RESONANCE CURVE

The curve obtained by plotting a graph between the current and the frequency is known as resonance curve. A resonance curve of a typical R–L–C series circuit is shown in Figure 7.33. It may be noted that current reaches its maximum value at the resonant frequency (f_r), falling off rapidly on either side of that point. It is because when the value of frequency is lower than resonance frequency, X_C > X_L and when the value of frequency is higher than f_r, X_C < X_L. In both the cases, impedance of the circuit increases (Z > Z_r) and the value of current decreases.

Fig. 7.33  Graph between f and I for R–L–C series circuit

Note that resistance of the circuit also plays its own role. The smaller the resistance, the greater is the current at resonance.

7.14.1  Bandwidth

The range of frequency over which circuit current is equal to or more than 70.7% of maximum value (i.e., I_r, current at resonance) is known as the bandwidth of a series resonant circuit.

Figure 7.34 shows a resonance curve of a typical R–L–C circuit where the circuit current is equal to or greater than 70.7% of maximum current (i.e., I_r = V/R) between frequency range f₁ to f₂.

Fig. 7.34  Graph representing band width in

Bandwidth,

 

BW = f₂ − f₁

Here, the frequency f₁ is called the lower cutoff frequency and the frequency f₂ is called the upper cut−off frequency. The bandwidth represents the frequency range at which the circuit offers low impedance to circuit current.

The following points may be noted here:

1. If the resonant frequency is not located at the centre of upper and lower cut−off frequency, then 
2. When the resonant frequency is located sufficiently near to the centre of the two cut−off frequencies and Q of the circuit is ≥10, then 

7.14.2  Selectivity

From the resonance curve, it is clear that for smaller resistance the resonance curve is sharp and flat for the larger resistance. A sharper resonance curve provides smaller band of frequencies to give reasonable response, and hence, provides better selectivity. It also shows that selectivity is reciprocal of bandwidth.