Design a first-order, 3-way speaker system shown in Fig. 12.1 as follows:
Select loudspeaker drivers by searching the internet for a tweeter, midrange, and woofer. For each driver, note the following specifications:
Frequency Range
Impedance, Z
Sensitivity
Resonance Frequency, Fs
Select crossover frequencies for your 3-way speaker system according to the following specifications:
Tweeter (T)
Fc2 ≥ 4 kHz
Fc2 / FsT ≥ 3 (1.5 octaves)
Midrange (M)
Fc2 / Fc1 ≥ 6 (3 octaves)
Woofer (W)
Fc1 ≥ 500 Hz
Fc1 / FsW ≥ 3 (1.5 octaves)
Design the frequency filters for the loudspeaker drivers using the tweeter as a high-pass filter, the midrange as a band-pass filter, and the woofer as a low-pass filter. Calculate the capacitor and inductor component values of each respective filter as follows:
Tweeter (T)
C1 = 1 / (2π × Fc2 × ZT)
Midrange (M)
L1 = ZM / (2π × Fc2)
C2 = 1 / (2π × Fc1 × ZM)
Woofer (W)
L2 = ZW / (2π × Fc1)
Model the circuit in Fig. 12.1 using PSPICE or LTSPICE using the previously calculated component values. The speaker drivers can simply be represented by their appropriate component(s) equivalent values based on the impedance of that driver. Set your voltage source as a type SINE function with Voffset = 0, Vamp = 120, and Freq = 60. Use the AC Analysis simulation setting to show a Bode plot of your 3-way speaker system design.
Procedure
Construct the circuit shown in Fig. 12.1 using industry standard component values that match as closely as possible to your calculated component values. Adjust the amplitude of the function generator to 2 V.
Attach your signal probe across the impedance components (that represents that respective loudspeaker driver) of each of your three filter types only one-at-a-time while performing the next step for each filter.
Vary the frequency generated by the function generator and observe the output on the oscilloscope. What happens to the gain as the frequency approaches the cutoff frequency(s) from a frequency that is less than and greater than the cutoff frequency(s)?
A 2-way speaker system has been setup in the lab room. Adjust the frequency of the function generator that is attached to the speaker and listen to the output of the speakers. As you listen and vary the frequency, the sound of the frequency transition will generally sound smooth. However, as you approach the cutoff frequency, you should hear a notable abrupt transition in the sound of the frequency as the sound transitions from one speaker driver to the other.
By listening to the output of the speakers as previously described, estimate the cutoff frequency of the 2-way speaker system and derive the component values.
Questions and Conclusions
Compare your preliminary calculations to your observations. Give plausible reasons for the discrepancies.
