Lab 9

1. Measure the resistance of the speaker. Compare this value with the value you would find online.

The resistance of our speaker was about 18.8 Ohms, how ever we noticed it was moved even a little it would change the resistance, so our DMM ended up varying from about 13-20 ohms. Looking online, most speakers have a resistance of either 4, 8 or 16 ohms.

2. Build the following circuit using a function generator setting the amplitude to 5V (0V offset). What happens when you change the frequency? (video)

Image: Simple Speaker Circuit Diagram

Frequency (Hz)	Observation
1	No sound
15	Quiet chirping sound
222.22	Quiet low pitched hum
1000	High pitched hum
23000	No sound

Table: Sound observations from the varying frequency

Video: Explanation of the Effect of Varying frequency.

As stated in the table above, very low frequency and very high frequencies were inaudible from the speaker. In the range of audible frequencies, the lower ones had a lower pitch, and as the frequency was gradually increased, the pitch of the sound from the speaker increased. This increase was not gradual, but occurred in step-like increments. 

3. Add one resistor to the circuit in series with the speaker (first 47 Ω, then 820 Ω). Measure the voltage across the speaker. Briefly explain your observations.

Resistance (Ω)	Oscilloscope output over speaker (V)	Observation
47	1.2	Same pitch as without resistance, but it is quieter
820	0.16	The pitch still remains the same, and it is even quieter.

Table: Voltage across certain resistances and what was observed

This data shows that the resistance values of a circuit involving a speaker do not have an apparent impact on the pitch of the resulting sound. This means that the resistance does not affect the frequency of the voltage. Resistance, does, however, affect volume i.e.; the higher the resistance the lower the volume.

4. Build the following circuit. Add a resistor in series to the speaker to have an equivalent resistance of 100 Ω. Note that this circuit is a high pass filter. Set the amplitude of the input signal to 8 V. Change the frequency from low to high to observe the speaker sound. You should
not hear anything at the beginning and start hearing the sound after a certain frequency. Use 22 nF for the capacitor.

Image: Speaker Circuit Diagram with a Capacitor

a. Explain the operation. (video)

Video: Operation of the High pass filter

b. Fill out the following table by adding enough (10-15 data points) frequency measurements. Vout is measured with the DMM, thus it will be rms value.

Frequency (Hz)	Vout (rms) (mV)	Vout (rms)/ Vin (rms) (mV)
0	1	.18
20	1	.18
100	2	.3536
500	2	.35
1000	5	.884
1500	6	1.061
2000	7	1.238
2500	8	1.45
3000	9	1.59
3500	10	1.77
4000	11	1.95
5000	12	2.12
10000	12	2.12
15000	8	1.45
20000	6	1.061

Table: Varying frequency and the measured output

c. Draw Vout/Vin with respect to frequency using Excel.

Graph: Vout/Vin and frequency

d. What is the cut off frequency by looking at the plot in b?

The cut-off frequency from this set of data appears to be about 8000 Hz. This can be seen in the graph above and the two graphs below because the cut-off frequency is where the Vin/Vout stops increasing with respect to frequency.

e. Draw Vout/Vin with respect to frequency using MATLAB.

Vout/Vin Vs Frequency

Graphs: Top one is Vout/Vin with respect to frequency, Bottom is loglog graph with same values

f. Calculate the cut off frequency theoretically and compare with one that was found in c.

Our calculated value for the cut-off frequency was 72kHz, while our observed cut-off frequency was about 8000 Hz. This large discrepancy could have been avoided if we had tested larger values for Frequency instead of assuming that this apparent downward trend after 8000 Hz would continue.

g. Explain how the circuit works as a high pass filter.

A high pass filter blocks waves of lower frequencies from passing while allowing higher frequency waves, depending on the setting of the filter, to pass. This means that the the input and output voltages for the higher frequency waves should be about the same. the result of this is that the higher frequencies are audible, and the lower ones are silenced.

5. Design the circuit in 4 to act as a low pass filter and show its operation. Where would you put the speaker? Repeat 4a-g using the new designed circuit.
5a.
5b. Low pass filter

Frequency (Hz)	Vout (rms) (V)	Vout (rms)/ Vin (rms) (V)
0	.001	.001707
20	.286	.0505
100	.287	.0507
220	.29	.0512
500	.297	.05249
650	.32	.0565
700	.326	.0576
750	.331	.05848
830	.329	.058
1000	.315	.0556
1500	.293	.0518
3000	.239	.0472
5000	.197	.0348
10000	.116	.0205
15000	.069	.012
20000	.042	.0074

Graph: Low pass filter with varying frequency

5c.

Graph: The x axis is the frequency in Hz, and the y-axis is the Vout/Vin voltage

e. 

Graphs:  Top one is Vout/Vin with respect to frequency, Bottom is loglog graph with same values

6. Construct the following circuit and test the speaker with headsets. Connect the amplifier output directly to the headphone jack (without the potentiometer). Load is the headphone jack in the schematic. “Speculate” the operation of the circuit with a video.

Image: Circuit Diagram with a Microphone and Headphone Jack