1. Lab 6: Filter Design Project ENG214: Circuit Analysis Laboratory Tim Laux, Eric Brokaw, Thomas Approvato, Alin Bojkovic The College of New Jersey December 11 th 2014

2. Table of Contents 1.Application 2.Requirements 3.Research 4.Calculations 5.Solution 6.Equipment 7.Procedure 8.Results 9.References

3. Application A singular loudspeaker is generally incapable of reproducing the entire audio spectrum with a linear frequency response and without distortion. Most professional and high-end systems use two or more drivers, each catering to a specific range of frequencies. Each loudspeaker needs to be driven by a signal with frequencies in its linear range of operation. Figure 1. Three-way speaker system

4. Requirements Figure 3. HiVi M4N Frequency Response Figure 2. HiVi M4N We picked out the HiVi M4N, a commercially available driver. After examining its frequency response plot, we determined that it responded linearly between 100Hz and 5kHz. This makes it a low-midrange driver. Therefore, we require a band-pass filter which has -3dB cutoff frequencies of 100Hz and 5kHz.

5. Research There are two ways to filter audio signals: before or after amplification (active or passive crossovers) Before amplification (active): Better overall sound quality Highly tunable Less expensive Smaller/lighter  Requires multiple amplifiers After amplification (passive): Requires only one amplifier Lower complexity  Potentially expensive  Bulky/heavy  Power losses and non-linearities Figure 4. Active Crossover Figure 5. Passive Crossover

6. Research We chose the active filter route. The two popular active filter topologies are Sallen-Key and multiple feedback (MFB). We chose the Sallen-Key topology because of its simplicity and its suitability for our application. In order to pass a wide band of frequencies, we need to cascade two filters, one high-pass and one low-pass. Figure 6. Sallen-Key Figure 7. Multiple Feedback

7. Research There are three major responses possible from an active filter. o Bessel o Butterworth o Tschebyscheff We chose a Butterworth response because of its passband flatness and its relatively sharp transition into the stopband. Bessel was not steep enough, while Tschebyscheff introduces some ringing in the passband. Figure 8. Comparison of different filter responses

8. Calculations

9. Solution First, we used LTSpice to confirm the design worked. Then, we swapped in the closest E12 capacitor values and the closest E24 resistor values. We resimulated with these values. We were able to achieve acceptable performance even with the adjusted values. Figure 9. Schematic diagram of the filter

10. Solution Bill of materials   Op-amp 1.LM324 Quad Op-amp  Carbon film resistors 1.12K 2.15K 3.22K 4.30K  Ceramic capacitors 1.0.1μF (2x) 2.1nF (3x) Total cost (single quantity) : $0.98 Figure 10. Circuit on a breadboard

11. Equipment Figure 11. HP 64645D Oscilloscope Figure 12. Agilent 33220A Function Generator HP 54645D Oscilloscope Agilent 33220A Function Generator Elenco XP-581 Quad Power Supply Breadboard

12. Procedure 1.Using sources from online about op-amps and filter design techniques, we drew the schematic for our filter 2.We built the circuit on a breadboard 3.We tested this filter using frequencies ranging from 10Hz to 60kHz The op amp was powered by a ±12V supply The function generator was used to create the test frequencies The output was probed with the oscilloscope and the peak-to-peak voltage was recorded at each frequency 4.We created the circuit using LTSpice 5.We compared our experimental data with our calculated data using LTSpice

13. Results Figure 13. Gain vs. Frequency Plot (Simulated and Measured)

14. Results Figure 13. Results comparison The results from LTSpice were very close to the ideal figures. The measured results were close, and had errors less than 10%. Taking component variations into consideration, our results were satisfactory. Figure 14. Percent error

15. References Carter, B. (2001). Active Filter Design Techniques. In Op-Amps for Everyone. HiVi Speaker. (2006). M4N Full Frequency. Retrieved from Swan Speaker: http://www.swanspeaker.com/product/htm/view.asp?id=83 Maxim Integrated Products. (2003, February 4). A Beginner's Guide to Filter Topologies. Retrieved from Maxim Integrated: http://www.maximintegrated.com/en/app-notes/index.mvp/id/1762 bibin3210. (2012, May 8). Active vs. Passive Crossovers. Retrieved from HiFi Vision: http://www.hifivision.com/active-speakers/17925-active-vs- passive-crossover.html