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 1320 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 steplike 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.
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 (1015 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 cutoff 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 cutoff 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 cutoff frequency was 72kHz, while our observed cutoff 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 4ag 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
Graph: The x axis is the frequency in Hz, and the yaxis is the Vout/Vin voltage
e.
Graphs: Top one is Vout/Vin with respect to frequency, Bottom is loglog graph with same values
Image: Circuit Diagram with a Microphone and Headphone Jack
i think we get the same values for the cut off frequency for question 4 and 5 for question #4 we get 700kHz and we get 600kHz for question 5
ReplyDeleteAdmittedly, my group struggled a bit with the cutoff frequencies because our experimental values were nowhere near the ones we calculated, so this confirmation is encouraging.
DeleteWe got very similar graphs for 4 and 5. I do wish my group used more points to get a more defined and precise graph like you guys, but my group was able to get the cutoff frequencies from the data points we collected.
ReplyDeleteIt is good to know that our graphs look right. Thank you for the feedback.
DeleteOur resistance was around 8 ohms. I wonder if we had different speakers since this is such a drastic change. Your graph seemed to look very similar to ours for the different filters. Your logarithmic scaling seemed to be confusing because of your outlier frequency values. When we eliminated these values, it made the graphs look a lot more like they were supposed to. I like that you made your tables and graphs very large so it is easy to see details. Overall, good job this week.
ReplyDelete