# Rlc filters tutorial

You can use series and parallel RLC circuits to create band-pass and band-reject filters. An RLC circuit has a resistor, inductor, and capacitor connected in series or in parallel. Start with the voltage divider equation:. In math terms, this means that.

The cutoff frequencies are at the —3 dB half-power points. You basically have a quadratic equation, which has four roots due to the plus-or-minus sign in the second term. The bandwidth BW defines the range of frequencies that pass through the filter relatively unaffected.

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Another measure of how narrow or wide the filter is with respect to the center frequency is the quality factor Q.

The quality factor is defined as the ratio of the center frequency to the bandwidth:. Here is a series band-pass circuit and gain equation for an RLC series circuit. The frequency response is shaped by poles and zeros. You form a band-reject filter by measuring the output across the series connection of the capacitor and inductor. You start with the voltage divider equation for the voltage across the series connection of the inductor and capacitor:.

You can rearrange the equation with some algebra to form the transfer function of a band-reject filter:. You see how the poles and zeros form a band-reject filter. John M. Santiago Jr. During that time, he held a variety of leadership positions in technical program management, acquisition development, and operation research support. About the Book Author John M.A general two terminal network consists of resistive and reactive components and hence offers a complex impedance.

If a sinusoidal voltage is applied to this network, the resulting current is, in general, out of phase with the applied voltage. Under special circumstances, however, the impedance offered by the network is purely resistive and the circuit is said to be in resonance. The frequency of the applied signal at which resonance occurs is called the frequency of response. Under resonance, the circuit has unity one power factor. This condition of resonance unity power factor or purely resistive impedance may occur in two ways: 1 In series RLC circuit due to cancellation of inductive reactance with capacitive reactance.

Such a circuit is called is called series RLC resonant circuit. Accordingly, all resonance circuits may be put as:. Figure 1 shows a series RLC circuit. A sinusoidal voltage V rms value sends a current I through the circuit. This circuit is resonant when the resultant reactance is zero i.

At resonance, putting in equation 2 we get. This condition, under with inductive reactance equals the capacitive reactance is called the series resonance. Series resonance at any desired frequency f 0 may be obtained by varying either L or C or both. Alternatively, for fixed values of L and C, series resonance may be achieved by varying the frequency of applied signal.

The nature of the phasor diagram of a series RLC circuit depends upon the frequency f of applied voltage relative to the frequency of response f 0. Three different cases may then be considered:. Circuit is then purely resistive and the voltage V across the terminal is then in phase with the current I.

The phasor diagram of the series RLC circuit is then as shown in figure 2 a. Hence, the overall reactance is capacitive. Hence current I leads the applied voltage V by angle 0 as shown in figure 2 b. The phasor diagram is shown in figure 2 b. Overall reactance is inductive. Current I lags behind the applied voltage V by 0 as shown in phasor diagram of figure 2 c. Calculate the frequency of response. A sinusoidal voltage of rms value 20 Volts at the frequency of response is applied across the circuit.

Draw the phasor diagram showing the value of each phasor.The power supply block diagram clearly explains that a filter circuit is needed after the rectifier circuit. A rectifier helps in converting a pulsating alternating current to direct current, which flows only in one direction.

### RLC Low-Pass Filter Design Tool

Till now, we have seen different types of rectifier circuits. The outputs of all these rectifier circuits contains some ripple factor.

We have also observed that the ripple factor of a half wave rectifier is greater than that of a full wave rectifier.

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The ripple in the signal denotes the presence of some AC component. This ac component has to be completely removed in order to get pure dc output.

## Create Band-Pass and Band-Reject Filters with RLC Series Circuits

So, we need a circuit that smoothens the rectified output into a pure dc signal. A filter circuit is one which removes the ac component present in the rectified output and allows the dc component to reach the load. A filter circuit is constructed using two main components, inductor and capacitor.

We have already studied in Basic Electronics tutorial that. As an inductor allows dc and blocks ac, a filter called Series Inductor Filter can be constructed by connecting the inductor in series, between the rectifier and the load.

The figure below shows the circuit of a series inductor filter. The rectified output when passed through this filter, the inductor blocks the ac components that are present in the signal, in order to provide a pure dc. This is a simple primary filter. As a capacitor allows ac through it and blocks dc, a filter called Shunt Capacitor Filter can be constructed using a capacitor, connected in shunt, as shown in the following figure. The rectified output when passed through this filter, the ac components present in the signal are grounded through the capacitor which allows ac components.

The remaining dc components present in the signal are collected at the output. The above filter types discussed are constructed using an inductor or a capacitor.

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These are combinational filters. A filter circuit can be constructed using both inductor and capacitor in order to obtain a better output where the efficiencies of both inductor and capacitor can be used.The whole of electronics components can be slip into two broad categories, one being the Active components and the other as Passive components. These are the three most used components in electronics circuit and you will find them in almost every application circuit. These three components together in different combinations will form the RC, RL and RLC circuits and they have many applications like from filtering circuits, Tube light chokes, multivibrators etc.

So in this tutorial we will learn the basic of these circuits, the theory behind them and how to use them in our circuits. Before we jump into the main topics lets understand what an R, L and C does in a circuit. A resistor is an element that dissipates energy mostly in form of heat. It will have a Voltage drop across it which remains fixed for a fixed value of current flowing through it.

A capacitor is an element which stores energy temporarily in form of electric field. Capacitor resists changes in voltage. There are many types of capacitors, out of which the ceramic capacitor and the electrolytic capacitors are mostly used.

They charge in one direction and discharge in opposite direction. A Inductor is also similar to capacitor, it also stores energy but is stored in form of magnetic field.

Inductors resist changes current. Inductors are normally a coil wound wire and is rarely used compared to the former two components. When these Resistor, Capacitor and Inductors are put together we can form circuits like RC, RL and RLC circuit which exhibits time and frequency dependent responses that will e useful in many AC applications as mentioned already.

Before we start with each topic let us understand how a Resistor, Capacitor and an Inductor behave in an electronic circuit. For the purpose of understanding let us consider a simple circuit consisting of a capacitor and resistor in series with a power supply 5V. In this case when the power supply is connected to the RC pair, the voltage across the Resistor Vr increase to its maximum value while the voltage across the capacitor Vc stays at zero, then slowly the capacitor starts to build charge and thus the voltage across the resistor will decrease and the voltage across the capacitor will increase until the resistor voltage Vr has reached Zero and Capacitor voltage Vc has reached its maximum value.

The circuit and the wave form can be seen in the GIF below. Let us analyse the wave form in the above image to understand what is actual happening in the circuit is. A well illustrated waveform is show in the image below. When the switch is turned on the voltage across the resistor red wave reaches its maximum and the voltage across capacitor blue wave remains at zero. Then the capacitor charges up and Vr becomes zero and Vc becomes maximum.

Similarly when the switch is turned off capacitor discharges and hence the negative voltage appears across the Resistor and as the capacitor discharges both the capacitor and resistor voltage becomes zero as shown above.More informationMore informationAll you need to know to take advantage of our services and detailed explanations to make you an expertIf you have any doubt about any of the concepts described in the academy, you can submit us your questionsSign up Our mobile apps fit the needs of all our customers and maximizes the speed when receiving forecasts.

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### Electronic Circuits - Filters

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