Why can a high pass filter become a differentiator?

In the field of data acquisition ,RC Filter is the most common signal conditioning circuit , I've introduced... Before RC low pass filter , Today, I will introduce the corresponding RC High pass filter , See the following figure for the comparison of the two structures .

RC High pass filter is used to suppress low-frequency interference or noise , Only one resistor and capacitor can achieve , Its cut-off frequency is Fc=1/(2πRC) Hz, Allow higher than Fc Hz The signal passed through , And below Fc Hz Your signal doesn't pass . First order RC The filter has a wide transition band , The signal will not decay so violently , If you want to get a narrower transition band , The order of the filter can be increased , This will be explained in detail later .

Some students will have heard RC Differentiator , It has the effect of derivation , Its structure and RC The high pass filter is exactly the same , What's the difference between them ？ When is a high pass filter ？ When is it a differentiator ？

High pass filter

First look at the high pass filter , The resistance of the high pass filter in the figure is 33 ohm , The capacitance is 500nF, The calculated cut-off frequency is 10KHz, The cut-off frequency is the gain of -3dB( The magnification is 0.707 times ) Frequency point of . To be frank, the explanation is , The frequency is Fc Hz The signal of , After passing through the filter , The amplitude becomes the original 0.707 times .

Let's look at the response curve in the frequency domain , stay 10K Hz It's about , The gain is -3dB, It is the same as the previous calculation .

Take another look at the time domain waveform , Red is input 1V 10Khz Sine signal , The green output is 0.7V The sine signal of , The signal changes to the original 0.7 times , It is consistent with the previous calculation results .

If the signal frequency decreases , For example, by 10KHz Rise to 1Khz, Then it is inhibited by Qualcomm , Low frequency is difficult to pass , Only high frequency signals can pass through ,1Khz The signal will be seriously attenuated . The following figure [email protected] Hz The input of , After low-pass filtering , Only 100mV.

Let's talk about differential ： Triangular wave becomes square wave

At the end of the day ,RC A circuit is a process of charging and discharging a capacitor . If RC Enough hours , The high pass circuit will act like a differential , With 1Khz The triangle wave signal is like a chestnut , The red signal is the input triangle wave , The blue signal passes through the high pass （ differential ） Square wave after . In the rising edge time of the triangular wave , Derivative of triangular wave （ Find differentiation ） The result is a positive constant , The corresponding blue is a high level ; And in the falling edge time of triangular wave , Derivative of triangular wave （ Find differentiation ） The result is a negative constant , The corresponding blue is a negative level , This is the effect of high pass differential circuit , You can turn a triangular wave into a square wave .

Square wave narrowing pulse

Let's take a look at the more extreme square wave to pulse wave , Red is the input square wave , Blue is the output square wave . If you take the derivative of a square wave at its rising edge , The derivative is very large （ Contains very high frequency components ）, The corresponding blue waveform is a positive narrow pulse ; If you take the derivative of a square wave at its falling edge , The derivative is very small （ Contains very high frequency components ）, The corresponding blue waveform is a negative narrow pulse ;

If you add an operational amplifier , Constitute an active low-pass filter , That's another way to play , I won't discuss it here for the time being .

Hardware circuit design must be rigorous , The circuit parameters should be set reasonably according to the target signal , Avoid not achieving the desired effect .