## 3 Low-Power Electronic Converters
### Switching DC/DC Regulators  
To reduce output voltage variations due to input voltage changes or load current fluctuations, voltage regulators or so-called _DC/DC_ (or _DC-DC_) _regulators_ or _converters_ are often connected after the rectifiers. In general, voltage regulators can be thought of as controllable series resistances that are connected in series to the load. More specifically, voltage regulators are electronic devices designed to regulate the DC power of the input source after the rectifier by the methods of pulse-width modulation (PWM) or frequency modulation (FM). Regardless of the type of modulation used, the output voltage can be of a value greater or less than the input voltage after the rectifier. The regulators for which the output voltage level is less than the input voltage are called _buck regulators_ (or step-down converters), and the regulators for which the output voltage level is greater than the input voltage are called _boost regulators_ or (or step-up converters) [64; 65; 66; 52]. In the realization of control circuits for low-power stand-alone regulators designed to extract electrical energy from piezoelectric generators, the regulation of DC power using PWM is used relatively more often. Implementing control circuits with the application of PWM allows lower power dissipation with a smaller number of passive and active components and at a lower frequency of the pulse oscillator. In some cases, the input AC voltage obtained from the piezoelectric generator is also used as a rectangular waveform of the signal for controlling the duty cycle, i.e., the intervals during which the series resistance has a small and large value are obtained by an additional latching circuit. A functional diagram [46] of a voltage rectifier with a DC-DC converter or PSD intended for extracting electrical energy from piezoelectric generators is given in Figure 20. As can be seen in Figure 21, after the rectifier or voltage multiplier, the series-controlled resistance can be replaced by a switching circuit that uses a bipolar or MOS transistor operating as an electronic switch. This switch produces a pulsating voltage whose average value varies from zero to approximately the amplitude of the input voltage depending on the duty cycle \(\delta\). After the switch, a low-pass filter is usually included, which reduces the ripples of the output voltage. The PWM controller is an electronic device that compares the output voltage \(v_{o}\) with a set reference voltage \(V_{ref}\) and produces a control pulse signal with a variable duty cycle. For example, if \(v_{o}<V_{ref}\), then a signal with a larger duty cycle is received at the output terminal of the regulator, i.e., the time interval during which the switch is closed increases. In this case, the frequency \(f\) of the control pulse signal remains constant. In cases where the input voltage is used as feedback (dashed line) to change the duty cycle, the output DC voltage forms the supply voltage of the active components in the PWM controller. One of the basic electrical parameters of the DC-DC converter is the _overall electrical energy efficiency_ (or power conversion efficiency), which can be calculated based on the measured values of the average currents at certain nodes:  
\[\eta=\frac{P_{out}}{P_{in}}\times 100\%, \tag{21}\]where \(P_{in}\) is the power of the extracted input signal and \(P_{out}=P_{OS}-P_{C}\) is the output power of the circuit (\(P_{OS}\) is the output power after the low-pass filter and \(P_{C}\) is the power consumption of the PWM controller). The losses in the switching circuit and the low-pass filter as well as in the PWM controller versus the power received by the piezoelectric element can be determined by \(P_{SW}/P_{in}\) and \(P_{C}/P_{in}\), respectively. Additionally, for the DC-DC converter, the efficiency of the circuit configuration used is evaluated by a figure of merit (FoM).