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ENCYCLOPEDIA OF RADIO ELECTRONICS AND ELECTRICAL ENGINEERING Using the Miller effect in timing RC circuits. Encyclopedia of radio electronics and electrical engineering
Encyclopedia of radio electronics and electrical engineering / Radio amateur designer In pulse shapers of a certain duration (timers, generators, etc.), time-setting RC circuits are often used, the operation of which is based on charging and discharging a capacitor through a resistor (Fig. 1, a). A constant voltage U0 is applied to the input of the RC circuit, and the charging of the capacitor C1 will begin through the resistor R1, as shown in the graph (Fig. 1, b). In this case, the voltage UC1 on the capacitor C1 will increase exponentially, and its value at any time can be found by the formula UC1(t)=U0(1 - et/R1-C1).
It should be noted that, theoretically, a capacitor will never charge up to a voltage Uo, so it is customary to determine the time during which it will charge to a certain value. As a measure of the charging time, the time constant τ = R1·C1 is taken - the interval during which UC1 reaches the value Uo (1 - 1/e). When the capacitor is discharged, the process proceeds in the reverse order. When building generators, timers and other similar devices, the RC circuit is connected to various transistor devices, op-amp comparators, etc., which in one way or another affect the charging-discharging process. To be negligible, the current drawn by these devices must be at least ten times less than the charging current of the capacitor. To increase the time constant, you either have to choose a larger capacitor or a larger resistor. In the first case, the dimensions of the capacitor and the leakage current increase. In the second, the charging current decreases, which leads to an increase in the influence of the leakage current of the capacitor and connected devices on the time constant. The Miller effect can help in this situation, the essence of which is as follows. If a capacitor with a capacitance C2 is included in the negative feedback circuit of the voltage amplifier (Fig. 1) with a gain, then the equivalent capacitance of such a circuit will be Ky times greater: Сeq = С1·Кy. In amplifying stages, especially at high frequencies, this effect has to be dealt with, but here it can be useful.
The current flowing through the resistor R1 branches into two: the collector current of the transistor VT1 and the charging current of the capacitor C1. In this case, most of the charging current flows through the emitter junction of the transistor. Since the base current of the transistor is h21E times less than the collector current (where h21E is the static current transfer coefficient of the base of the transistor), the charging current of the capacitor will be about the same times less than the current through the resistor R1. In the described node, a transistor with a high transmission coefficient, low reverse collector current and the ability to operate at low collector current, for example, KT3102, KT3130 with any letter indices, should be used. For resistor R1 with a resistance of 300 kΩ (with a tolerance of ±2%), a tantalum oxide capacitor with a nominal value of 100 μF for a voltage of 16 V (real capacitance is about 120 μF) and a KT3130B-9 transistor, the experimentally determined time constant turned out to be 380 s. The same elements without a transistor provided a time constant of 39 s. Thus, the use of a transistor provided an increase in the time constant by about 10 times. As a practical example of using the considered node in Fig. 3 shows a diagram of a timer that connects a powerful load to a power source after a certain period of time. A switching field-effect transistor VT2 is used as a controlled "contact pair". The comparator is assembled on the OS DA1 with a positive OS.
At the initial moment, the capacitor C1 is discharged and the output of the op-amp will have a voltage close to the supply voltage. Because of this, the field effect transistor is closed and the load is de-energized. As the capacitor C1 charges, the voltage at the collector of transistor VT1 increases, and when it exceeds the voltage at the non-inverting input of the comparator, it will switch. Its output voltage will decrease to almost zero - the field-effect transistor will open. To restart, briefly press the button SB1. With the type ratings of the elements indicated in the diagram, the delay time is approximately 10,5 minutes (without the VT1 transistor - about 1 minute). If the transistor is replaced by an op amp with a higher input impedance, the delay time can be increased even further. Author: I. Nechaev, Kursk
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