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BANDWIDTH

If circuit Q is low, the gain of the circuit at resonance is relatively small. The circuit does not discriminate sharply (reject the unwanted frequencies) between the resonant frequency and the frequencies on either side of resonance, as shown by the curve in figure 1-12, view (A). The range of frequencies included between the two frequencies (426.4 kHz and 483.6 kHz in this example) at which the current drops to 70 percent of its maximum value at resonance is called the BANDWIDTH of the circuit.

Figure 1-12A. - Bandwidth for high- and low-Q series circuit. LOW Q CURRENT CURVE

Figure 1-12B. - Bandwidth for high- and low-Q series circuit. HIGH Q CURRENT CURVE

It is often necessary to state the band of frequencies that a circuit will pass. The following standard has been set up: the limiting frequencies are those at either side of resonance at which the curve falls to a point of .707 (approximately 70 percent) of the maximum value. This point is called the HALF-POWER point. Note that in figure 1-12, the series-resonant circuit has two half-power points, one above and one below the resonant frequency point. The two points are designated upper frequency cutoff (f_co) and lower frequency cutoff (f_co) or simply f₁ and f₂. The range of frequencies between these two points comprises the bandwidth. Views (A)and (B) of figure 1-12 illustrate the bandwidths for low- and high-Q resonant circuits. The bandwidth may be determined by use of the following formulas:

For example, by applying the formula we can determine the bandwidth for the curve shown in figure 1-12, view (A).

If the Q of the circuit represented by the curve in figure 1-12, view (B), is 45.5, what would be the bandwidth?

If Q equals 7.95 for the low-Q circuit as in view (A) of figure 1-12, we can check our original calculation of the bandwidth.

The Q of the circuit can be determined by transposing the formula for bandwidth to:

To find the Q of the circuit using the information found in the last example problem:

Q.12 What is the relationship of the coil to the resistance of a circuit with high "Q"?
Q.13 What is the band of frequencies called that is included between the two points at which current falls to 70 percent of its maximum value in a resonant circuit?