Lab 6: Filter Design Project ENG214: Circuit Analysis Laboratory

Tim Laux, Eric Brokaw, Thomas Approvato, Alin Bojkovic

The College of New JerseyDecember 11th 2014

Table of Contents1. Application2. Requirements3. Research4. Calculations5. Solution6. Equipment7. Procedure8. Results9. References

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

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.

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

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

Research• There are three major

responses possible from an active filter.o Besselo Butterwortho 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

• We used “Op-Amps for Everyone” by Texas Instruments to design our filter according to our needs.

Calculations

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

Solution• Bill of materials

Op-amp1. LM324 Quad Op-amp

Carbon film resistors1. 12K2. 15K3. 22K4. 30K

Ceramic capacitors1. 0.1μF (2x)2. 1nF (3x)

Total cost (single quantity) : $0.98

Figure 10. Circuit on a breadboard

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

Procedure1. 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

Results

10 100 1000 10000-36

-33

-30

-27

-24

-21

-18

-15

-12

-9

-6

-3

0

3

Band-pass Filter Gain vs. Frequency

LTSpice

Frequency (Hz)

Ga

in

(dB

)

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

ResultsIdeal LTSpic

eMeasure

d

Cutoff frequency 1(-3dB)

100 Hz 103 Hz 107 Hz

Cutoff frequency 2 (-3dB)

5000 Hz

5010 Hz 5400 Hz

-3dB bandwidth 4900Hz

4907 Hz 5293 HzFigure 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.

LTSpice

Measured

Error (cutoff frequency 1)

2.96 % 6.76 %

Error(cutoff frequency 2)

0.20 % 7.69 %Figure 14. Percent error

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