# Analysis of AC DC Four-Switch Boost-Buck Battery Charger Converter for EV Applications
## 5 Simulation Results  
After the small-signal model analysis of the converter in the previous section, the controller can be designed to achieve the desired converter performance. In Figure 7, a showcase steady-state waveform in different operating modes is presented wherein Figure 7a illustrates the boost mode, while Figure 7b displays the buck-boost mode. Each plot includes the input voltage \(v_{g}(t)\), input current \(i_{g}(t)\), output voltage \(v_{o}(t)\), and output current \(i_{o}(t)\) at full load. In both modes, the regulation of the output voltage is achieved, demonstrating the converter's ability to maintain stability and the desired output voltage level. For both modes, the PFs are more than 0.98, with 4.7% THD for the buck mode, and 3.4% THD for the boost mode.  
In addition to the observed stable operation and satisfactory performance of the converter, it is important to note that there may still be underlying internal problems that require further investigation. Despite the min-phase characteristic of the transfer function relating the duty cycle to the input current transfer function, the system exhibits internal dynamics instability. This instability arises as an oscillation in the intermediate voltage \(v_{c}\) in both the boost and buck modes. The Bode plots for both modes illustrate the presence of a resonance frequency range between 1 kHz and 3 kHz. This resonance frequency is also evident in the time domain waveform, manifesting as internal dynamic oscillation. The internal dynamics instability can have significant implications for the converter's overall performance and stability. It can lead to issues such as output voltage fluctuations, reduced efficiency, and potential system damage. Managing and mitigating this instability is crucial to ensure the reliable and robust operation of the converter.  
Simulation results further support the presence of high-Q oscillations caused by an internal poorly damped resonance. Figure 8 illustrates the intermediate capacitor \(v_{c}(t)\) waveform in the boost mode, while Figure 9 depicts the waveform in the buck mode. Each figure includes two subplots: (a) showcasing the intermediate capacitor \(v_{c}(t)\) waveform, which reveals the high-Q oscillations behavior, and (b) displaying the normalized Fast Fourier Transform (FFT) of the intermediate voltage \(v_{c}(t)\), highlighting the resonance frequency that aligns with the Bode plot, where the high-Q oscillations' behavior occurs. These simulation results provide visual evidence of the internal poorly damped resonance with the observations made in the frequency domain analysis.  
Figure 7: Boost mode steady-state waveforms of output voltage \(v_{o}(t)\), output current \(i_{o}(t)\), input voltage \(v_{g}(t)\), and input current \(i_{g}(t)\) for the following: (a) Boost mode. (b) Buck mode.  
The presence of high-Q oscillations, as evident from the waveform and FFT analysis, emphasizes the importance of addressing these oscillations to ensure the stable and efficient operation of the converter. Efforts to address internal dynamic oscillation can involve various control techniques. One approach is to reduce the bandwidth by adjusting the control parameters to push the resonance frequency away from the closed-loop system bandwidth. This helps to dampen the oscillations and improve stability. Additionally, active control strategies, such as feedback control or adaptive control algorithms, can be implemented to actively regulate the intermediate voltage and suppress the internal dynamics oscillations. Another approach, which will be applied and analyzed in this work, is the introduction of a passive snubber RC circuit to damp this resonance.