# The measurement of frequency characteristics of r rc and rlc circuits

Set up and plan your measurements. We want to measure the magnitude and the phase of the voltage Vout at 3 frequency points for each filter. The 3dB point is measured with respect Vmax, not Vin. You will need to measure all three frequencies.  Energy can be transferred from one to the other within the circuit and this can be oscillatory. A mechanical analogy is a weight suspended on a spring which will oscillate up and down when released.

This is no passing metaphor; a weight on a spring is described by exactly the same second order differential equation as an RLC circuit and for all the properties of the one system there will be found an analogous property of the other.

The mechanical property answering to the resistor in the circuit is friction in the spring—weight system. Friction will slowly bring any oscillation to a halt if there is no external force driving it.

Likewise, the resistance in an RLC circuit will "damp" the oscillation, diminishing it with time if there is no driving AC power source in the circuit. The resonance frequency is defined as the frequency at which the impedance of the circuit is at a minimum.

## Series RLC Circuit

Equivalently, it can be defined as the frequency at which the impedance is purely real that is, purely resistive. This occurs because the impedances of the inductor and capacitor at resonance are equal but of opposite sign and cancel out.

Circuits where L and C are in parallel rather than series actually have a maximum impedance rather than a minimum impedance. For this reason they are often described as antiresonatorsit is still usual, however, to name the frequency at which this occurs as the resonance frequency.

Natural frequency[ edit ] The resonance frequency is defined in terms of the impedance presented to a driving source. It is still possible for the circuit to carry on oscillating for a time after the driving source has been removed or it is subjected to a step in voltage including a step down to zero.

This is similar to the way that a tuning fork will carry on ringing after it has been struck, and the effect is often called ringing. This effect is the peak natural resonance frequency of the circuit and in general is not exactly the same as the driven resonance frequency, although the two will usually be quite close to each other.

Various terms are used by different authors to distinguish the two, but resonance frequency unqualified usually means the driven resonance frequency. The driven frequency may be called the undamped resonance frequency or undamped natural frequency and the peak frequency may be called the damped resonance frequency or the damped natural frequency.An RLC circuit is an electrical circuit consisting of a resistor (R), RLC circuits have many applications as oscillator circuits.

that is, one with no resistor present. The resonant frequency for an RLC circuit is the same as a circuit in which there is no damping, hence undamped resonance frequency. The peak resonance frequency, on . In this lab we will only discuss series RLC circuits. Since the R, L, and C components are in series, The impedance of a circuit is a generalized measurement of the resistance that includes the frequency dependent e ects of the capacitor and the inductor.

is the resonant frequency of the RLC circuit. Now change the display setting. In this lab we will only discuss series RLC circuits. Since the R, L, and C components are in series, The impedance of a circuit is a generalized measurement of the resistance that includes the frequency dependent e ects of the capacitor and the inductor.

is the resonant frequency of the RLC circuit. Now change the display setting.

## The Impedance for a Series RLC Circuit

The RLC series circuit is a very important example of a resonant circuit. It has a minimum of impedance Z=R at the resonant frequency, and the phase angle is equal to zero at resonance. One way to visualize the behavior of the RLC series circuit is with the phasor diagram shown in the illustration above.

Draw the low frequency and high frequency equivalents of these networks, and also for the series RL and RLC circuits you considered in Sections and On this basis, classify each of these networks as a low pass, high pass, or band pass filter. Now we will calculate the voltage VC by using the impedance method.

Now let’s continue by graphically exploring the response of RLC circuits. R L CV +-c Vs The amplitude and phase of Vc are given by Equations () and () which we significance with regard to their frequency selectivity characteristics.

/ Spring

RLC circuit - Wikipedia