# A Dual Stage Low Power Converter Driving for Piezoelectric Actuator Applied in Micro Mobile Robot
## 5 Experiment Realization
### Performance Optimization  
To optimize the parameters and improve circuit performance, energy efficiency optimization experiments of the DC/DC and DC/AC stages are conducted to understand the design tradeoffs. For the DC/DC step-up stage, four parameters, namely, magnetizing inductance, switching frequency, drive voltage, and output power, are considered as critical parameters that affect the efficiency of the circuit. Six flyback transformers with different magnetizing inductances are selected for the optimization test. In addition, switching frequency varies from 40 kHz to 200 kHz with 20 kHz steps. Within a drive voltage range of up to 160 V, the circuit changes from 20% load (0.1 W) to full load (0.5 W).  
Figure 16 depicts the efficiency variation of the flyback stage with different magnetizing inductances and switching frequencies at 60% load and 90 V drive voltage. When the switching frequency is constant, a large magnetizing inductance results in high conversion efficiency, because a large magnetizing inductance can reduce current swing, thereby decreasing hysteresis eddy losses.  
When magnetizing inductance is constant, switching frequency significantly affects conversion efficiency, as reflected in switching and iron losses. At low switching frequencies (\(<\)80 kHz), iron losses become dominant, due to the high magnetizing forces caused by a large current swing of the coupled inductors. A low switching frequency results in a small current swing, which reduces iron losses and improves system efficiency. However, MOSFET switching losses become dominant when operating at high switching frequencies (\(>\)80 kHz).  
Figure 17 shows that at 60% load operation and 90 V drive voltage, a maximum efficiency of 81.8% is detected with 60 uH magnetizing inductance at 100 kHz switching frequency.  
This figure illustrates how conversion efficiency varies with output power and drive voltage when switching frequency is 100 kHz and magnetizing inductance is 60 uH. Efficiency is measured under the condition that the output power range is 0.1-0.5 W and the drive voltage range is 40-160 V. At a  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Output Power (maximum)** & 500 mW \\ \hline
**Efficiency (maximum)** & 64.5\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Specific characteristics of the dual-stage circuit.  
Figure 16: Conversion efficiency of flyback stage vs. switching frequency and magnetizing inductance.  
low output power, parasitic MOSFET losses are dominant. When output power increases to a certain value, the conduction loss of a MOSFET and the copper loss of the transformer become dominant.  
Under the condition of a constant load, low drive voltages lead to large currents, with conduction losses being dominant. At high drive voltages, conduction losses will be reduced in correspondence to the smaller currents, thereby increasing efficiency. When drive voltage exceeds a certain value, iron losses will become dominant, because of the large current swing caused by large duty cycles. Maximum efficiency occurs at nearly 0.3 W output power and 90 V driving voltage with a switching frequency of 100 kHz and a magnetizing inductance of 60 \(\upmu\)H.  
In the half-bridge stage, a high-quality factor inductor can effectively reduce conduction loss. Simultaneously, an inductance with a small value is selected to increase resonance frequency. Similar to the flyback converter, the experimental results exhibit high efficiency (ranging from 70.1% to 80.3%) under the desired operation as illustrated in Figure 18.