C + PDrop_ Diodoes + PRF _ Diodes ⇒ 2 ⋅ V2 ,PT ⋅ I DC

2 = V DC ⋅ I DC + 2 ⋅V F ⋅ I DC + 2 ⋅ R F ⋅ I DC π Thus, the rectifier efficiency is:

=

(9)

2 ⋅ V2, PT ⋅ I DC

(13)

π

Ls

The AC equivalent resistance, REQ, can be obtained by balancing the input and output powers in the rectifier. The input power in the rectifier, P2,PT, can be obtained as:

=

2 ⋅ VF 2 ⋅ RF π ⋅ 1 + + V out , DC RL

From this equation, the AC equivalent resistance of the full-bridge rectifier becomes: 2 ⋅V F 2 ⋅ R F π2 (14) REQ = ⋅ RL ⋅ 1 + + 8 VDC RL Similar approach can be followed with other types of rectifiers such as synchronous rectifiers or center tapped rectifiers. Of particular interests are synchronous rectifiers, a type of rectifier that optimizes the efficiency of the rectifier and thus the DC-DC converter. Introducing the result given in equations (6) and (14), the equivalent circuit of Figure 5 can be now be evaluated in simplified way provided in the following Figure 8:

Figure 7. Full-bridge rectifier configuration and waveforms used to determine the AC equivalent resistance

1 T ⋅ ∫ i2, PT (t) ⋅ v 2 , PT (t ) ⋅ dt = TS 0

=

Comparing the PSEC,PT with the output power of an AC equivalent resistance, REQ, we have:

-I DC

P2, PT =

V 2, RMS

=

R

V1,PT VLr(1) V Lr (1 ) (t ) =

C

L

V2,PT

Cd1 R ESR1

Cd2

R EQ

2 ⋅ Vin ⋅ sin(πD ) ⋅ sin (ωt ) π

Figure 8. Simplified equivalent circuit for the converter including the first harmonic voltage source for the half-bridge input inverter and the AC equivalent load for the rectifier The simplified circuit of Figure 8 can be used to design or select the parameters of the transformer required to meet the DC/DC converter specifications. In this case scenario, the transformer has to be design such as it meets the output voltage requirement VDC = 6V for the minimum input voltage and the minimum equivalent resistance expected. In our case, the maximum load will be Pout,DC = 15W under Vout,DC = 6 V. This gives an output load of RL = 2.4 Ω. Assuming the forward drop in the output diodes as VF = 0.5V and RF = 0.025 Ω, then the equivalent load and the output voltage required in the secondary of the PT, V2,PT will be:

2 ⋅V F 2 ⋅ RF π2 ⋅ RL ⋅ 1 + + 8 VDC RL

V 2 , PT = ( RMS )

= 3.52Ω

V o u t, DC ⋅ V o u t, DC + 2 ⋅V F + 2 ⋅ R F ⋅ RL 2⋅ 2 π

(15) = 7 .92V

(16)

Note, that this will be the “minimum” voltage that will ensure that we can meet regulated 6V in the output. It is a good practice to allow an “extra room” for the voltage in the secondary. Thus, in this example we consider the secondary requirement for the PT as V2,PT(rms) = 9V. As mentioned above, the transformer parameters and transformer ratio have to be selected to meet this output voltage specifications under minimum input DC voltage, Vin,DC, conditions. In our specifications this is given for an input voltage of V in,DC = 25 V. Third Step: Determination of the equivalent circuit. The determination of the components of the equivalent circuit typically involves a reiterative process where dimensions and material properties are considered to meet the input and output voltage requirements. This process is typically undertaken by the manufacturer of the piezoelectric transformer once the input and output voltage in the transformer as well as the power requirements are known and involves the circuit of Figure 4.a. The detailed calculation of the parameters of the transformer is far beyond the limits of this paper. However, we will introduce some of the initial steps in this calculation to familiarize the reader. The first step is to calculate the output section to ensure that the transformer will operate at maximum efficiency under maximum load conditions (REQ = 3.52 Ω). This condition is achieved when the output capacitance of the piezoelectric transformer equivalent circuit, Cd2, is selected as: 1 (17) Cd 2 = ω res ⋅ R EQ Once the value of Cd2 is known, the number of secondary layers n2 and the force factor of the secondary section, A2, are obtained using the following equations: A2 =

n out ⋅ 2π ⋅ r ⋅ d 31,out

im = v =

(18)

s11E ⋅ (1 − σ )

Pout,DC ⋅ 2 ⋅ ω res ⋅ C d 2

(19) A2 where v is the vibration velocity, d31,out is the piezoelectric coefficient for the output section, s11E is the mechanical compliance, and σ is the Poisson ratio, A2 is the force factor for the output section, and v is the maximum radial vibration velocity admissible for the material considered. The value of the maximum vibration velocity is selected such as the temperature increase of the transformer does not exceed 30 oC. In a first approximation, for standard PZT materials v max can be taken as 0.15-0.20 m/s for a first design iteration. The design of the output section is completed by determining the thickness of each layer and the total thickness, as follows:

(

) π ⋅ rC ⋅ n

T t 2,layer = ε 33 ⋅ 1 − k 2p,out ⋅

t 2 = t2 ,layer ⋅ n out

(21)

Once the output section is defined, the design of the input layer involves a reiterative process where the value of the input inductance plays a significant role to determine the input voltage in the transformer and thus the transformation ration. In a first iteration, the volume of the input and output section can be selected as equals. Once the volume is defined, the mass of the transformer will be known and thus, the parameters of the motional resonant tank of Figure 4.a., Lm, Rm and Cm, can be defined. Finally, the value of A1 is defined to ensure the required transformation ratio to meet the output voltage for the minimum input voltage. The value of the capacitance Cd1 should be confirmed to ensure the ZVS with the input inductance while allowing the inductance to have a small package for the expected input current. Fourth Step: Series inductor for driving the PT. As briefly indicated above, the external series inductor, Ls, and the PT input capacitance, Cd1, form a low-pass filter for the squarelike input voltage VLr. The Ls-Cd1 filter formed by these components should pass the resonant frequency, required by the piezoelectric transformer, yet attenuate higher harmonic components, so the input voltage driving the PT become sinusoidal. An inductor value that is too low (very high Ls-Cd1 resonant frequency) will result in non-sinusoidal primary waveforms since higher order harmonics are allowed through the filter. A low value also allows excess circulating currents, impacting the efficiency. An inductor value that results in the Ls-Cd1 resonant frequency too close to the resonant frequency of the piezoelectric transformer (Case 1 of Fig. 9) will cause interference, making control of the primary voltage difficult. The interference occurs since the gain of the Ls-Cd1 tank depends heavily on load in this region of operation. Finally, an inductor value that is too large (Case 2 in Fig. 9) will result in an attenuation of the input voltage, increasing the gain requirements of the PT and/or the system. In general, the choice of the series inductor requires bench measurements and modeling of the resonant circuit. Figure 9 shows three different inductance values considered in a specific converter design as illustrative example. The best solution in this case (Case 3 of Figure 9) was to allow around 25kHz between the PT resonant frequency and the Ls-Cd1 resonance frequency: 18

Voltage Transfer [Vin_PT/Vout_PT]

REQ =

f PT =

16

1

f 0,Ls −C d1 =

2 ⋅π ⋅ L ⋅C

14

1 2⋅ π ⋅ L S ⋅ Cd1

12 10

Case 1 Ls=47uH

8 6

Case 3 Ls=22uH

4

Case 2 Ls=150uH

2 0 3

4

5

6

7

8

9

Frequency [Hz]

10

11

12 4

x 10

2

d2

out

(20)

Figure 9. Effect of the series Ls in the resonance and voltagetransfer response

V. FINAL COMMENTS

V. REFERENCES

In this case study, we have mainly focused our attention in the design process to select the main components of the resonant tank. Due to the extension of this paper, other issues have not been included in here. The control strategy of the piezoelectric transformer such as voltage regulation is an additional issue that will be discussed during the presentation of this paper. Figure 10 shows a prototype board (one sidePCB) with all the components required for a piezoelectricbased dc/dc converter. An optocoupler was used to close the loop between the input and the output circuits.

[1] A.Vazquez Carazo, “50 Years of piezoelectric transformers. Trends in the technology,” MRS –Proc, v. 785, Materials and Devices for Smart Systems, 2003, p 33-44. [2] C. Rosen, K. Fish, H. Rothenberg. “Electromechanical Transducer,” U.S. Patent No. 2,830,274, 1958. [3] C. A. Rosen, “Ceramic Transformers and Filters,” Proc. Electronics Comp. Symp., 1956, pp. 205-212. [4] H.W.Katz, Solid State Magnetics and Dielectric Devices, New York, John Wiley & Sons, 1959, Chapt. 5, pp. 170-232. [5] S. Kawashima, O.Ohnishi, H. Hakamata, S. Tagami, A.Fukuoka, T.Onoue and S. Hirose, “Third order longitudinal mode piezoelectric ceramic transformer and its application to high-voltage power inverter,” Proc. IEEE US Symp., 1994, pp. 525-530. [6] F.E. Bisogno, M.Radecker, A. Knoll, A. Vazquez Carazo, A. Riedlhammer, G. Deboy, N. Norvez, J.M. Pacas, “Comparison of resonant topologies for step-down applications using piezoelectric transformers,” IEEE 35th PESC04, 2004, pp. 2662-2667

Figure 10. 15W step down prototype circuit VI. CONCLUSIONS This paper introduces the piezoelectric transformer as a potential candidate to replace the magnetic transformers in applications requiring high power density, such as portable devices. The application of the technology is briefly introduced with a simplified case example. Design equations are described by performing fundamental approximation on the equivalent circuit of the input inverter circuit and the output load.

Abstract – This paper introduces a cutting-edge transformer technology – the piezoelectric transformer – currently considered as a potential candidate to replace magnetic transformers in resonant switching converters. Magnetic transformers are extensively used for providing step-up and step-down voltages while allowing input to output isolation in ac-dc and dc-dc converters. Even with the extensive use, this component is still the largest, heaviest, and magnetically noisiest component in the power conversion chain. The paper introduces the reader in the piezoelectric transformer technology and proposes a simplified dc/dc converter case scenario to illustrate the different steps involved in applying this technology.

Furthermore, the technology development was accelerated thanks to the market demand of alternative products to magnetic transformers to be use in the backlighting of CCFL (cold cathode fluorescent lamps) for color liquid crystal displays (LCD). Currently, PTs are used in the high voltage backlighting inverter of laptop computers and flat-panel TV displays [4,5]. This type of PTs are so-called, “Rosen-type” PTs, since their structure follow the design envisioned by C.A. Rosen back in the 50s. INPUT ELECTRODES

OUTPUT ELECTRODE

I. INTRODUCTION Resonant dc/dc and ac/dc converters have attracted a great deal of attention over the last decade. Their ability to operate efficiently at high frequencies allows for considerable miniaturization of power supplies. When considering isolated topologies, the use of high frequencies wire-wound magnetic transformers is the most extended technology to provide step down and isolation between the primary and the secondary circuits. Recently, planar magnetic transformers have been introduced to replace standard wire-wounded transformers and provide lower-profile converters. In spite of this technological advancement, the transformer continues to be the largest and bulkiest component in dc/dc and ac/dc isolated converters. From a component perspective, the use of higher power density piezoelectric transformers (PTs) may allow a breakthrough to the existing state of the art of transformer leading to a more compact, lower profile converter designs. The first studies [1] on PTs took place in the late 20s and early 30s with the use of single crystal materials. In the 1945, B. Jaffe announced the discovery of a high performance ceramic material, called lead zirconia titanate (hereafter PZT), which had exceptional properties. Soon after the development of the PZT, Charles A. Rosen et al. applied for the first patent on a PT using the new material [2,3]. Today, C.A. Rosen is considered the “father” of the PT technology. Multiple applications were targeted during the 70s and 80s for piezoelectric transformers. However, initially the technology suffered from serious challenges related to: i) immature materials fabrication technology ; (ii) mechanical reliability problems at the nodal point; (iii) under-developed driving circuits. These problems created a barrier for technological advancement till the early 90’s. The 90’s saw several Japanese companies amending a revision in the concept of PT taking advantage the improvements in novel piezoelectric materials, more reliable manufacturing technologies like multilayer co-fired processes, new concepts in integrated circuits and housing solutions for the PTs.

Figure 1. “Rosen-type” piezoelectric transformers used in the LCD screen of laptop computers In this LCD backlighting application, PTs offer several advantages compared to magnetic transformers, such as: • Inherent high gain at no load, that provides the lamp ignition voltage. • Load dependent gain that avoids the use of the ballast capacitor in series with the lamp. • Absence of leakage magnetic field. • High Q factor, that gives low distorted sinusoidal lamp current waveform. • Small size and weight. • High reliability due to the absence of a high voltage secondary winding. Recently, the interest on PT technology has been extended to ac/dc and dc/dc power converter applications typically requiring higher power requirements and step -down capability compared to backlighting inverters. It is difficult in using the Rosen-type PTs for step -down voltage applications by simply reversing the input and output terminal connections. When the terminal connections are reversed, the driving electrical field becomes very small

because the transducer input part (output part when used in LCD applications) is too long. In order to allow the use of piezoelectric transformer technology to dc/dc and ac/dc converters new transformer designs have been proposed in the last years. These transformers must provide higher power output along with low output impedance. Since 1996, Face Electronics, LC has developed and patented different types of piezoelectric transformers with input and output multilayer topology thus allowing the adaptation of the input and output impedance to the different requirements of step -down applications. Some of these designs have already demonstrated to reach 20-50W with power densities in the order of 25W/cc. This represents over 6 times increase in power capabilities as compared to its magnetic counter parts. With these properties, piezoelectric technology is currently being envisioned as a potential candidate to replace magnetic transformers in certain low and medium power level applications, meeting the technical demands required for OEMs across all application ac/dc and dc/dc groups, including a) lower profiles, b) smaller footprints, c) high efficiency, and d) higher power densities. The purpose of this paper is to introduce this family of new transformers and present a simplified design case analysis for the development of a 15W regulated dc/dc converter operated under input voltages of 25 to 42 V to familiarize the reader with some of the application-related aspects of this technology. II. TRANSONER. CONSTRUCTION AND OPERATION PRINCIPLE Piezoelectric transformers, like magnetic devices, are basically energy converters. A magnetic transformer operates by converting electrical input to magnetic energy and then reconverting the magnetic energy back to electrical output. A piezoelectric transformer has an analogous operating mechanism. It converts an electrical input into mechanical energy and subsequently reconverts this mechanical energy back to an electrical output. In the piezoelectric transformer, an input and an output section made of piezoelectric ceramic material are placed in perfect mechanical contact with each other (through bonding or by integrating both sections in the same mechanical body). When an alternating voltage is applied to the input section with a frequency equal to one of the mechanical resonances of the transformer, the input section – due to the inverse piezoelectric effect - will vibrate creating an ultrasonic standing wave on the body of the transformer. This standing wave excites mechanically the output section which, due to the direct piezoelectric effect, will generate an electrical output. In this way, the input section acts as an actuator while the output section acts as a transducer. The dimensions of input and output sections as well as certain parameters of the piezoelectric material determine the transformer ratio between the input and output voltage as well as the efficiency of the device. Piezoelectric transformers do not require winding electrodes and all the entire piece – made of non-magnetic ceramic material - is used in the acoustic transfer. This design

reduces weight and size and allows the achievement of higher power densities. A typical design of a piezoelectric transformer manufactured and patented by Face Electronics is shown in Figure 2, and is commercially know as “Transoner®”. Transoner refers to a radially-operated piezoelectric transformer having a multilayer structure for the input and output sections. Transoner operates in the first fundamental radialextensional vibration mode. Different configurations are available. Figure 2 shows a topology including an input and an output section. Other topologies having the input layers divided in two parts sandwiching the output section have been also suggested to provide a symmetric structure. This allows the suppression of the spurious bending modes which may occur in a non-symmetrical structure. In the design illustrated in Figure 2, the input section includes a single layer polarized in the thickness direction. In contrast, the output part consists of many stacked thin piezoelectric ceramic layers, and the layers have alternating inverse polarizations to each other in the thickness direction. This allows increasing the transformer output capacitance and thus allows its operation to low output loads and step -down applications. One insulation layers is set between the input and output parts to isolate them electrically. The insulation layer has a slightly larger diameter compared to the PT body to enlarge the creepage distance between the input and the output sections.

INPUT

OUTPUT

Figure 2. Configuration of the laminated radial-type piezoelectric transformer, Transoner. When an AC voltage is applied to the input parts of the transformer of Figure 1, at a frequency that generates the fundamental radial-extensional vibration mode, the input parts oscillate in fundamental radial-extensional vibration mode, which depends upon the electromechanical coupling factor kr. The vibrations are simultaneously transmitted to the output part, which converts them into electric energy by the direct piezoelectric effect, which depends on the electromechanical coupling factor k p. Generally, k p of a piezoelectric ceramic material is approximately twice as high as the electromechanical coupling factor k 31 of longitudinal vibrations, leading to higher energy conversion efficiency of the radial vibration mode than that of the longitudinal vibration mode. Therefore, the power transmission efficiency of the piezoelectric transformer is higher, so that the volume of the transformer can be further reduced. Piezoelectric transformers are narrow band devices. This means that the transformer have to be operated in a frequency range close to the resonance frequency. In this operation, the driving circuit design must take into account that PTs are frequency and load dependent devices. Under these conditions, the PT operates in a window having the higher efficiency condition. Practically, the selected driving frequency is

chosen slightly above the resonant frequency. There are two main reasons for this selection: (i) the maximum efficiency is achieved at a frequency slightly higher than the resonant frequency and (ii) the control of the transformer is easier in the inductive window (above resonance). The frequency and load dependence can be easily evaluated by plotting the voltage gain against frequency curves for different output loads, as shown in Figure 3. 0.6

0.5 100 Ω

Gain

0.4

0.3

0.2

characteristics of the device and allows the manufacturer to relate the required electrical specifications to the physical dimensions of the device. In this circuit, Cd1 and Cd2 are the input and output damped capacitances, A1 and A2 are the socalled force factors for the input and output parts, and Lm , cm and rm are the equivalent mass, equivalent compliance, and equivalent mechanical resistance. The force factor represents the electrical-to-mechanical transformation ratio for each section (input and output). The intensity im indicated in the circuit is also called motional current and in a piezoelectric transformer is equal to the vibration velocity of the sample. The vibration velocity is an essential parameter during the design of the transformer. The maximum vibration velocity we can drive our sample will allow the determination of the maximum power capabilities.

60 Ω

rm

1:A1

10 Ω

cm

A2 :1 i 2 V2,PT

im

V1,PT 20 Ω

Lm

Cd2

Cd1

0.1

(a) 0

R 120

130

140

150

160

L

C

170

Frequency [kHz]

i2 V2,PT

i

V1,PT

Figure 3. Frequency and load dependence of a step-down piezoelectric transformer

1:N

Cd2

Cd1 (b)

Due to this double dependence, transformer ratio and efficiency are strongly dependent on frequency control, load fluctuation and input voltage variations. Consequently, in order to ensure stable operation of the PT, the driving circuit has to correct the influences of these electrical variables. The implementation of a compact and reliable controlling circuit using discrete components is complex and, thus has discouraged many researchers from entering this field. Currently, different IC makers have developed integrated circuit solutions which include frequency tracking control to achieve for input voltage and load regulation, and internally built protection circuitry, among other features Although this ICs have been, so far, focusing in the high-voltage backlighting applications, some IC-makers, case of Infineon in collaboration with Face Electronics [6], are currently developing ICs for ac/dc and dc/dc power conversion applications. III. EQUIVALENT CIRCUIT The integration of a piezoelectric transformer in the design of a power converter can be made by considering its lumped equivalent circuit. For a given off-the-shelf transformer, the equivalent circuit is typically given by the manufactured or can be easily determined using an impedance analyzer. However, in general, the application engineer will require a specific customized PT design to be manufactured in order to meet the specifications of a given converter design. Figure 4 includes two typical equivalent circuit used in the process of designing and using a piezoelectric transformer. The circuit of Figure 4.a. is typically used by the PT manufacturer during the design of the piezoelectric transformer. The advantage of this transformer is that it separates the two electrical ports and the mechanical

Figure 4. Lumped constant equivalent circuits. The circuit of Figure 4.b is more often provided in publications and by the transformer manufacturer to be used by the dc/dc or ac/dc application engineer. This second circuit is useful to perform simulations and circuit analysis during the design process of the converter. Its use will be illustrated in the following case study. In the circuit of Figure 4.b, the components of the resonant part of Figure 4.a. have been referred to the primary side using the following relationships:

R=

rm L A ; C = cm ⋅ A12 ; L = m2 ; N = 1 2 A A A1 2 1

(1)

IV. CASE STUDY: 15W DC/DC HALF-BRIDGE PIEZOCONVERTER The design of a piezoelectric-based converter involves several steps, similar to those related to the design of a conventional magnetic-based isolated converter, including: i) defining the design specifications, ii) selection of the converter topology, iii) design of the transformer, iv) control strategy and regulation including close loop, v) prototype development, vi) evaluation of performances. Each of these steps may require a detailed evaluation of the specific application. In this case study, we consider a first approach to the steps associated to the components selection and transformer design for a specific converter design. Due to the limit of this paper, we will not be able to consider in detail the issues related to the driving strategy and the feedback control. Comments on these matters will be provided during the presentation of this paper.

Piezoelectric Transformer

VGS1 Ls

VinDC VGS2

VLr

R

C

Vout,DC

L Lo

C d1 V 1_PT

RESR1

Co

Cd 2 V 2_PT

RL

Figure 5. Circuit diagram for the design of a piezoelectric-based DC-DC converter For the proposed case study, we have selected a Class-D (half-bridge) topology using a full-bridge diode-based rectifier to meet the following specifications: Vin = 25 V – 48 V Vout = 6 V; Iout = 2.5 A (Pout = 15 W)

From the theoretical waveform of this circuit and as a first approach, the ZVS operation can be achieved naturally when the switching frequency fs is greater than the resonant frequency of Ls-Cd1, fo, where:

f 0,Ls − Cd 1 =

1 TON

VGS1

Figure 5 shows the basic circuit configuration of the halfbridge piezoelectric-based DC-DC converter.

t VGS2

First Step: AC equivalent circuit of the input. The input half-bridge inverter is composed of two bi-directional twoquadrant switches S1 and S2. The switches consist of transistors and internally built anti-parallel diodes (usually body diodes of metal-oxide-semiconductors field-effect transistors (MOSFET)) that can conduct current in either direction. The active power switches of the inverter are gated by two complementary signals, VGS1 and VGS2, with a short dead time. Neglecting the dead time, the duty-ratio of VGS1 is D when the VGS2 is (1-D). The asymmetrical square-wave voltage, V Lr, illustrated in Figure 6, can be represented by the following function: V , for 0 < ωt ≤ ωt ON (2) v Lr = in,DC 0 , for ωt ON < ωt ≤ 2π This voltage V Lr can be represented by the following Fourier series: 2V V Lr (t ) = D ⋅ V DC + ∑ DC sin(nπD ) ⋅ sin(nωt + π + θ n ) (3) n nπ where sin (2nπ D ) θ n = tan −1 1 − cos (2nπ D )

(4)

where D = TON T s is the duty cycle of the high-side switch of the half-bridge amplifier. The Ls-Cd1 resonant circuit converts the square-wave voltage VDS2 into a sinusoidal output voltage driving the piezoelectric transformer if the loaded quality factor QL is high. The low-pass filter created by Ls is needed to prevent the harmonic contents from entering into the PTs and is regarded as an input matching network. The inductor Ls works not only as a low-pass filter of the voltage VLr but also as an important element which affects on the resonant characteristics and the ZVS operation of the converter. Therefore, the value of Ls must be selected to be an optimum value. Some guidelines will be given later in this paper.

(5)

2 ⋅ π ⋅ L s ⋅ C d1

0

TON

T 0

t VDS = VLr t iLs

t

V1,PT t

Figure 6. Typical waveforms for the input half-bridge inverter With a high quality factor of the load resonant circuit (intrinsically characteristic in piezoelectric transformers), almost all the harmonic contents, as well as the DC term, will be filtered out by the resonant circuit. Thus, only the fundamental current of the switching frequency is present in the load resonant inverter. Therefore, an approximate analysis can be made using phasor representation of the fundamental harmonic on the switching voltage, V Lr, which is at the inverter switching frequency, fs. The equivalent circuit of the load resonant inverter for the fundamental approximation is shown in Figure 7. V Lr (1) (t )

Ls V1 ,PT VLr(1)

R

C

L

RL

Cd1 R ESR1

Cd2

V2,PT

Figure 7. Equivalent circuit of the converter with the inverter reduced to an equivalent AC power supply VLr(1) is the RMS value of the fundamental component of VLr and can be expressed as follows:

VLr (1) = RMS

2 ⋅ sin (πD ) ⋅ Vin, DC = 0 .4502 ⋅ sin (πD )⋅ Vin ,DC π

(6)

In order to provide enough dead time between the two gate drives and to enhance transient response performance, typically the maximum duty cycle is chosen around 0.45. The voltage transfer ratio, MSW, for the switching ClassD (half-bridge) inverter can then be expressed as: V Lr( 1), RMS 2 ⋅ sin(π D ) (7) M SW = = ≈ 0.4502 ⋅ sin(π D ) Vin, DC π Second Step: AC equivalent resistance of the output rectifier. The output voltage required to design the piezoelectric transformer, V2,PT, can be determined once the output rectifier topology is chosen. Once the rectifier-type is decided, an equivalent AC resistance can be applied to the output of the piezoelectric transformer to compute the effect of the output rectifier. The method of calculating the AC equivalent resistance is shown here for the diode-bridge rectifier circuit, which is the suggested topology for this example. Figure 7 shows the full-bridge rectifier circuit with a constant current load (having a large enough filtering inductance connected in series at the DC output of the rectifier) and the associated waveforms. IDC

Lo

V out,DC

I2 ,PT Co

V2 ,PT

V 2,PT

RL

V 2, PT

I2,PT

ID C

Pout,REC

PDC 1 (10) = 2 ⋅ V 2 ⋅ RF Pin,REC P2,PT 1 + F + V out,DC RL where VF is the forward voltage drop of a rectifying diode and RF is the conduction resistance of the diode. Reorganizing the terms and using I DC = VDC R L we obtain: 2 Vout,DC = ⋅V 2, PT − 2 ⋅ VF − 2 ⋅ RF ⋅ I DC = π (11) V out,DC 2⋅ 2 = ⋅V 2 ,PT − 2 ⋅V F − 2 ⋅ R F ⋅ π RL ( RMS ) This equation can be also written in terms of the voltage transfer function of the rectifier: V out , DC (12) 2⋅ 2 η REC =

M REC =

V2

2 , PT ( RMS )

REQ

=

S

2π 1 π ⋅ ∫ I DC ⋅ V2, PT ⋅ sin ω s t + ∫ − I DC ⋅ V2 , PT ⋅ sin ω s t = 2 ⋅ π 0 π 2 ⋅ V2 , PT ⋅ I DC

(8)

π

Considering the forward voltage drop of the diodes, VF, and the losses for conduction in the forward resistance of the diodes, RF, and taking ?REC as the efficiency of the rectifier, the balance of input to output power is: P2,PT = PD C + PDrop_ Diodoes + PRF _ Diodes ⇒ 2 ⋅ V2 ,PT ⋅ I DC

2 = V DC ⋅ I DC + 2 ⋅V F ⋅ I DC + 2 ⋅ R F ⋅ I DC π Thus, the rectifier efficiency is:

=

(9)

2 ⋅ V2, PT ⋅ I DC

(13)

π

Ls

The AC equivalent resistance, REQ, can be obtained by balancing the input and output powers in the rectifier. The input power in the rectifier, P2,PT, can be obtained as:

=

2 ⋅ VF 2 ⋅ RF π ⋅ 1 + + V out , DC RL

From this equation, the AC equivalent resistance of the full-bridge rectifier becomes: 2 ⋅V F 2 ⋅ R F π2 (14) REQ = ⋅ RL ⋅ 1 + + 8 VDC RL Similar approach can be followed with other types of rectifiers such as synchronous rectifiers or center tapped rectifiers. Of particular interests are synchronous rectifiers, a type of rectifier that optimizes the efficiency of the rectifier and thus the DC-DC converter. Introducing the result given in equations (6) and (14), the equivalent circuit of Figure 5 can be now be evaluated in simplified way provided in the following Figure 8:

Figure 7. Full-bridge rectifier configuration and waveforms used to determine the AC equivalent resistance

1 T ⋅ ∫ i2, PT (t) ⋅ v 2 , PT (t ) ⋅ dt = TS 0

=

Comparing the PSEC,PT with the output power of an AC equivalent resistance, REQ, we have:

-I DC

P2, PT =

V 2, RMS

=

R

V1,PT VLr(1) V Lr (1 ) (t ) =

C

L

V2,PT

Cd1 R ESR1

Cd2

R EQ

2 ⋅ Vin ⋅ sin(πD ) ⋅ sin (ωt ) π

Figure 8. Simplified equivalent circuit for the converter including the first harmonic voltage source for the half-bridge input inverter and the AC equivalent load for the rectifier The simplified circuit of Figure 8 can be used to design or select the parameters of the transformer required to meet the DC/DC converter specifications. In this case scenario, the transformer has to be design such as it meets the output voltage requirement VDC = 6V for the minimum input voltage and the minimum equivalent resistance expected. In our case, the maximum load will be Pout,DC = 15W under Vout,DC = 6 V. This gives an output load of RL = 2.4 Ω. Assuming the forward drop in the output diodes as VF = 0.5V and RF = 0.025 Ω, then the equivalent load and the output voltage required in the secondary of the PT, V2,PT will be:

2 ⋅V F 2 ⋅ RF π2 ⋅ RL ⋅ 1 + + 8 VDC RL

V 2 , PT = ( RMS )

= 3.52Ω

V o u t, DC ⋅ V o u t, DC + 2 ⋅V F + 2 ⋅ R F ⋅ RL 2⋅ 2 π

(15) = 7 .92V

(16)

Note, that this will be the “minimum” voltage that will ensure that we can meet regulated 6V in the output. It is a good practice to allow an “extra room” for the voltage in the secondary. Thus, in this example we consider the secondary requirement for the PT as V2,PT(rms) = 9V. As mentioned above, the transformer parameters and transformer ratio have to be selected to meet this output voltage specifications under minimum input DC voltage, Vin,DC, conditions. In our specifications this is given for an input voltage of V in,DC = 25 V. Third Step: Determination of the equivalent circuit. The determination of the components of the equivalent circuit typically involves a reiterative process where dimensions and material properties are considered to meet the input and output voltage requirements. This process is typically undertaken by the manufacturer of the piezoelectric transformer once the input and output voltage in the transformer as well as the power requirements are known and involves the circuit of Figure 4.a. The detailed calculation of the parameters of the transformer is far beyond the limits of this paper. However, we will introduce some of the initial steps in this calculation to familiarize the reader. The first step is to calculate the output section to ensure that the transformer will operate at maximum efficiency under maximum load conditions (REQ = 3.52 Ω). This condition is achieved when the output capacitance of the piezoelectric transformer equivalent circuit, Cd2, is selected as: 1 (17) Cd 2 = ω res ⋅ R EQ Once the value of Cd2 is known, the number of secondary layers n2 and the force factor of the secondary section, A2, are obtained using the following equations: A2 =

n out ⋅ 2π ⋅ r ⋅ d 31,out

im = v =

(18)

s11E ⋅ (1 − σ )

Pout,DC ⋅ 2 ⋅ ω res ⋅ C d 2

(19) A2 where v is the vibration velocity, d31,out is the piezoelectric coefficient for the output section, s11E is the mechanical compliance, and σ is the Poisson ratio, A2 is the force factor for the output section, and v is the maximum radial vibration velocity admissible for the material considered. The value of the maximum vibration velocity is selected such as the temperature increase of the transformer does not exceed 30 oC. In a first approximation, for standard PZT materials v max can be taken as 0.15-0.20 m/s for a first design iteration. The design of the output section is completed by determining the thickness of each layer and the total thickness, as follows:

(

) π ⋅ rC ⋅ n

T t 2,layer = ε 33 ⋅ 1 − k 2p,out ⋅

t 2 = t2 ,layer ⋅ n out

(21)

Once the output section is defined, the design of the input layer involves a reiterative process where the value of the input inductance plays a significant role to determine the input voltage in the transformer and thus the transformation ration. In a first iteration, the volume of the input and output section can be selected as equals. Once the volume is defined, the mass of the transformer will be known and thus, the parameters of the motional resonant tank of Figure 4.a., Lm, Rm and Cm, can be defined. Finally, the value of A1 is defined to ensure the required transformation ratio to meet the output voltage for the minimum input voltage. The value of the capacitance Cd1 should be confirmed to ensure the ZVS with the input inductance while allowing the inductance to have a small package for the expected input current. Fourth Step: Series inductor for driving the PT. As briefly indicated above, the external series inductor, Ls, and the PT input capacitance, Cd1, form a low-pass filter for the squarelike input voltage VLr. The Ls-Cd1 filter formed by these components should pass the resonant frequency, required by the piezoelectric transformer, yet attenuate higher harmonic components, so the input voltage driving the PT become sinusoidal. An inductor value that is too low (very high Ls-Cd1 resonant frequency) will result in non-sinusoidal primary waveforms since higher order harmonics are allowed through the filter. A low value also allows excess circulating currents, impacting the efficiency. An inductor value that results in the Ls-Cd1 resonant frequency too close to the resonant frequency of the piezoelectric transformer (Case 1 of Fig. 9) will cause interference, making control of the primary voltage difficult. The interference occurs since the gain of the Ls-Cd1 tank depends heavily on load in this region of operation. Finally, an inductor value that is too large (Case 2 in Fig. 9) will result in an attenuation of the input voltage, increasing the gain requirements of the PT and/or the system. In general, the choice of the series inductor requires bench measurements and modeling of the resonant circuit. Figure 9 shows three different inductance values considered in a specific converter design as illustrative example. The best solution in this case (Case 3 of Figure 9) was to allow around 25kHz between the PT resonant frequency and the Ls-Cd1 resonance frequency: 18

Voltage Transfer [Vin_PT/Vout_PT]

REQ =

f PT =

16

1

f 0,Ls −C d1 =

2 ⋅π ⋅ L ⋅C

14

1 2⋅ π ⋅ L S ⋅ Cd1

12 10

Case 1 Ls=47uH

8 6

Case 3 Ls=22uH

4

Case 2 Ls=150uH

2 0 3

4

5

6

7

8

9

Frequency [Hz]

10

11

12 4

x 10

2

d2

out

(20)

Figure 9. Effect of the series Ls in the resonance and voltagetransfer response

V. FINAL COMMENTS

V. REFERENCES

In this case study, we have mainly focused our attention in the design process to select the main components of the resonant tank. Due to the extension of this paper, other issues have not been included in here. The control strategy of the piezoelectric transformer such as voltage regulation is an additional issue that will be discussed during the presentation of this paper. Figure 10 shows a prototype board (one sidePCB) with all the components required for a piezoelectricbased dc/dc converter. An optocoupler was used to close the loop between the input and the output circuits.

[1] A.Vazquez Carazo, “50 Years of piezoelectric transformers. Trends in the technology,” MRS –Proc, v. 785, Materials and Devices for Smart Systems, 2003, p 33-44. [2] C. Rosen, K. Fish, H. Rothenberg. “Electromechanical Transducer,” U.S. Patent No. 2,830,274, 1958. [3] C. A. Rosen, “Ceramic Transformers and Filters,” Proc. Electronics Comp. Symp., 1956, pp. 205-212. [4] H.W.Katz, Solid State Magnetics and Dielectric Devices, New York, John Wiley & Sons, 1959, Chapt. 5, pp. 170-232. [5] S. Kawashima, O.Ohnishi, H. Hakamata, S. Tagami, A.Fukuoka, T.Onoue and S. Hirose, “Third order longitudinal mode piezoelectric ceramic transformer and its application to high-voltage power inverter,” Proc. IEEE US Symp., 1994, pp. 525-530. [6] F.E. Bisogno, M.Radecker, A. Knoll, A. Vazquez Carazo, A. Riedlhammer, G. Deboy, N. Norvez, J.M. Pacas, “Comparison of resonant topologies for step-down applications using piezoelectric transformers,” IEEE 35th PESC04, 2004, pp. 2662-2667

Figure 10. 15W step down prototype circuit VI. CONCLUSIONS This paper introduces the piezoelectric transformer as a potential candidate to replace the magnetic transformers in applications requiring high power density, such as portable devices. The application of the technology is briefly introduced with a simplified case example. Design equations are described by performing fundamental approximation on the equivalent circuit of the input inverter circuit and the output load.