Active filter circuit and voltage comparator

The function of the filter circuit: allow signals within the specified range to pass through; and prevent signals outside the specified range from passing through.
Classification of filter circuits: (according to different operating frequencies)
Low-pass filter: allow low-frequency signals to pass through and attenuate high-frequency signals.
High-pass filter: allow high-frequency signals to pass through and attenuate low-frequency signals.
Band-pass filter: allow signals within a certain frequency band to pass through and attenuate signals outside this band.
Band-stop filter: prevent signals within a certain frequency band from passing through, and allow signals outside this band to attenuate.
We have learned in the circuit analysis course that filter circuits are composed of passive components such as resistors and capacitors, but they have great defects such as: small circuit gain; poor load driving capacity, etc. For this reason, we need to learn active filter circuits.

2: Active filter circuit
(1) Low-pass filter circuit
Its circuit diagram is shown in Figure (1): (We take the passive filter network RC connected to the in-phase input terminal of the integrated operational amplifier as an example)

Its amplitude-frequency characteristics are shown in Figure (2):
Its transfer function is:

(2) High-pass filter circuit
Its circuit diagram is shown in Figure (3): (We take the passive filter network connected to the inverting input terminal of the integrated operational amplifier as an example)

Similarly, we can get its amplitude-frequency characteristics as shown in Figure (4):
Its transfer function is:

(3) Bandpass filter circuit and band-stop filter circuit
By combining the low-pass filter circuit and the high-pass filter circuit in different ways, we can obtain the bandpass filter circuit and the band-stop filter circuit. Their circuit diagrams are as follows: the bandpass filter circuit shown in Figure (5); the band-stop filter circuit shown in Figure (6):

1: Basic knowledge of voltage comparator
Function of voltage comparator: compare the size of two voltages (use the high or low level of output voltage to indicate the size relationship of two input voltages)
Function of voltage comparator: it can be used as an interface between analog circuits and digital circuits, and can also be used as a waveform generation and conversion circuit, etc.
Note: The integrated operational amplifier in the voltage comparator usually works in the nonlinear region. And satisfy the following relationship:

2: Simple voltage comparator
We connect the reference voltage and input signal to the in-phase and inverting input terminals of the integrated operational amplifier respectively to form a simple voltage comparator. As shown in Figures (1) and (2):

Let's analyze them below (only analyze the circuit shown in Figure (1)).
Its transfer characteristics are shown in Figure (3):
It shows that when the input voltage gradually increases from low to low through UR _, u _o will change from high level to low level. On the contrary, when the input voltage gradually decreases from high to low, u _o will change from low level to high level.

Definition: Threshold voltage: The value of the input voltage corresponding to the change in the output voltage of the comparator from one level to another. It is also called the threshold voltage. Abbreviated as: threshold. Represented by the symbol U _TH .
A simple voltage comparator can be used to convert a sine wave into a square wave or rectangular wave of the same frequency.
Example: The circuit is shown in (1), and the input voltage is a sine wave as shown in Figure (4). Try to draw the output waveform

The simple voltage comparator has a simple structure and high sensitivity, but poor anti-interference ability, so we need to improve it. The improved voltage comparators include: hysteresis comparator and window comparator. No requirements are made here.

The comparators we studied earlier are all made of integrated operational amplifiers, which have certain disadvantages. We generally use integrated voltage comparators to replace them. The inherent characteristics of integrated voltage comparators are: they
can directly drive digital integrated circuit devices such as TTL;
their response speed is faster than comparators made of integrated operational amplifiers of the same price;
in order to increase the speed, the input stage operating current of the internal circuit of the integrated voltage comparator is relatively large.