MM0704, Lesson 1
to define since there
is no exact point
on the curve
designated as the limit of the bandpass. However, because it is often necessary to state the band of frequencies that a
resonant circuit will pass, an arbitrary standard has been set up. The limiting frequencies are those at either side of
resonance at which the current falls to 0.707 of the current at resonance. These are known as the half power points (A
and B, fig 1-6). The circuit shown in figure 1-6 has a bandwidth of 1,000 Hz between half power points. The bandpass
is from 1,000 Hz to 2,000 Hz.
Figure 1-6. Band Pass of a Series Resonant Circuit.
In this circuit, 0.707 is equivalent to half power. This is because, in any circuit, power is proportional to I2. The power
at resonance is I2R. At the half power point, the current is less. Call it I1. Then,
Therefore, the current at the half power point is 0.707 times the current at the resonant peak.
Some Uses for Series Resonant Circuits. The resonant rise
in the series LCR circuit
is valuable in giving
selectivity to radar and radio receivers. The reason for this is that, with a high Q circuit, the feeble signal voltages with
the desired frequency can be increased tremendously, while there is little gain in voltage at adjacent frequencies.