Case Study On The Model Of The Design Is Represented In The Diagram Below

Published: 2021-07-02 20:35:04
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This report is about the design of a two-way crossover laud speakers. The major task is the building of the circuit diagram.
In the design, I have ensured that the 12dB crossover follows the Linkwitz-Riley alignment. This is achieved through the use of a sub-Bessel filter whose Q is 0.5 instead of the common Butterworth alignment resulting from a Q of 0.707.
At the crossover frequency, the Butterworth crossovers have a 3dB peak. This is the main problem of such crossovers. This problem occurs when the outputs are acoustically or electrically summed. With a filter whose Q is 0.5, the signal is below the cross over frequency by 6dB for both sections (low pass section and high pass section). the resulting summed output is flat absolutely. The capacitors used here should have a tolerance of 1%. The resistors recommended here are the 1% metal film resistors. In the output part, it is better to use operational amplifiers (opamps) of low noise. The high pass section should operate with the gain (6dB) as the other section (Low Pass Section) is inverted. Some noise is added by both.
The platform
Equalization of a two-way speaker gives a flat response; however, the low distortion output is not sufficient in the frequency range where the sensitivity of the ear is low. The cabinet is then designed as either a vented or a closed box, with open baffle. In the frequency which is below the range of 200Hz, box speakers are prone to suffer from resonances and uneven base response.
The cross over filter is used so that the acoustic polar response can be maintained all through the crossover frequency range. The summation of both the high-pass and low-pass outputs is required to have an all-pass behavior in the absence of high peaks of Q.
The Butterworth Filter is designed to give a flat frequency response. The design of the filter is discussed here in.
The main requirements are: variable power supplies, two resistors, three capacitors, and an opamp.
Each of the two resistors are of 10kilo-ohms while the capacitors are of 0.1µF. the resulting circuit diagram is shown below.
Let us use the s-domain analysis for the above circuit.
With a voltage Vc(t) across the capacitor and a current of ic(t) through the capacitor;
We therefore obtain
From what we can see in the above equation; in the s-domain circuit analysis, a capacitor can be replaced with an impedance (1/Cs) in series with supply voltage.
The transfer function G(s) is given by
In a second order transfer function (standard), the above equation can be written as
The above filter is a second order low pass Butterworth filter with a transfer function of
β= √ (1/2) = 0.707
K = 1 and is specified by the user
The figure given above represents a summary of both the Low Pass filter and the High Pass Filter. The section that represents a low pass filter is given by AEFB as shown below.
In this filter, the inductive reactance of the choke (L) block higher frequencies. The capacitor C is used to produce a ground short. The result is that only the low frequencies below the cut-off frequency fc are passed without attenuation (the reactance X is very low).
The high pass filter is given by section ACDB as shown below
This is an inverted L type high pass filter. At lower frequencies, XC is large and XL is small. Most of the input voltage drop is experienced across XC, however, XL has very little voltage drop. When there is an increase in frequency, XC reduces as XL increases making the output voltage to increase. High frequencies are passed as low frequencies are attenuated.
The figure below shows the circuit diagram for the filter section (active filter)
Fig. 1
This circuit diagram is for a completely conventional filter. The primary aim of this design is for systems electronically crossed over in 2-way. An example of such systems includes the addition of a subwoofer or biampication of an already existing system of loudspeaker. Only one channel (the left channel) is shown in this diagram; however, the other channel (right channel) is practically identical.
The input buffer, as shown in figure 1, ensures accurate response by ensuring that the networks (filter networks) are driven a point of low impedance. We cannot omit or assume this. The buffer stage outputs are used to drive both the high pass section and the low pass section for every channel. The filter types used here are of conventional feedback hence, they have good performance.
The output buffers are given in the figure 2 bellow.
Fig. 2
Here, same designators of components have been used; however, there are slight changes. The first change is the inversion of the low pass section. The phase of one signal is always inverted by the 12dB crossovers.
Only the left channel is shown here, just as fig.1. In this connection, the high pass section gives a 6dB gain. At the same time, it gives room for adjustment of the level using a pot. This allows for different sensitivities of speakers. This gain can approximately be adjusted in the range of +6dB to -8dB. This gives a great allowance for installation. A gain of -1 is results from the low pass buffer, which in technical terms is an inverted unity gain. Therefore, there can be an incorporation of a phase switch as indicated. This allows for the correction of the sub-woofer phase; however, a biamp setup does not need this arrangement.
It is also possible that instead of inverting the low pass section, the high pass section can be inverted. The inversion of the high pass section is shown in figure 3 below (an alternative arrangement for the output buffers)
Fig. 3
A full vision (stereo vision) containing the two identical sections of the filter is given in figure 4 below.
Fig. 4 - Stereo Version of a 2-Way L-R Crossover
The 2-way channel shown above is divided into three sections. Every channel has the input buffer section whose major role is to ensure that frequency and phase shifts are prevented. This is possible when all the filters are driven from a low impedance source. The second part is the High pass section, and lastly, the Low pass section.
The filters should be properly matched, both between the individual filters themselves, and between the channels. Poor matching or inaccurate matching of both the high pass section and the low pass section results into both phase errors and amplitude errors.
Arthur B. Williams & Fred J. Taylor, Electronic Filter Design Handbook, McGraw-Hill, 1995.
Henry W. Ott, Noise Reduction Techniques in Electronic Systems, John Wiley, 1976.
Herman J. Blinchikoff & Anatol I. Zverev, Filtering in the Time and Frequency Domains, John Wiley, 1976.
Jasper J. Goedbloed, Electromagnetic Compatibility, Prentice Hall,1990.
Martin Hartley Jones, A practical introduction to electronic circuits, Cambridge University Press, 1995.
Walter G. Jung, editor, “Op Amp Applications,” Analog Devices, 2002.
Theraja B. L and A. K Theraja, Electrical Technology S. Chand and Company Ltd, New Delhi, 2005.

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