The crossover network is another application filter.
This application is used as a coupling that couples the audio amplifier to speakers.
Another typical application of filters is the crossover network that couples an audio amplifier to woofer and tweeter speakers, as shown in Figure.(1a). The network basically consists of one highpass RC filter and one lowpass RL filter.
It routes frequencies higher than a prescribed crossover frequency fc to the tweeter (high-frequency loudspeaker) and frequencies below fc into the woofer(low-frequency loudspeaker).
These loudspeakers have been designed to accommodate certain frequency responses. A woofer is a low-frequency loudspeaker designed to reproduce the lower part of the frequency range, up to about 3 kHz.
A tweeter can reproduce audio frequencies from about 3 kHz to about 20 kHz. The two speaker types can be combined to reproduce the entire audio range of interest and provide the optimum in frequency response.
By replacing the amplifier with a voltage source, the approximate equivalent circuit of the crossover network is shown in Figure.(1b), where the loudspeakers are modelled by resistors. As a highpass filter, the transfer function V1/Vs is given by
Similarly, the transfer function of the lowpass filter is given by
The values of R1, R2, L, and C may be selected such that the two filters have the same cutoff frequency, known as the crossover frequency, as shown in Figure.(2).
The principle behind this crossover is also used in the resonant circuit for a TV receiver, where it is necessary to separate the video and audio bands of RF carrier frequencies.
The lower-frequency band (picture information in the range from about 30 Hz to about 4 MHz) is channelled into the receiver’s video amplifier, while the high-frequency band (sound information around 4.5 MHz) is channelled to the receiver’s sound amplifier.
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Crossover Network Example
In the network of Figure.(1), suppose each speaker acts as a 6-Ω resistance. Find C and L if the crossover frequency is 2.5 kHz.
For the highpass filter,
For the lowpass filter,