## 3 Theoretical Analysis of Proposed Smart Home Control System
### Design of VLC LED Lightbulb  
In our proposed system, the core hardware infrastructure is made up of the VLC LED lightbulbs which serve as beacons and generate the VLC signals. Considering that the typical ceiling height of housing is around 3 m and suitable illumination intensity needs to be more than 300 lx, the VLC link distance should cover this range and the total output power of the lightbulb must provide sufficient illumination for lighting. Furthermore, most VLC-enabled light sources require an external modulator, which is inconvenient for installation for standard ceiling light sockets. To meet the above requirements, our proposed solution is shown in Figure 3. The proposed driverless VLC lightbulb consists of four parts: an AC-DC converter circuit, a DC-DC converter circuit, a Bluetooth Low Energy (BLE) control circuit [33], and 24 LEDs connected in series. In the AC-DC converter circuit, a resistor-capacitor (RC) parallel circuit is connected in series with a bridge rectifier, and the impedance of capacitor C1 can be employed as a voltage divider to decrease the large AC input voltage down to the desired output voltage for supplying loads. The resistor R1 connected in parallel with C1 is the bleeder resistor, which helps to neutralize the remaining charges in the capacitors during the power-off state, while they can be treated as open circuits during the power-on state, guaranteeing less power waste. The capacitance of C1 can be determined using the following equation:  
\[\mathrm{X_{c}}=\frac{1}{(2\pi\mathrm{fC})} \tag{1}\]  
where \(\mathrm{X_{c}}\) is the capacitive reactance of capacitor C1, C is the capacitance and f is the frequency of AC input voltage. The required value of \(\mathrm{X_{c}}\) for dividing the input voltage can be determined as follows:  
\[\mathrm{I_{LED}}=\frac{\mathrm{V_{total}}}{\mathrm{X_{c}}}, \tag{2}\]  
where \(\mathrm{V_{total}}\) is the decrease value of input 220 V AC voltage using the voltage divider and is equal to 148 V, and \(\mathrm{I_{LED}}\) is the driving current of the LED string and is directly provided by the LED datasheet as equal to 130 mA. Since the target electric power of this lightbulb is 10 W and the turn-on voltage of each LED is 3 V, the total number of LEDs required can be calculated by the following equation:  
\[\mathrm{P_{LED}}=\mathrm{N_{LED}}\times\mathrm{V_{LED}}\times\mathrm{I_{i,R}}, \tag{3}\]  
Figure 2: Architecture of proposed smart home control system. where P\({}_{\text{LED}}\) is the target electric power of this lightbulb and is equal to 10 W, and V\({}_{\text{LED}}\) is the 3 V supply voltage of each LED. Therefore, the total number of required LEDs is 24. The bridge rectifier converts the decreased AC input voltage to a 72 V DC output, and the following RC filter connected in parallel with the rectifier smooths the ripple of this 72 V output voltage which is utilized to supply both the LED series and the subsequent control block. Therefore, the calculated value of C1 is around 2.7 uF for decreasing the 220 V AV input voltage to 72 V. The following RC filter connected in parallel with the rectifier smooths the ripple of this 72 V output voltage. This output is then supplied to both the LED string and the VLC control module. The DC-DC converter circuit and BLE control circuit constitute a control block realizing the function of a normal external modulator, but with a more compact scale that can be integrated into the shell of a lightbulb. In the DC-DC converter circuit, the first low dropout regulator (LDO) decreases the 72 V DC input voltage to 5 V and supplies the pre-driver with resistors R3 and R4 serving as an output voltage controller. The second LDO converts 5 V to 3.3 V DC voltage and guarantees that the BLE module works at the proper voltage. Capacitors C3, C4, and C5 help to smooth input and output DC voltage. The BLE control circuit contains a pre-driver, BLE module, and high-threshold power MOSFET.