Introduction to switching operations

Switching operations are compensation processes that occur immediately after switching in electrical networks. As the term „electrical circuit“ suggests, switching plays an important role in electrical engineering. Even electrical networks in which no switching takes place are commonly referred to as circuits.

Switches are used in a variety of applications, including power electronics, information technology, communications and control engineering. After each effective switching operation, balancing processes occur, which can sometimes cause desirable or undesirable effects.

This module focuses on the investigation of these compensation processes.

1 Settlement procedures

Compensation processes are generally processes in which a system strives to achieve a state of equilibrium after a disturbance.

A look at physics shows that balancing processes occur in many different ways in many areas. According to the second law of thermodynamics, a system always strives to achieve a state of equilibrium. Accordingly, every process can be regarded as a balancing process within the corresponding system boundaries. To a certain extent, switching processes can be described using analogies to other balancing processes.

Examples of compensation processes include heating a liquid, the oscillation of a pendulum, or the control process of a control loop.

2 Switching operations

Switching operations are defined as compensation operations immediately following switching. These are the main subject of the module, whereby ideal switches are always assumed.

Figure 2 shows an example of the time curve of a system variable \(s(t)\) (e.g. current or voltage) during a switching operation. For comparison, two cases are shown for the connection of an excitation: one for a direct current (DC) and one for an alternating current (AC).

The switching process shown begins with switching at \(t=0\) (dashed boundary, left) and ends when a steady state (persistent) is reached (dashed boundary, centre). The steady state of \(s(t)\) corresponds to a constant value (DC) when excited with a constant value and a periodic value (AC) when excited with an alternating value.

The process shown in Fig. 2 during the transition (transient) from switching to reaching a steady state can also be referred to here as a balancing process (in general), a switching process (in particular) or a transient process (in particular).

Compensation processes during switching, as they occur in real switches, are not referred to as switching processes and are not examined in detail in this module. However, for the sake of completeness, a brief explanation can be found in section 4 when comparing ideal and real switches.

3 Examples of switching operations

In principle, switching operations occur every time a switch is made in electrical networks.

Typical examples are converters (power converters) in power electronics, which convert electrical energy into another form of electrical energy. By selectively switching semiconductor components (e.g. transistors, thyristors) the voltage, current or frequency can be changed. In each clock cycle, capacitances and inductances are alternately charged and discharged.

Figure 2a shows an example of a buck converter with a smoothing capacitor. This converts a DC voltage \(U_1\) into a lower DC voltage \(U_2\). Figure 2b also shows the time curves of voltages and currents at the input and output of the buck converter.

Without detailed calculation, it is apparent that the output voltage is not constant even in steady-state operation. The output voltage across the smoothing capacitor fluctuates because the capacitance discharges and recharges slightly in each switching period. The methods described in this module can be used to calculate and analyse such switching processes.

For a better understanding, however, simpler examples of switching processes without periodic switching are considered in Chapter ??. Other examples of switching processes are the switching on and off of devices, analogue-to-digital and digital-to-analogue conversion, and the charging of a capacitor by a bicycle light.

4 Comparison of ideal and real switches

For simplicity, this module always assumes ideal switches. To understand the limitations of this assumption, the difference between ideal and real switches is explained below. As shown in the circuit diagram in Figure 4, the switch voltage across a switch is considered. For this purpose, the switch is connected to a linear DC voltage source with voltage \(U_q\).

Figure 5 shows the switch voltage in forward and reverse operation and in the transition phases when opening or closing the switch. On the left is the voltage curve for an ideal switch, on the right for a real switch.

An ideal switch changes instantaneously and without loss from a conductive state (\(R=0\)) to a blocking state (\(G=0\)) or vice versa as shown in Figure 4a. A real switch, on the other hand, does not conduct or block instantaneously as shown in a simplified form in Fig. 4b. Instead, latencies and losses occur. In forward mode, a small voltage is still present (forward resistance \(R>0\)) and in reverse mode, a small current still flows (reverse conductance \(G>0\)). This results in losses in the switch, especially during the transition phases when both voltage and current are present.

The latencies and losses of real switches result from their resistive, inductive and capacitive properties. Due to these properties, switching is always associated with compensation processes when viewed in real terms – within the switch. In practice, such effects are referred to as parasitic when undesirable.

Abbildung 6 zeigt exemplarisch einen MOSFET als Schalter zur Veranschaulichung. Zum Vergleich ist der MOSFET einmal ideale (ohne) und einmal real (mit kapazitiven Effekten) dargestellt.

The capacitive effects between the terminals of the MOSFET cause a delay in switching, as the respective capacitances must first be charged or discharged during switching. The MOSFET example serves only to illustrate the differences between ideal and real switches. Compensation processes during switching operations are not considered further in this module. Switching operations always refer to the compensation processes after switching.