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For this project you will be designing and simulating a three-way crossover network. These networks are commonly used in good quality stereo speaker systems. It turns out that it is difficult to get
a single cone speaker that can cover the entire audible range from 20 Hz to 20 kHz effectively. In a
three-way system three speakers are required. For deep bass a woofer for is used. This is the largest
speaker of the three and is suitable for reproducing sounds with a frequency of a couple of hundred
hertz or below. For the midrange frequencies a midrange speaker is used. It is typically able to reproduce sounds from a couple of hundred hertz to a few kilohertz. To reproduce the highest frequencies
a tweeter is used. It is the smallest speaker of the system and is able to reproduce sounds with frequencies above a few kilohertz.
Each of these speakers works well to reproduce sounds within its designed frequency range. Operating a speaker beyond that range of frequencies, however, will waste power and can potentially be
damaging. So it is important to make sure that the frequencies fed into each speaker (driver) are right
for them. In order to accomplish this task three passive filters are employed. For the tweeter a highpass filter is used. For the midrange frequencies a bandpass filter is employed. And for the deep
bass going to the woofer a low-pass filter is employed. When the outputs of these three filters are
combined a relatively flat all pass response will be observed. A stereo system has two identical copies
of the crossover network and speakers. One for the left channel and one for the right channel. For
our project, only one three way crossover system will be designed and simulated.
As the power output from a home stereo system can easily exceed 100W per channel a passive
filter network has to be employed. Active filters are not suitable for a speaker crossover network.
The Task

  1. Using nodal analysis, find the transfer function H(s) for each filter subsection (high-pass, lowpass, and bandpass) of the schematic in Fig. 1 in terms of L1, L2, L3, L4, C1, C2, C3, C4, and Rspeaker. For the purpose of this project assume that all three speakers have an impedance of
    eight ohms (purely resistive).
  2. Design your crossover network by finding the inductor and capacitor values that will provide
    the desired response for your system. The desired system frequency response is as follows:
    Given a 1 VRMS sinusoidal input into the combination of the three filters (as seen in Fig. 1) each
    filter section will have a 1 VRMS (0 dB) output in the passband and a 0.5 VRMS (-6 dB) output at
    the crossover frequency. In addition, the combined response of the three filter sections will
    have a flat response within ±0.2 VRMS and the individual response of each of the three filter sections shall not exceed 1.2 VRMS. Note that some of the component values may need to be adjusted slightly in order to meet this design criteria. Also note that the crossover frequency is
    not the same as the -3dB frequency.
    The upper and lower crossover frequencies for your project will depend on the first letter of
    your last name (as it appears on the official class roster) as specified in Table 1 below.
    Note: Using crossover frequencies, for your project, other than the ones specified herein will
    result in a 15% reduction in your overall grade for the project. Although a small deviation
    (within ± 5%) in crossover frequency is allowed in order for you to meet the filter design criteria
    st Letter of Your Last
    Lower Crossover Frequency (Hz)
    Upper Crossover Frequency (Hz)
    Design Type
    A-H 100 2500 A
    I-Q 250 5000 B
    R-Z 400 6000 C
    Table 1
  3. Provide a Bode plot for each of your three filter section designs (high-pass, low-pass, and
    bandpass) using the MATLAB ‘tf’ and ‘bode’ commands. Be sure to include a description under
    each plot. Note that the MATLAB ‘bode’ command plots the frequency in radians per second
    and not Hertz by default. The frequency axis should extend from 60 R/s to 600,000 R/s.
  4. Using a SPICE circuit simulator (like LTSpice) simulate your three-way crossover system as
    one combined circuit. The schematic diagram of the 3-way crossover is shown in Fig. 1.
    Provide using SPICE:
    • A bode magnitude and phase plot for the output of each filter section from 10 Hz to 100 kHz
    (3 separate plots).
    • One combined magnitude plot of the three filter sections in dB (add the 3 output voltages together) versus frequency from 10 Hz to 100 kHz.
    • One combined magnitude plot of the three filter sections in linear volts (add the 3 output voltages together) versus frequency from 10 Hz to 100 kHz.
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