# Piezoelectric Transformers: An Historical Review
## 1 Historical Introduction
### 1990s-2000s: Commercial Introduction of PTs for CCFL Backlighting
The combination of the ZVS technique and the PT can reduce the capacitive turn-on loss due to the input capacitance of the PT, and achieve high efficiency. There are two main strategies to achieve ZVS in a PT-driven topology. First, and most common, the PT should present an inductive characteristic at the operating frequency. In order to achieve this, normally an inductor is connected in series with the PT. In this type of strategy, the PT can be driven at a fixed duty cycle of 0.5. A second approach to achieve ZVS is to use the PT without an external inductor (so-called \"inductor-less\" driving). In this case, a variable duty-cycle is required for the control signal to the Mosfets to achieve ZVS. Figure 10 shows some of the standard topologies [54] used to drive PTs using a series inductor, including push-pull [53], half-bridge and Class-E [57; 58; 59]. Inductor-less techniques is discussed in Section 1.6. Figure 9: Piezoelectric inverter used in Apple Powerbook 15” and 17” computer for LCD backlighting (courtesy of Micromechatronics, Inc., State College, PA, USA). (**a**) 5W piezoelectric transformer; (**b**) Assembled piezoelectric inverter. In order to ensure the ZVS condition and to maintain the stability of the converter under load and input voltage fluctuation, strategies for controlling the PTs were developed and integrated within ICs. The first control circuits were designed as fixed frequency oscillators near the resonant frequency. However, due to the high mechanical quality factor (Q), of the PT, changes in the resonant frequency associated with aging, temperature, load variation, or input voltage, could not be compensated for, negatively affecting the performance of the PT. Progressively, different control schemes have been developed to ensure the stability of the output voltage or current, as well as maximize the circuit efficiency under different operation conditions. Since PTs are frequency-dependent devices, a way to control the operation of the PT is to vary the frequency according to output load changes or to input voltage variations. One of the first control techniques introduced was the so-called \"frequency control,\" sometimes referred as PFM (pulse frequency modulation). Frequency control requires one or several feedback control loops. These feedback loops provide information about the output voltage (or current) variations so they can be appropriately regulated. Different companies such as Rohm (Tokyo, Japan (BA9785 [58], BA9802), Sanyo (Tokyo, Japan) (LA5663V), Texas Instrument (Dallas, TX, USA) (UCC3975 [59]), O2 Micro (Santa Clara, CA, USA) (OZ9913), and Maxim (Sunnyvale, CA, USA) (MAX8785), among others, have developed ICs integrating a combination of these strategies to provide full control of the PTs. There are several possibilities that have been proposed regarding the parameters to be measured to determine the frequency control, including:  
1. Frequency control by measuring the output voltage. 2. Frequency control by measuring the output current (Figure 11a). 3. Frequency control by measuring the phase difference between input voltage and current. 4. Frequency control by measuring the input to output phase difference (Figure 11b). Figure 11: Different tracking control schemes for piezoelectric transformers: (**a**) based on measuring the output current; (**b**) based on the input to output phase difference. In some applications, the use of a single frequency loop cannot ensure the complete control of the PT under large variations of the input voltage and/or the output load. When this happens, the frequency shift required in the transformer to adjust the output conditions may be so large that the efficiency of the PT will be significantly affected or/and the correct transformation ratio to achieve the expected values is not possible. In order to overcome these limitations, a second voltage feedback loop control is sometimes considered to extend the regulation range of the converter. The voltage feedback has been implemented in two basic ways.