A new interpretation of the principle of integral circuits: the transformation of amplifiers and capacitors

If the feedback resistor in the inverting amplifier is replaced by a capacitor, it becomes an integrating amplifier circuit as shown in Figure 1. Resistors seem to be more real things, and the circuit output state can be seen at a glance. However, if it is replaced by capacitors, due to the uncertainty of charging and discharging, capacitors are more "virtual" objects, and the circuit output state is a little difficult to figure out.

Figure 1: The structure of the integration circuit and the signal waveform

To understand its output state, you must first understand the nature of the capacitor. The basic function of a capacitor is to charge and discharge, and it is an energy storage element. It is sensitive to changing voltage (strongly reacts), insensitive to direct current (even indifferent), and has the characteristics of passing alternating current and blocking direct current. For those who see everything in the world as exhibiting resistance characteristics, capacitors can also be regarded as changing resistors, which can solve the mystery of the output of the integral circuit.

According to the law of conservation of energy, energy cannot be generated or disappeared without reason, and the theorem that the voltage across the capacitor cannot change suddenly is derived from it. At the moment of charging, the charge has not yet accumulated between the two plates of the capacitor, so the original state of zero voltage across the two ends can be maintained, but the charging current at this moment is the maximum, which can be equivalent to a very small resistance or even a wire. If the capacitor is short-circuited at the moment of charging, it is also possible. For example, in the main circuit of the inverter, there must be current-limited charging measures for the loop capacitor. This is the reason; during the charging of the capacitor, as time goes by, the charging voltage gradually increases, while the charging current gradually decreases. It can also be considered that the equivalent resistance of the capacitor changes from the minimum to the maximum at this time; after the capacitor is fully charged, the voltage across the two ends is the highest, but the charging current is basically zero. At this time, the capacitor is equivalent to the maximum resistance. For direct current, it can even be equivalent to an open circuit, an infinite resistance.

To summarize, during the charging process of the capacitor, there are three states: equivalent to the minimum resistance or wire, equivalent to the resistance changing from small to large, and equivalent to the maximum resistance or open circuit. It is this changing characteristic of the capacitor that can transform the integrating amplifier circuit into the three identities shown in Figure 2.

Figure 2: The “three transformations” of the integrator circuit during operation

See Figure 2.

1. Voltage follower. At t0 (positive transition) of the input signal, the capacitor charging current is the largest and the equivalent resistance is the smallest (or regarded as a wire). The circuit immediately turns into a voltage follower circuit. From the virtual ground characteristics of the circuit, it can be seen that the output is still 0V.

2. Inverting amplifier. During the flat-top period after the input signal t0, the capacitor is in a relatively gentle charging process, and its equivalent RP goes through three stages: less than R, equal to R, and greater than R. Therefore, in the amplification process, under the effect of the amplification characteristics, it actually goes through three small processes: inverting attenuation, inversion, and inverting amplification. Whether it is attenuation, inversion, or inverting amplification, it means that at this stage, the integrator circuit actually plays the role of a linear amplifier.

3. In the second half of the input signal flat period, the charging process of the capacitor has ended, the charging current is zero, the capacitor is equivalent to an open circuit, the integral amplifier amplifies from a closed loop to an open loop comparison state, and the circuit is transformed into a voltage comparator. At this time, the output value is a negative power supply value.

It is said that people can change their faces, but in fact, circuits can also change their appearance. Under the control of capacitors, the amplifier changes into three identities in an instant. If you can see through these three identities of the integrating amplifier, the "true identity" of the integrating amplifier will be revealed.