Capacitor Basics---RC Filtering

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Capacitor Basics---RC Filtering [Copy link]

The impedance of the capacitor is related to the signal frequency, and different impedances can be obtained under the input of different frequency signals. Using this feature, filters can be designed.

The most basic filter is an RC filter constructed of resistors and capacitors. There are low-pass and high-pass filters. The cutoff frequency of the RC filter is calculated by the formula: F (cutoff) = 1 / (2πRC). The cutoff frequency is the frequency at which the filter frequency response has an inflection point.

1. RC Low-Pass Filter

The RC low-pass filter circuit is constructed as follows, and the output signal is connected to both ends of the capacitor:

Figure 1 - RC low-pass filter

Assume that the resistance in the circuit is 10KΩ and the capacitance is 10nF. Applying the above formula, the cutoff frequency is 1592Hz. For the convenience of discussion, it is rounded to 1600Hz.

Let's look at the changes in the output signal when the input signal amplitude is 1V and the frequency is 100Hz, 1.6KHz, and 16KHz respectively. The blue waveform represents the input signal, the yellow waveform represents the signal at both ends of the resistor, and the green waveform represents the signal at both ends of the capacitor (i.e., the output signal):

Figure 2- Voltage waveforms across resistors and capacitors when the input signal is 100Hz

Figure 3- Voltage waveforms across resistors and capacitors when the input signal is 1.6KHz

Figure 4- Voltage waveforms across resistors and capacitors when the input signal is 16KHz

It can be seen that when the input signal frequency is relatively low (100Hz), the output signal is close to the input signal, and the amplitude hardly weakens (blue and green waveforms overlap); when the input signal frequency is the cutoff frequency (1.6KHz), the output signal is about 0.7V; when the input signal frequency is much greater than the cutoff frequency (16KHz), the output signal becomes very weak, and the main energy consumption is in the resistor (blue and yellow waveforms overlap). In this way, filtering of signals of different frequencies is achieved.

If it is an ideal low-pass filter, the frequency response of the filter should be very steep at the cutoff frequency. When it is less than the cutoff frequency, the output signal is the same as the input signal; when it is greater than the cutoff frequency, the output signal is 0:

Figure 5 - Frequency response of an ideal low-pass filter

But this is not possible in reality. The frequency response of our simple RC low-pass filter is actually as follows:

Figure 6 - Frequency response of a low-pass filter based on RC

For an RC low-pass filter, when the frequency response is less than the cutoff frequency, the frequency response is almost flat, indicating that the output and input signals do not change much; at the cutoff frequency, the output signal amplitude drops to 70.7% of the input signal amplitude (a decrease of 29.3%, also known as 3dB), indicating that the frequency response has an inflection point, and the output signal begins to drop significantly compared to the input signal; when the frequency is greater than the cutoff frequency, the output signal drops further sharply as the frequency increases.

3dB attenuation, when used on a single voltage or current indicator, means a 29.3% drop, which is about 70% of the original signal; and when used on a power indicator, it is usually expressed as a drop to half of the original. This is also easy to understand, power = voltage × current, and the multiplication of two 3dB attenuations is ~50%.

One thing to note: When the filter attenuates the signal amplitude, it is also accompanied by a change in phase. Note that in Figure 3, there is a phase difference between the output signal and the input signal.

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2. RC High-Pass Filter

After understanding the RC low-pass filter, let's look at the RC high-pass filter. The circuit is as follows, and the output signal is connected to both ends of the resistor:

Figure 7 - RC High Pass Filter

You can imagine the frequency response of a high-pass filter as a mirror image of the low-pass filter:

Figure 8 - Frequency response of a high-pass filter based on RC

In particular, for DC signals, when the capacitor is fully charged, the capacitor voltage is equal to the input signal voltage, and the circuit is in an open circuit state. Therefore, capacitors are said to "block DC and pass AC."

Below we use a periodic square wave as the signal source. Compared to a single-frequency sine wave, a square wave contains many frequency components. We pass it through an RC high-pass filter to see the state of the output signal. The blue waveform represents the input signal, the yellow waveform represents the signal at both ends of the capacitor, and the green waveform represents the signal at both ends of the resistor (that is, the output signal):

Figure 9 - Square wave passing through RC high pass filter

Is it the same as you imagined?

3. Application Cases

The microphone capsule outputs an audio signal containing a DC component. Before amplification, a high-pass filter composed of RC is connected to filter out components below 15.9Hz and the DC component. In this way, only the audio signal of interest is amplified, non-related signals are prevented from directly entering the post-amplifier, and the DC component is prevented from being amplified and causing amplifier saturation.

Figure 10 - RC high-pass filter in microphone capsule circuit