Three-way Crossover Filter Network

Three-way Crossover Filter Network

Introduction
Students were tasked with designing a three-way crossover network of filters to drive a multiple speaker system, similar to three-way crossover networks found in home and car stereo systems. Since speakers are designed with a specific range of output frequencies, it is necessary to filter frequencies outside of their intended operational range to prevent damage to the speakers. Additionally, students were tasked with achieving a maximum amplitude as close to 0dB as possible for each filter in the network, prior to amplification.

For a typical stereo system, there are three sizes of speakers, each with their own operational frequencies. A subwoofer can typically produce sounds below 200 Hz, while midrange speakers can typically produce sounds from 200Hz to 6kHz, and tweeters can produce sounds from 6kHz up to the limits of human hearing (20kHz). With these parameters in mind, target corner or “cutoff” frequencies, where the gain is -3dB of the maximum, for each filter were chosen as follows:

Low Pass: 200 Hz
Band-Pass 1: 200 Hz
Band-Pass 2: 6kHz
High-Pass: 6kHz

An allowable tolerance of 20% was designated as acceptable, meaning that the actual cutoff frequency could be within 20% of the target. i.e., for the low-pass filter, anywhere from 160Hz to 240Hz would be an acceptable outcome and for the high-pass filter, anywhere from 4.8kHz to 7.2kHz would be an acceptable outcome.

Students were also given restrictions on components. No more than one inductor was to be used per filter circuit and only those inductor values found in the lab. Additionally, inductors were to be chosen first, as there was a significantly smaller array of values to choose from than for other components. As few capacitors as possible were to be used for each circuit and only those capacitor values found in the lab. In order to prevent drawing excessive current from the audio jack, no resistors smaller than 100Ω were to be used. Finally, the schematic and values for the operational amplifier section of the circuit was provided with a gain of 20, making the final output about 0.6V(pk-pk).

Design

For the design phase, circuit layouts were chosen with simplicity in mind. As specified in the lab, for those circuits with inductors, inductors were selected first. Smaller inductors were deemed preferable in the selection process after excessive signal noise was encountered when one prototype was tested with a 100mH inductor. For those circuits without inductors, capacitors were selected first as the array of available values was significantly smaller than for resistors.

Low-Pass Filter Design
For the low-pass filter, a simple first-order RC circuit was chosen. By placing a resistor in series with a capacitor, and then placing the output parallel to the capacitor, a low-pass filter is achieved. This is due to the nature of the reactance of the capacitor. A capacitors reactance varies with the frequency of the signal. At low frequencies, a capacitor provides extremely high resistance, which effectively blocks any low frequency signal from passing through. In fact, at DC voltages (0Hz), a capacitor acts as an open circuit (infinite resistance).

By placing the capacitor C in parallel with the output, the circuit allows high frequencies to bypass the capacitor and travel the path of least resistance directly to ground. Conversely, the capacitor blocks low-frequency signals from ground and forces them into the output node Vo. In this case, the resistor R simply acts as a way to restrict excessive current from entering the circuit, potentially damaging the audio jack providing the signal.

Figure 1: Basic Low-Pass Filter Schematic


Band-Pass Filter Design
For the band-pass filter, a slightly more complex second-order circuit was chosen. By placing an inductor and capacitor in series with a resistor, and placing the resistor parallel to the output, a band-pass filter is achieved. This is due to the nature of the reactance of the inductor and capacitor respectively. Both components reactance varies with the frequency of the signal. However, while a capacitor acts as an open circuit at low frequencies, an inductor acts as an open circuit (infinite resistance) at high frequencies.

By placing the inductor L and the capacitor C in series, both low and high frequencies are filtered before the signal gets to the output node Vo. In this case, the resistor R simply regulates the amplitude of the signal flowing to Vo by allowing a certain amount of current to flow directly to the ground.

Figure 2: Basic Band-Pass Filter Schematic

High-Pass Filter Design
For the high-pass filter, a simple first-order RL circuit was chosen. While this layout is nearly identical to the design of the low-pass filter, the placement of the inductor parallel to the output, instead of a capacitor, achieves the opposite result; a high-pass filter. This is due to the nature of the reactance of the inductor. An inductors reactance varies with the frequency of the signal. At high frequencies, an inductor provides extremely high resistance, which effectively blocks any high frequency signal from passing through. Opposite the behavior of a capacitor, at DC voltages (0Hz), an inductor acts as a short circuit (zero resistance).

By placing the inductor L in parallel with the output, the circuit allows low frequencies to bypass the inductor and travel the path of least resistance directly to ground. Conversely, the inductor blocks high-frequency signals from ground and forces them into the output node Vo. In this case, the resistor R simply acts as a way to restrict excessive current from entering the circuit, potentially damaging the audio jack providing the signal, similar to the low-pass filter.

Figure 2: Basic High-Pass Filter Schematic

Measured Results

Figure 3: Breadboard Prototype

Each filter was assembled on a breadboard and an 8V signal was generated and applied to the source input. A range of frequencies from 10Hz to 300kHz were observed, logged, and plotted. Cutoff frequencies were determined by observing the point at which the amplitude equaled (-3dB), or as close to that value as the oscilloscope would allow. All three filters were functional and had cutoff frequencies well within the acceptable tolerance. Finally, a speaker was attached at the output of the operational amplifier and the behavior was qualitatively verified by the lab TA.