You may have heard of or seen an RC low pass filter circuit. In this article, we will explore how to build an RC filter circuit and the basics behind it. If you don’t have an electronics background or even experience with building electronics projects; we’ll go step-by-step to help you. We will learn what each component does and how they interact with each other to make the whole thing work. So that you can take your newfound knowledge and apply it to future projects. Let’s get started!
What is an RC Low pass filter?
A resistor and a capacitor are the basic components of an RC low pass filter circuit (A resistor and a capacitor circuit). We can classify RC low pass filter circuits into an RC series filter circuit and an RC parallel filter circuit. This depends on the arrangement of resistors and capacitors.
Simple RC parallel filter circuits cannot resonate due to the fact that resistors are not able to store energy. On the other hand, LC parallel circuits can resonate as inductors can store energy. Energy storage of inductors happens due to the fact that current is leading in inductors by 90 degrees.
Why do we call it a low pass Filter?
Most analog circuits employ these RC low pass filter circuits and you can also find its applications in pulse digital circuits. In an RC low-pass filter circuit, we connect the resistor and capacitor in parallel. Then we connect this combination in a series of any circuit, and it will pass the low-frequency signals.
Now, if we connect the same combination in parallel, it will pass the high-frequency signals in the circuit. This is the reason we call an RC circuit an RC Filter because it filters the low and high-frequency components. It blocks all signals outside its band. An RC filter circuit will always use energy because the perfect form of the circuit doesn’t include a resistor. But on the other hand, the RC circuit resistor consumes energy in the form of heat.
Low pass Filter Circuit
We will connect a reactive element with resistance to make a passive low-pass filter. We can also use the RL low-pass scheme to filter the signals because when we compare them theoretically they are identical. Both schemes in terms of their capacity filter the signals. However, in reality, the resistor-capacitor variant is considerably more typical. let’s have a look at the RC filter circuit.
From the above figure, we can derive the result that this circuit is simply a voltage divider circuit. As the capacitor is at the output, we will calculate the combined impedance, and then using the voltage divider we will derive formulas.
Most of the input power drops across the terminals of the capacitor. When we apply the low-frequency signals, the capacitor has a large reactance comparing it to the resistor. Because the load is connected across the terminals of the capacitor. So the resultant impedance also becomes low.
When the input frequency is high, the capacitor’s reactance drops as compared to resistance. In this way, it suppresses High frequencies while transmitting low frequencies. On the other hand, the opposite happens in high-pass filter circuits where the high-pass filter allows the high-frequency signals to pass and stops low-frequency signals.
We can write the output voltage equation as below,
From the above equation, we can see the output voltage depends on the impedance value. As the frequency of the input signal increases the reactance “Xc” starts decreasing. As we already know the reactance formula is as below.
Cut-off or corner Frequency of Low Pass Filter
With the frequency at which the electrical circuit’s output signal starts to decrease, we can call it the cutoff frequency or corner frequency of an electrical circuit. So the question arises that how much reduction in output signal occurs.
The output signal reduces by a factor of 1/√2 or we can say 0.707. at any stage, we define the output gain as below.
At the start when output voltage Vout= Input Voltage Vin then the output gain will be equal to zero because 20log1 is equivalent to zero.
So, what happens at cut-off or corner frequency?
At the corner frequency, the output voltage reduces with respect to input by a factor of 0.707. So,
Output Gain in dB= 20log (0.707)
Output Gain in dB = -3dB
As we can see the output gain at corner frequency comes out to be -3dB. Therefore we sometimes also call this corner frequency a -3dB frequency so that we can relate it to the fact discussed above. The frequency response has been shown below figure where we can see the passband and stopband.
The passband is the area shown where all signals will pass the RC filter circuit. The stopband is the area where all high-frequency signals will be stopped by the RC filter circuit.
Example of Low Pass RC Filter
Let’s take an example, we have a circuit having an input voltage of 1 volt, a capacitor value of 5nF, and a resistor value of 100Ω. we will try to calculate its gain or output voltage by applying signals of 4KHz.
We can see the output voltage shows that the gain is maximum which means the circuit will pass all the signals of these frequencies. Now let’s try some higher frequencies and increase the frequency of the signals to 400KHz and have a look at output voltage or gain.
As we can see in the above circuit when we increase the frequency of the signals from 4KHz to 400KHz, its output voltage significantly drops. This calculation tells us if we increase the frequencies any further, this RC filter circuit will block all the signals having higher frequencies.
Now, what if we increase capacitor size from 5nF to 100nF and increase frequencies from 400KHz to 500KHz?
As we can see from the above calculation that when we increase the frequencies and capacitor value, the output becomes nearly zero. This happens because the reactance of the capacitor drops significantly. When we will increase frequencies further this reactance will act like a short circuit and we know that across a short circuit we get voltages equal to zero. Read about high-pass filter circuits.
Want to know more regarding filters and how can we apply them in real circuits? Read our informative article regarding ac to dc converters, you will find the application of filters with a better understanding. Also, explore the converters category, and read our detailed article on dc to dc converter circuits. Further, you can also read about oscillator circuits to have a basic understanding of oscillations.
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