Square wave pulse wave series capacitor

zhaoyanhao

Square wave pulse wave series capacitor [Copy link]

 

A square wave in series with a capacitor will produce a pulse wave, so what waveform will be produced when a pulse wave is connected in series with a capacitor? The simulation and actual measurement show that it is still a pulse wave. So, I would like to ask all the seniors, why does the pulse wave not undergo a differential operation? What is the approximate proportional relationship of the amplitude of the square wave after the capacitor is differentiated? If RC changes, the amplitude will also change, but it is not a simple RC multiple relationship. I am very confused here, and I hope that some seniors can give me some advice, thank you.

maychang

"A square wave connected in series with a capacitor will produce a pulse wave" Whether a pulse wave is generated after connecting a capacitor in series depends on the capacitance of the capacitor and the resistance of the subsequent circuit. If the capacitance is large enough and the resistance of the subsequent circuit is large enough, then the square wave will still be a square wave after passing through the capacitor.

maychang

"Why doesn't the pulse wave go through a differential operation?" Similarly, after the pulse passes through the capacitor, if the capacitor is large enough and the subsequent resistor is large enough, then it will still be the original pulse wave. If the capacitor is small and the subsequent resistor is also small, then the pulse will be a narrower pulse after passing through the capacitor.

maychang

"What is the approximate proportional relationship between the amplitudes of the square wave after being differentiated by the capacitor?" This depends on how steep the rising and falling edges of the input square wave are.

zhaoyanhao

maychang posted on 2018-7-17 17:07 "What is the approximate proportional relationship between the amplitudes of the square wave after being differentiated by the capacitor?" This depends on how steep the rising and falling edges of the input square wave are.

Thank you for your detailed answer. I also roughly understood that it mainly depends on the RC time constant. It can be fine as long as the constant is small enough. But the last thing you said is that if it is an ideal square wave, it will have equal amplitude output. If it is not ideal and has a rise time, will there be attenuation? Is the attenuation linear? The less steep it is, the smaller it is. What is the relationship? Thank you

maychang

zhaoyanhao posted on 2018-7-18 07:57 Thank you for your detailed answer. I also roughly understood that the RC time constant is the main factor. It can be small enough. But the last one you said is if...

"The last one you said is that if it is an ideal square wave, it will have a constant amplitude output, and if it is not ideal and has a rise time, there will be attenuation?" If an ideal square wave is input, the RC time constant is relatively large, and the output is close to a square wave, but the flat top will tilt toward the zero line, and the tilting method is an exponential curve (not linear).

maychang

zhaoyanhao posted on 2018-7-18 07:57 Thank you for your detailed answer. I also roughly understood that the RC time constant is the main factor. If the constant is small enough, it will be fine. But the last question you asked is, if...

There are three lines of waveforms in the figure. The first line is the input voltage, an ideal square wave. The second line is the output waveform when the RC time constant is large. The third line is the output waveform when the RC time constant is small.

maychang

zhaoyanhao posted on 2018-7-18 07:57 Thank you for your detailed answer. I also roughly understood that the RC time constant is the main thing to look at. If the constant is small enough, it will be fine. But the last question you asked is, if...

The red arrows in the figure point to exponential curves. It's just that the second row of exponential curves drops (or rises) slowly, and the third row of exponential curves drops (or rises) quickly. Slow or fast, this just reflects the size of the "time constant".

zhaoyanhao

maychang posted on 2018-7-18 10:52 The red arrows in the figure point to exponential curves. It's just that the second row of exponential curves drops (or rises) slowly, and the third row of exponential curves drops (or rises) slowly...

Thank you for your trouble. You are right, and I noticed that the amplitude of the unidirectional pulse is actually the same as the amplitude of the square wave. That is to say, if the amplitude of the square wave is 1V, after differentiation with a suitably small time constant, the pulse converted into it has a positive amplitude of 1V at the rising edge of the square wave, and a negative pulse of 1V at the falling edge of the square wave, that is, a bidirectional pulse with a peak-to-peak value of 2V. My question is whether the unidirectional amplitude of the converted pulse and the amplitude of the input square wave have any other linear or exponential relationship besides being equal. If there is a relationship, is it also determined by the time constant?

chunyang

zhaoyanhao posted on 2018-7-18 13:33 Thank you for your trouble. You are right, and I noticed that the amplitude of the unidirectional pulse is actually the same as the amplitude of the square wave. That is to say, for example, the amplitude of the square wave...

Why don't you first tell me why you think so? What is the reason? There is no point in guessing blindly. That is a crooked trick used by test-oriented education to answer questions, and it must not be used in practice.

zhaoyanhao

chunyang posted on 2018-7-18 14:03 Then why don't you tell me why you think so? What is the reason? There is no point in guessing, that is a crooked way of answering exam questions in exam-oriented education, and it must not be used in practice...

This is the data I measured, and the simulation is the same

chunyang

zhaoyanhao posted on 2018-7-18 14:06 This is my measured data, and the simulation is the same

This is what you said - "My doubt is whether the unidirectional amplitude of the converted pulse and the amplitude of the input square wave have other linear or exponential relationships besides being equal. If there is a relationship, is it also determined by the time constant?" What about the data? What about the simulation?

zhaoyanhao

I also often visit forums and I respect you as the moderator. I am debugging a project and don't have much time to post a lot of evidence. Please forgive me. The phenomena I observed may be wrong. I just raised my doubts and conjectures. It is good to get useful positive answers to confirm my doubts. I will certainly accept the doubtful suggestions that show that I am wrong. I just want more opportunities and more people to help me understand this knowledge. I think it is normal to give reasonable conjectures when problems arise. Otherwise, how can we solve the problems? The conjectures may be wrong, but they are absolutely necessary.

maychang

zhaoyanhao posted on 2018-7-18 13:33 Thank you for your trouble. You are right, and I noticed that the amplitude of the unidirectional pulse is actually the same as the amplitude of the square wave. That is to say, for example, the amplitude of the square wave...

My doubt is whether the unidirectional amplitude of the converted pulse and the amplitude of the input square wave have other linear or exponential relationships besides being equal. If there is a relationship, is it also determined by the time constant? If the input signal is an ideal voltage source and an ideal square wave (which is impossible), and the capacitor and resistor are also ideal components, then the unidirectional amplitude of the output is equal to the input square wave. This part can be found in the textbook "Circuit Analysis". If the input signal is not an ideal voltage source, not an ideal square wave, and the capacitors and resistors are not ideal components, then the problem becomes complicated. It is necessary to consider the distributed parameters of the components, the rise and fall speeds of the signal, the internal resistance of the signal source, and so on.

chunyang

zhaoyanhao posted on 2018-7-18 14:16 I also often visit forums and respect you as the moderator. Because I am debugging a project, I don’t have much time to post a lot of evidence. Please forgive me. The phenomena I observed...

A guess must have a basis. Without a basis, it becomes a blind guess. In an exam, if you do multiple-choice questions, you have a chance of guessing correctly if you don’t know the answer, so of course you should guess, even if it is a blind guess. However, in practice, even in all cases of non-finite definite choices, you cannot guess blindly, but you must have a basis. This is a very beneficial way of thinking. This is how science comes. Based on the existing phenomena and knowledge, you can infer the conjecture, and then verify and correct the conjecture based on practice. After enough cycles, the conjecture will get closer and closer to the truth. I have seen many young people on the forum, especially students, who often feel uncomfortable when being questioned or asked back. Their reactions are either blindly scolding, cursing or playing missing. Of course, irrelevant explanations are also a kind of reaction. To be frank, they still want to vent their dissatisfaction and comfort their fragile nerves... However, all these responses are wrong, and one is more outrageous than the other. The only one who will suffer in this way is yourself. Although this has a lot to do with the form and content of education in China, it is also inseparable from your own attitude and way of thinking. Saying these is many times better than telling you the ready-made answers directly. Whether you can grasp it depends on your attitude. Let's look at your question - "My doubt is whether the unidirectional amplitude of the converted pulse and the amplitude of the input square wave have other linear or exponential relationships besides being equal. If there is a relationship, is it also determined by the time constant?" Asking this way shows that your guess is related, but you just don't know what the relationship is. It is very likely that you have no basis for your guess and rely entirely on your feelings. The following irrelevant answer almost confirms this point. If there is a basis, you should say the basis. Maybe you will understand it when you say it. The thought process about this question: First, we analyze the ideal model. The edge of a square wave or pulse is 90 degrees, and it has an infinite harmonic spectrum. Capacitors block direct current and pass alternating current. For signals with infinite frequency, they pass directly. That is to say, the voltages at both ends of the capacitor are strictly equal at the moment of the edge, regardless of the resistance. With this basis, your question can be easily solved, and the knowledge used is all middle school knowledge except for the spectrum characteristics of the edge. Yes, middle school knowledge or even junior high school knowledge is enough for qualitative analysis of this problem. What we learned in college is to conduct quantitative analysis and calculation of this problem, so we need to consider the characteristics of the signal source (spectrum and internal resistance), device parameters, etc. The "Circuit Principles" course is to solve this problem. Then considering frequency, internal resistance, capacitive reactance, loop voltage division, etc., we can immediately conclude that the output amplitude must be less than the input amplitude, and the specific amount can be calculated. At work, we should further know the structure and manufacturing process, materials and characteristics of the device, so there is the theory of distributed parameters. Under certain conditions, the original RC circuit may no longer be valid, and it may even become an LC resonant circuit, and the circuit characteristics will be completely different. All of these cannot be memorized by rote. You can only remember the most basic knowledge and then reason based on this knowledge. For example, for this problem, you only need to remember the frequency characteristics of the edge and the properties of the capacitor, and the rest can be reasoned. This is how I reasoned, and I believe Maychang does the same. This reasoning process can be very fast, much faster than typing these words. Therefore, all conclusions, opinions, and even conjectures must have a basis, and then use logic to reason based on the basis. If you can do this in everything, at least it is not difficult to reach a considerable level on the road of technology.

zhaoyanhao

chunyang posted on 2018-7-18 22:11 Guessing must have a basis. Without a basis, it becomes a blind guess. In an exam, if you do multiple-choice questions, you have a chance of guessing correctly if you don't know the answer. So of course you should guess, even if...

Hello, last time I said "I didn't post the evidence because of time constraints, please forgive me" and you thought that I didn't answer your question about posting evidence. I apologize. I am really busy and don't have time to take screenshots and mark them one by one and then post them online. I just briefly expressed my views on the guess, which made you misunderstand. I'm sorry. I also generally agree with your views above. Now I will organize my test results and post them. A very simple differential circuit, input signal 30KHz square wave, capacitor + resistor, capacitor 1pF, resistor 1M ohm. The output waveform is as follows: Control variable method, other things remain unchanged, only change the resistance value to 100K ohm, the output waveform is as follows: Regarding the change of the circuit waveform after only changing the resistance value, I temporarily expressed my doubts about it, and based on the phenomenon, I gave a guess that there may be a certain relationship between amplitude and RC. What's wrong? If it were you, as a newcomer, would you also have a similar guess? I said before that the guess may not be right, but it is absolutely necessary. I don't know how I became a baseless and meaningless guess. It may be because I didn't post the evidence. I apologize again. Later, I had another idea (I'm sorry I guessed again). The reason why changing the resistance value will attenuate is that although the time constant RC is small enough, this circuit is still a high-pass filter circuit after all, and the cutoff frequency 1/2 RC does not meet the complete output conditions of the input signal frequency. If you have any opinions on my new conjecture, please point them out. I will definitely accept them with pleasure. I will only treat learning with truth. Let me say a few more words. I have expressed my respect for you and other forum seniors for their tireless guidance before. Now I still think the same way. Moreover, I have told my colleagues and junior students more than once that some forum seniors are very dedicated. I am very moved and hope they will visit the forum more and help others. What I said above is just my opinion on this post and this question. I think it is okay to ask seniors for advice and discuss with them. Even if I am criticized, I will maintain the greatest respect for them. Above, I once again express my respect for all the seniors and friends who are active in all technical forums and silently contribute without asking for anything in return.

maychang

zhaoyanhao posted on 2018-7-19 22:23 Hello, my last statement, "I did not post the evidence due to time constraints, please forgive me," made you think that I did not respond to your request to post the evidence...

"Now I will organize my test results and post them." This is not a test result, but a simulation result.

maychang

zhaoyanhao posted on 2018-7-19 22:23 Hello, I said last time that "I didn't post the evidence because of time constraints, please forgive me" and you thought that I didn't answer your request to post the evidence...

In simulation, the signal source is not an ideal square wave, and the capacitor is not an ideal capacitor. The simulated square wave also has the rise and fall time, and the simulated capacitor also has an equivalent resistance. In particular, the simulation is calculated step by step. If the step size is not appropriate (too long), the simulation will also have errors, especially in more extreme cases.

zhaoyanhao

maychang posted on 2018-7-20 09:15 "Now I will sort out my test results and post them." This is not a test result, but a simulation result.

The test result is the same as the simulation result, but it is not archived. I don't need to make up stories to tease you.

zhaoyanhao

maychang posted on 2018-7-20 09:22 In simulation, the signal source is not an ideal square wave, and the capacitor is not an ideal capacitor. The simulated square wave also has rising and falling edge times, and the simulated capacitor also has...

If the simulation is not an ideal situation, then the actual measurement will not be an ideal situation.