# Intuitive understanding of RC circuits

2023-10-08Archive

RC circuit is a relatively common combination circuit that is often used in circuit design process. There are various materials on RC on Internet at present, but it is actually hard to find waveforms measured by adding sinusoidal excitation to RC; there are even fewer waveforms that can simultaneously connect voltages across capacitors and resistors. Without these signals, we actually lack an intuitive understanding of RC circuits.

This article will analyze sinusoidal characteristic of an RC circuit based on measured waveform, and we will try to give you an intuitive and sensual understanding. For articles on deriving frequency response of RC circuits, you can simply Baidu.

First, we give a circuit diagram of our measured circuit. Everyone has seen this circuit diagram, too, but there is nothing unusual in it.

The blue part in figure below is input sine wave, which is equal to Ui; yellow part is power supply on capacitor, which is indicated as Uo in diagram.

From this waveform diagram, we can first see that capacitor voltage phase must lag signal source:

①In one cycle, input signal Ui causes output signal Uo to peak;

② According to waveform diagram, even in first trigger cycle, phase difference of two signals is steady state. Also, you can see apparent amplitude decay, which is actually a filtering effect. Since frequency of sine wave continues to increase when peak value Uo reaches 0.707 times peak value Ui, frequency of sine wave is cutoff frequency.

Let's look at second image below. The waveform in purple part of image is result of subtracting input voltage waveform from output voltage waveform. In fact, is this voltage shape voltage across resistor? It has function of subtracting amplitude of signal of different channels). So, from figure, we intuitively draw following conclusions: ①The phase of voltage across resistor leads phase of signal voltage; ②The phase of voltage across resistor leads phase of voltage across capacitor. . In fact, second is easy to understand: for a capacitor i=c*du/dt, that is, capacitor current is voltage difference. Differentiation means progress in phase. If we visualize this leading phase angle, it is 90 degrees. Since this article does not use derivation of formula, it is actually a complex rotation calculation, but you can intuitively see from graph that phase angle difference between purple and yellow waves is 90°.

What if we add a square wave to RC circuit? The square wave in figure below is a high frequency square wave,

The duty cycle is 50%. You can look, because square wave period is too short, if you are familiar with capacitor charge and discharge formula, capacitor voltage will charge to a relatively high value, and voltage rises when charging in another cycle will be equal to discharge voltage. Because when capacitor voltage is relatively low, capacitor charging rate is relatively fast and discharge rate is relatively slow. As voltage across capacitor increases, charging rate constantly decreases, but discharge rate continues to increase, so when capacitor reaches a certain voltage amplitude, charging and discharging times are simply equal.

You can see from figure above that high frequency AC signal needs to be filtered. You can also measure that higher frequency, smaller difference between triangular wave output peaks and peaks.

There is an additional gain in this process, which is DC voltage component of capacitor. Ideally, this DC voltage component is only related to duty cycle of square wave. I don't know if you're thinking about duty cycle of buck circuit. Actually, idea here is same: DC voltage output by buck circuit is coupled to duty cycle, and AC component is filtered out by LCD filter. The LC filter, on one hand, has a relatively strong filtering capacity, and on other hand, energy loss is also small, so step-down circuit uses an LC filter instead of an RC filter.