# RC Filter Circuits – An Introduction

|Hello Friends! In this tutorial we are going to learn about RC circuits and their applications. What is a low pass RC circuit? By definition we can say that a low pass RC circuit is an electrical circuit consisting of resistors and capacitors which passes a required amount of signal frequency and rejects unwanted signal. How is it possible? It’s simple. We can decide the functioning of circuit by selecting the required cut off frequency. **Cut off frequency **is the frequency above or below which the output power decreases to the one half the pass band power usually referred to as **3dB **point .As a voltage ratio it corresponds to 0.707 times the pass band voltage or maximum value. The two common most circuits used are low pass filters.

### Low Pass RC Circuit:

Low pass filter is a circuit which passes only low frequency signals and attenuates high frequency signals when passed through a network over certain cutoff frequency and it is determined by the RC time constant. The below figure shows the circuit of Low pass RC circuit. Here we are going to discuss about different types of input signals given to the low pass circuit and observe the output response.

### Determination of Cutoff Frequency:

A simple Low pass RC circuit consists of a resistor and capacitor across the input and capacitor across the output. As we know that a Capacitor exhibits Reactance (opposition to the flow of alternating current). By analyzing the low pass RC circuit at zero frequency the capacitor offers high amount of reactance almost acts as an open circuit. Now the entire signal passes across the output terminals hence the signal is unattenuated. We can say in terms of frequency response as the gain is unity at zero frequency. Similarly at high frequencies we can say that the capacitor offers less amount of reactance and hence the output decreases as frequency increases. This concept can be clearly understood by considering the following notations.

Where *Xc=Capacitive reactance measured in ohms, f = frequency in hertz, C = capacitance in farad*.

When f = 0

**Xc = ∞**(Open Circuit)

**Xc = 0**(Short Circuit)

### Frequency Response:

It is defined as the plot drawn between magnitude of output voltage versus frequency. It defines the range of frequencies for which the circuit is operated.

Now we are going to learn about how a low pass RC circuit acts as an integrator.

### Low Pass RC Circuit as an Integrator:

In order to act circuit as an integrator it depends upon the time constant of the RC circuit .The time constant should be large enough when compared with the input signal so that the capacitor charges slowly and all the input voltage which is applied appears across the resistor. In this circuit the output is an integral function of the input voltage. In other words we can say that output is directly proportional to the input signal.

The output equation is given by the equation **V _{o} = 1 / c**

### Applications of Integrator:

- To analyse the signals and perform the integration.
- To convert a square wave input into a triangular wave
- To convert a rectangular wave input into a sawtooth wave.

### High Pass Circuit:

High pass filter is a circuit which passes only High frequency signals and rejects low frequency signals. The below figure shows the diagram of High pass RC circuit.

At Zero frequency the capacitor offers high amount of reactance hence as the capacitor is at the input it acts as a blocking capacitor. This circuit acts as capacitive coupling circuit and provides dc isolation between input and output. At high frequency capacitor offers less amount of reactance and a small amount of signal appears across the capacitor. Hence almost all the input applied appears across the output i.e. gain is unity.

### High Pass Circuit as Differentiator:

The high pass circuit acts as a differentiator depending upon the time constant of the RC network. It varies depending upon the circuit. The time constant of the circuit should be small so that the capacitor charges quickly and all the voltage is taken by the capacitor and small amount of voltage appears across the resistor. The current in the circuit is decided by the capacitance.

The output equation in terms of capacitance is given by:

### Applications of Differentiator:

- It converts triangular wave into square wave.
- It converts ramp input into step wave
- Generates spikes from square or triangular waves which are used in for triggering the circuits or for synchronization of clock circuits.

Hence from this tutorial we have learnt about RC low pass and high pass circuits with their applications. In the upcoming tutorials we will discuss about advanced topics of RC circuits as filters.

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