Question

Many stereo speakers are two-way speaker systems; that is, they have a woofer for low-frequency sounds and a tweeter for high-frequency sounds. To get the proper separation of frequencies going to the woofer and to the tweeter, crossover circuitry is used. A crossover circuit is effectively a bandpass, highpass, or low-pass filter. The system model is shown in Eigure P5 64. The function of the crossover circuitry is to channel frequencies below a given crossover frequency, $f_c$, into the woofer and frequencies higher than $f_c$ into the tweeter. Assume an ideal amplifier such that $R_S=0$ and that the desired crossover frequency is $1,200 \mathrm{~Hz}$. Find $C$ and $L$ when $R_1=R_2=8 \Omega$. (FIGURE CAN'T COPY) Figure P5.64

   Many stereo speakers are two-way speaker systems; that is, they have a woofer for low-frequency sounds and a tweeter for high-frequency sounds. To get the proper separation of frequencies going to the woofer and to the tweeter, crossover circuitry is used. A crossover circuit is effectively a bandpass, highpass, or low-pass filter. The system model is shown in Eigure P5 64. The function of the crossover circuitry is to channel frequencies below a given crossover frequency, $f_c$, into the woofer and frequencies higher than $f_c$ into the tweeter. Assume an ideal amplifier such that $R_S=0$ and that the desired crossover frequency is $1,200 \mathrm{~Hz}$. Find $C$ and $L$ when $R_1=R_2=8 \Omega$.
(FIGURE CAN'T COPY)
Figure P5.64

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Principles and Applications of Electrical Engineering
Principles and Applications of Electrical Engineering
Giorgio Rizzoni,… 7th Edition
Chapter 5, Problem 64 ↓
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Many stereo speakers are two-way speaker systems; that is, they have a woofer for low-frequency sounds and a tweeter for high-frequency sounds. To get the proper separation of frequencies going to the woofer and to the tweeter, crossover circuitry is used. A crossover circuit is effectively a bandpass, highpass, or low-pass filter. The system model is shown in Eigure P5 64. The function of the crossover circuitry is to channel frequencies below a given crossover frequency, $f_c$, into the woofer and frequencies higher than $f_c$ into the tweeter. Assume an ideal amplifier such that $R_S=0$ and that the desired crossover frequency is $1,200 \mathrm{~Hz}$. Find $C$ and $L$ when $R_1=R_2=8 \Omega$. (FIGURE CAN'T COPY) Figure P5.64
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You have decided to build your own speaker system for your home entertainment system. The system will consist of two loudspeakers: a large "woofer," to which you want to send low audio frequencies (bass), and a small "tweeter," which should receive high audio frequencies (treble). To separate the high and low frequencies of the audio signal, you build the "crossover network" shown in Figure P32.45. The input voltage is the audio output of the amplifier in your system, shown in the figure as an AC source. You have two outputs as shown: one across the resistor and one across the capacitor. (a) Across which element should you connect the woofer? (b) Across which element should you connect the tweeter? (c) To choose the appropriate values of $R$ and $C$, you need to determine an expression for the ratio of the output voltage to the input voltage as a function of angular frequency $\omega$ for the resistor as an output. (d) You need to determine a similar expression for the ratio of the output voltage to the input voltage as a function of angular frequency $\omega$ for the capacitor as an output.

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Figure 31.12 a shows the crossover network in a loudspeaker system. One branch consists of a capacitor $C$ and a resistor $R$ in series (the tweeter). This branch is in parallel with a second branch (the woofer) that consists of an inductor $L$ and a resistor $R$ in series. The same source voltage with angular frequency $\omega$ is applied across each parallel branch. (a) What is the impedance of the tweeter branch? (b) What is the impedance of the woofer branch? (c) Explain why the currents in the two branches are equal when the impedances of the branches are equal. (d) Derive an expression for the frequency $f$ that corresponds to the crossover point in Fig. 31.12 $\mathrm{b} .$

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Transcript

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00:01 For part a, we have across the capacitor.
00:07 For part b, we have across the source...
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