9.15:
Design Example
An engineer designs a circuit for a speaker system with a 2 kHz crossover frequency requirement, considering the speaker's resistance of 8 ohms.
The circuit design connects a crossover network to an audio amplifier, linking it with the woofer and tweeter speakers.
The woofer, a low-frequency speaker, reproduces signals of lower frequencies, while the tweeter, a high-frequency speaker, reproduces signals of higher frequencies.
The equivalent circuit diagram includes a high-pass RC filter and a low-pass RL filter, with the amplifier represented by a voltage source.
The frequency response of the crossover network is determined using the transfer functions for the high-pass and low-pass filters.
The crossover frequency of a high-pass filter is inversely proportional to the product of resistance and capacitance.
Conversely, the crossover frequency of a low-pass filter is directly proportional to the ratio of resistance to inductance.
Known values of crossover frequency and speaker resistance are used to calculate the values of capacitance and inductance.
This design directs frequencies above 2 kHz to the tweeter and those below 2 kHz to the woofer.
9.15:
Design Example
The innovation of touch-tone telephony revolutionized the telecommunications industry by replacing the traditional rotary dial with a dual-tone multi-frequency (DTMF) signaling system. This system uses a matrix-style keypad with buttons arranged in four rows and three columns, creating 12 distinct signals each assigned to a pair of frequencies. Each button press results in a simultaneous generation of two sinusoidal tones – one from a low-frequency group (697 to 941 Hz) and one from a high-frequency group (1209 to 1477 Hz).
This dual-tone system is an advancement in user interface design and a sophisticated application of signal processing technology. The filtering of signals, as depicted in the example of the touch-tone telephone set, utilizes a combination of low-pass (LP) and high-pass (HP) filters, followed by bandpass filters to discern individual tones within the grouped frequencies. The bandpass filters play a pivotal role in signal detection, allowing only a narrow band of frequencies to pass through – effectively isolating the tones produced by the keypad.
The design of these filters involves precision electronics and can be exemplified by constructing a series RLC circuit, which operates as a bandpass filter. This is a resonant circuit consisting of a resistor (R), inductor (L), and capacitor (C), which allows it to pass a selective range of frequencies while blocking others.
The touch-tone system exemplifies the practical application of electronic filter design in real-world systems, showcasing the critical nature of frequency selection and signal clarity in communication technology. Through the meticulous design of RLC bandpass filters, touch-tone telephones can reliably interpret user inputs, thereby maintaining the integrity of the information transmitted across the vast networks connecting calls worldwide.