RC WaveForms

In previous RC Charging and Discharge training, we have found that a capacitor is capable of both charging and unloading itself through a series of connected resistance. The time it takes for this capacitor to fully charge or fully discharge is equal to five RC time constants or 5T when a constant DC voltage is applied or removed.

But what happens if we change this constant DC feed from the maximum to the minimum value to the continuously changing pulse or square wave waveform at a speed determined by the time period or frequency? How does this affect the output RC waveform for a specific RC time constant value?

Previously, we have seen that when a voltage is applied, the capacitor charges up to 5T, and when removed it ejaculates up to 5T. In RC charging and discharge circuits, this 5T time constant value always remains correct as it is fixed by resistance-capacitor (RC) combination. The actual time required to fully charge or discharge the capacitor can then be changed only by changing the value of the capacitor itself or the resistance in the circuit, and this is shown below.

Typical RC WaveForm

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Typical RC WaveForm

Square Wave Signal

Useful waveforms can be obtained by using RC circuits with the required time constant. If we apply a continuous frame wave voltage waveform to the RC circuit, whose pulse width exactly matches the circuit's 5RC time constant (5T), the voltage waveform along the capacitor looks like this:

5RC Input WaveForm

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5RC Input WaveForm

Voltage drop throughout the capacitor varies between charging up to Vc and discharge to zero according to the input voltage. In this example, the frequency of the input square wave voltage waveform (and therefore the resulting time period, ε = 1/T) exactly matches that of the 5RC time constant.

This (10RC) time constant allows the capacitor's input waveform to be fully charged during the "ON" period (0 to 5RC), and then fully discharged during the "OFF" period (5 to 10RC).

If the time period of the input waveform is made longer (low frequency, ε < 1/10RC): Örneğin "8RC"ye eşdeğer bir "AÇIK" yarım periyot darbe genişliğide kapasitör daha uzun süre tam şarjlı kalır. It then completely ejaculates and produces an RC waveform, as shown.

A Longer 8RC Input WaveForm

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A Longer 8RC Input WaveForm

However, if we had now reduced the total time period of the input waveform (higher frequency, ε > 1/10RC) to say "4RC", the capacitor would not have had enough time to fully charge or fully discharge during the "ON" period. Therefore, the voltage drop that occurs along the capacitor, Vc, will be less than the maximum input voltage, which produces an RC waveform, as shown below.

Shorter 4RC Input WaveForm

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Shorter 4RC Input WaveForm

Next, we can change the voltage on the capacitor by changing the RC time constant or the frequency of the input waveform, producing a relationship between VC and time, t. This relationship can be used to change the shape of various waveforms, so that the output waveform along the capacitor is almost nothing like that of the input.

Frequency response

RC Integrator

Integrator is a type of Low Pass Filter circuit that converts the square wave input signal to a triangular waveform output. As seen above, if the 5RC time constant is longer than the time period of the input RC waveform, the resulting output will be triangular. The higher the input frequency, the lower the output amplitude compared to the input.

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RC Integrator

Here's how we get the ideal voltage output for the integrator:

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RC Differentiator

The separator is a High Pass Filter type circuit that can convert the square wave input signal into high frequency increases at its output. If the 5RC time constant is shorter than the time period of the input waveform, the capacitor will charge more quickly before the next change in the input cycle.

When the capacitor is fully charged, the output voltage on the resistance is zero. The arrival of the falling edge of the input waveform causes the capacitor to reverse the load by giving a negative output increase. Then, as the frame wave input changes during each cycle, the output increase changes from a positive value to a negative value.

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RC Differentiator

Since we have an ideal voltage output for differentiator as follows:

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Alternate Sinus Wave Input Signal

Now if we replace the input RC waveform of these RC circuits with that of a sinusoidal Sinus Wave voltage signal, the resulting output RC waveform will remain unchanged and only its amplitude will be affected. Resistance, R or Capacitor can be changed to C positions, resulting in a simple first-degree Low Pass or High Pass filters with the frequency response of these two circuits depending on the input frequency value.

Low-frequency signals are transmitted from input to output with little or no weakening, while high-frequency signals are significantly weakened to almost zero. The opposite is true for the High Pass filter circuit. Normally, the point at which the response drops by 3dB (cutting frequency, εC) is used to define filter bandwidth, and a loss of 3dB corresponds to a decrease in output voltage to 70.7 percent of the original value.