# Regulated Power Supply with High Power Factor for Hyperspectral Imaging Applications
## 2 Background Concepts
### Power Supply  
The main purpose of a power supply is to provide a voltage value suitable for the operation of any device. To this end, it converts the alternating current input from the network into a continuous (or direct) voltage. This process consists of several stages: _transformation_, _rectification_, _filtering_, and _regulation_. There are mainly two types of power supplies: _linear_ (Figure 2a) or _switched_ (Figure 2b).  
A linear power supply (LPS) is a type of power supply that rectifies an alternating current (AC) signal and adjusts its output voltage. It operates by transforming the mains voltage to a lower, desired level using a transformer. This transformer is connected to the mains supply and provides a different output voltage suitable for the intended application. In contrast, a switched power supply directly rectifies the mains voltage and then changes it, usually reducing it, using a transformer switched by switches operating in cut-off or saturation mode.  
Each power supply consists of an AC/DC transformation stage based on a full wave rectifier bridge. As mentioned in the previous section, non-linear loads cause harmonic distortion. Rectifiers are an example of this and produce the following adverse harmonic effects:  
* Increase in RMS value of the current circulating in the conductors and transformers since it forces the transformers and conductors to be over-dimensioned in order to prevent overheating;  
Figure 1: Real input voltage v(t) waveform (red line) affected by a rectified and filtered input current i(t) waveform (blue line).  
* Increase in losses due to the Joule effect;
* Decrease in the lifespan of transformers and conductors due to overheating;
* Interferences with telecommunications systems;
* Decrease in the power system efficiency;
* Discharge of distorted current into the electrical network, impairing the network's ability to supply energy.  
Hence, it is necessary to apply corrective measures to reduce this distortion and consequently improve the PF. In order to comply with current regulations [18] and to counteract the negative effects, a set of solutions should be addressed. A possible solution consists of using semiconductor components, such as transistors (\(Q\)) and diodes (\(D\)), in addition to passive elements, such as resistors (\(R\)), coils (\(L\)), and capacitors (\(C\)). This solution is based on obtaining a current from the network with a sinusoidal or quasi-sinusoidal waveform. In our proposed solution, we employ a resistance emulator based on the model proposed by [PERSON], [PERSON], and [PERSON] [19], as presented in (9), where \(Rc\) is the resistance at the cold temperature \(Tc\) (assumed to be 300 K), and \(Th\) is the temperature of the tungsten filament (450 K in our case). This emulator is a DC/DC converter that, from the point of view of the electrical network side, emulates the behavior of a resistive load. This type of solution provides a PF very close to the maximum and thus a considerable reduction in the harmonic distortion of the input current signal.  
\[R_{h}=R_{c}\bigg{(}\frac{T_{h}}{T_{c}}\bigg{)}^{1.2285} \tag{9}\]