# Improved Performance of Li-ion Polymer Batteries Through Improved Pulse Charging Algorithm
## 2 Determination of Optimal Pulse Charging Parameters
### Pulse Charging Parameters  
Every pulse charger has the following parameters that need to be controlled in order to reap the benefits of pulse charging. These parameters are related as shown in Equation (1), where \(f\) is frequency, \(I_{peak}\) is the peak charge current amplitude, \(T_{on}\) is the time the battery is being charged, \(I_{avg}\) is the average charge current, and \(D\) is the duty cycle of the pulses.  
\[I_{avg}=I_{peak}\cdot f\cdot T_{on} \tag{1}\]  
Figure 3 shows the role of these parameters in a simplified schematic of a pulse charger. \(V_{IN,adapter,USB}\) is the input to the charger from an AC adapter or a universal serial bus (USB) port, and the transistor, _Switch_, switches on and off, pulsating the charge current into the battery depending on the frequency and duty cycle of the control block. \(I_{peak}\) can be controlled depending on the user application and specifications of the batteries.  
The battery charge and energy efficiencies are estimated as follows  
\[Eff_{CE}=100*\frac{\int_{0}^{I_{dis}}I_{dis}dt}{\int_{0}^{I_{ch}}I_{dv}dt} \tag{2}\]  
\[Eff_{EE}=100*\frac{\int_{0}^{I_{dis}}V_{dis}I_{dis}dt}{\int_{0}^{I_{ch}}V_{ch}I _{dv}dt} \tag{3}\]  
respectively, where \(Eff_{CE}\) is the battery charge efficiency, \(Eff_{EE}\) is the battery energy efficiency, \(t_{dis}\) is the discharge time, \(t_{ch}\) is the charge time, \(I_{dis}\) is the discharge current, \(I_{ch}\) is the charge time, and \(V_{dis}\) and \(V_{ch}\) are the average discharge and charge voltages.  
In previous works [26; 27; 31; 32], the different combination of these parameters, i.e., \(I_{peak},\ D\), and \(f\), resulted in different performances of the pulse charger. It was therefore necessary to determine which of these parameters and their respective values resulted in the best battery performance. The investigation of which combinations resulted in the best performance required a large number of one-variable-at-a time experiments, therefore making the process time consuming and costly. Orthogonal arrays can be used to solve the problem of large experimental domain size. Orthogonal arrays (OA) represent a design of experiment (DoE) technique that seeks to give comparable results to full factorial designs. Taguchi OA, which was developed by [PERSON] [35], is a robust experimental design method. It reduces  
Figure 3: General overview of a pulse charger.  
the number of experiments but ensures the results are comparable to fully factorial designs. Taguchi OA design process consists of tolerance design, parameter design, and system design. Tolerance design takes into account the random parameters that can influence the design of a system, an example can be the random manufacturing variations across different batteries under test, while parameter design is identifying the various factors that impact the design of the system. The parameters that can be controlled, in this case, can be duty cycle or frequency of the charge current. System design considers the design of a circuit, model, or process, by understanding what is expected. In this context, the battery charger is the system.