Lecture
One of the main characteristics of a switch's operation in the dynamic mode is the dynamic I-V characteristic (switching trajectory) — the dependence of the voltage across the switch us on the current is flowing through it during the switching transient process. Switching processes depend on the switch's speed and the parameters of the elements of the switched electrical circuit. Accordingly, the dynamic I-V characteristics also depend on the factors mentioned and therefore vary widely. In practice, dynamic I-V characteristics are represented on the plane of the current is and voltage us parameters, determined for specific switching conditions over the interval of the transient process.
An analytical description of the dynamic processes that adequately accounts for the physical phenomena in semiconductor devices is a complex task. In this connection, simplified mathematical models are used in the analysis of switching processes in electronic switches, which in many cases make it possible to obtain results with sufficient accuracy for practical purposes. It is generally accepted to represent an electronic switch, during the turn-on interval, as a source of linearly decreasing voltage, and during the turn-off interval, as a source of linearly decreasing current. The durations of the decay of the voltage and current to zero are respectively taken as equal to the turn-on and turn-off times of the switch. Such models correspond to an idealized representation of switches in dynamic operating modes when switching from one state to another. The corresponding voltage and current diagrams of the switch are shown in Fig. 10.20, and the equivalent voltage and current are written as
where UsQ, Iso are the steady-state values of the voltage on the switch and the switch current before the start of switching; ton, t0* are the turn-on and turn-off times of the semiconductor device.
Fig. 10.20. Voltage and current diagrams of the switch during switching:
a — voltage during turn-on; b — current during the turn-off process
The switch current during turn-on and the voltage across it during turn-off will characterize the response of the switched circuit to the change in the switch's state. If the switched circuit contains reactive elements (inductive or capacitive), their inertia will cause a slow change in current during turn-on of an inductive circuit and a slow change in voltage during turn-off of a capacitive circuit. In these cases, the switch's dynamic I-V characteristics will differ significantly from the switching trajectory when switching a circuit containing only resistive elements.
Figures 10.21 and 10.22 show examples of the simplest circuits for switching resistive and resistive-inductive loads. Here, the assumption of an ideal static I-V characteristic (see Fig. 10.18) of switch S is adopted, and during the switching intervals the switch models are used in accordance with expression (10.5).
Fig. 10.21. Switching of a resistive load:
a — circuit; diagrams of current, voltage, and instantaneous power: b — during turn-on; c — turn-off; d — dynamic I-V characteristic of the switch
The diagrams us(t), is(t), and the instantaneous power during turn-on pon(t) and turn-off poff(t), as well as the dynamic I-V characteristics, can be used to evaluate various switch parameters during switching and make it possible to calculate the power losses in the switch taking into account the nature of the load. For a circuit with a resistive load, the instantaneous power value pon(t) and the energy released during the turn-on process Won can be determined from the following relations, taking t0 = 0:
During the turn-off interval, the processes of current and voltage change on the switch are also linear (Fig. 10.21, c), so the expressions for poff(t) and Woff are similar: 
When switching a resistive load, the switch's dynamic I-V characteristics during turn-on and turn-off are linear (Fig. 10.21, d):
Thus, representing the semiconductor switch as an equivalent source of linearly decaying voltage during the turn-on interval and as a source of linearly decaying current during the turn-off interval, the dynamic losses are determined — the power losses in the switch during its turn-on and turn-off intervals, which are calculated as the ratio of the energy dissipated during the turn-on and turn-off process to the switching period of the switch:
The presence of inductance in the switched circuit leads to an increase in the voltage across the switch during the turn-off interval and a delay in the current rise process when the switch turns on (Fig. 10.22, a—v). When the voltage decreases during the turn-on interval, the dependence is(t) is the sum of a linear and an exponential function. The rise in voltage as the current decreases during turn-off is associated with the appearance of a self-induction EMF in the coil (EL = -Ldis/dt); the maximum value of the voltage on the switch is Usmax = E + EL. As a result, the power losses in the switch and the dynamic V-A characteristics change significantly compared with the losses and characteristics during switching of an R-load (Fig. 10.22, g, d). The energy dissipated when turning on an RL-load decreases owing to the slower current rise. During turn-off of an active-inductive load, the energy and losses are significantly greater than during turn-off of an R-load, since there is an abrupt increase in the voltage on the switch, the value of which depends on the inductance and the turn-off time. The dynamic V-A characteristic of the switch during turn-off is determined as us = E - isR + EL (see Fig. 10.22, d).
When switching a load containing capacitance, the turn-on and turn-off processes of the switch are identical to the processes with an RL-load, except that during turn-on a current surge occurs, and during the turn-off interval the voltage across the switch rises more slowly compared with the turn-off process of an R-load. Therefore, the dynamic losses during turn-on increase significantly, while the energy dissipated during turn-off decreases.
Fig. 10.22. Switching of an active-inductive load:
a — circuit; diagrams of voltage, current and instantaneous power:
b — during turn-on; c — turn-off; dynamic V-A characteristics of the switch: d — during turn-on; e — turn-off
The most common operating mode of electronic switches is periodic switching — the transition from the on state to the off state and back, at frequency f. In this case, static and dynamic modes alternate. As an example, let us consider the determination of power losses in the switch during periodic switching of an R-load (see Fig. 10.21, a); the static V-A characteristic of the switch is shown in Fig. 10.23, where ΔU « E, and Roff » R.
Taking into account the assumptions made, the processes of current and voltage variation correspond to the diagrams shown in Fig. 10.24, which allow the total power losses in the switch to be determined. The following loss components can be distinguished: static losses in the on and off states (Pc.on and Pc.off) and dynamic losses during turn-on and turn-off (Pd.on and Pd.off). Each of the loss components is determined as the average value of the instantaneous power over the switching period (see Fig. 10.24):
Fig. 10.23. Example of an approximated V-A characteristic of an electronic switch for calculating static losses
From the expressions obtained it is evident that if the ratio ton/T is constant, the value of the static losses in the switch does not depend on frequency. Dynamic losses, on the other hand, increase with increasing switching frequency. Therefore, when operating at higher frequencies, it is necessary to use high-speed switches with short switching times.
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