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1. NATIONAL COLLEGE OF SCIENCE AND TECHNOLOGY
Amafel Building, Aguinaldo Highway Dasmariñas City, Cavite
Experiment No. 4
ACTIVE BAND-PASS AND BAND-STOP FILTERS
Cauan, Sarah Krystelle P. July 21, 2011
Signal Spectra and Signal Processing/BSECE 41A1 Score:
Engr. Grace Ramones
Instructor
2. OBJECTIVES
1. Plot the gain-frequency response curve and determine the center frequency for an active
band-pass filter.
2. Determine the quality factor (Q) and bandwidth of an active band-pass filter
3. Plot the phase shift between the input and output for a two-pole active band-pass filter.
4. Plot the gain-frequency response curve and determine the center frequency for an active
band-stop (notch) filter.
5. Determine the quality factor (Q) and bandwidth of an active notch filter.
5. DATA SHEET
MATERIALS
One function generator
One dual-trace oscilloscope
Two LM741 op-amps
Capacitors: two 0.001 µF, two 0.05 µF, one 0.1 µF
Resistors: one 1 kΩ, two 10 kΩ, one 13 kΩ, one 27 kΩ, two 54 kΩ, and one 100kΩ
THEORY
In electronic communications systems, it is often necessary to separate a specific range of
frequencies from the total frequency spectrum. This is normally accomplished with filters. A
filter is a circuit that passes a specific range of frequencies while rejecting other frequencies.
Active filters use active devices such as op-amps combined with passive elements. Active filters
have several advantages over passive filters. The passive elements provide frequency selectivity
and the active devices provide voltage gain, high input impedance, and low output impedance.
The voltage gain reduces attenuation of the signal by the filter, the high input impedance
prevents excessive loading of the source, and the low output impedance prevents the filter from
being affected by the load. Active filters are also easy to adjust over a wide frequency range
without altering the desired response. The weakness of active filters is the upper-frequency limit
due to the limited open-loop bandwidth (funity) of op-amps. The filter cutoff frequency cannot
exceed the unity-gain frequency (funity) of the op-amp. Therefore, active filters must be used in
applications where the unity-gain frequency (funity) of the op-amp is high enough so that it does
not fall within the frequency range of the application. For this reason, active filters are mostly
used in low-frequency applications.
A band-pass filter passes all frequencies lying within a band of frequencies and rejects all other
frequencies outside the band. The low cut-off frequency (fC1) and the high-cutoff frequency (fC2)
on the gain-frequency plot are the frequencies where the voltage gain has dropped by 3 dB
(0.707) from the maximum dB gain. A band-stop filter rejects a band of frequencies and passes
all other frequencies outside the band, and of then referred to as a band-reject or notch filter. The
low-cutoff frequency (fC1) and high-cutoff frequency (fC2) on the gain frequency plot are the
frequencies where the voltage gain has dropped by 3 dB (0.707) from the passband dB gain.
The bandwidth (BW) of a band-pass or band-stop filter is the difference between the high-cutoff
frequency and the low-cutoff frequency. Therefore,
BW = fC2 – fC1
6. The center frequency (fo) of the band-pass or a band-stop filter is the geometric mean of the low-
cutoff frequency (fC1) and the high-cutoff frequency (fC2). Therefore,
The quality factor (Q) of a band-pass or a band-stop filter is the ratio of the center frequency (fO)
and the bandwidth (BW), and is an indication of the selectivity of the filter. Therefore,
A higher value of Q means a narrower bandwidth and a more selective filter. A filter with a Q
less than one is considered to be a wide-band filter and a filter with a Q greater than ten is
considered to be a narrow-band filter.
One way to implement a band-pass filter is to cascade a low-pass and a high-pass filter. As long
as the cutoff frequencies are sufficiently separated, the low-pass filter cutoff frequency will
determine the low-cutoff frequency of the band-pass filter and a high-pass filter cutoff frequency
will determine the high-cutoff frequency of the band-pass filter. Normally this arrangement is
used for a wide-band filter (Q 1) because the cutoff frequencies need to be sufficient separated.
A multiple-feedback active band-pass filter is shown in Figure 4-1. Components R1 and C1
determine the low-cutoff frequency, and R2 and C2 determine the high-cutoff frequency. The
center frequency (fo) can be calculated from the component values using the equation
Where C = C1 = C2. The voltage gain (AV) at the center frequency is calculated from
and the quality factor (Q) is calculated from
7. Figure 4-1 Multiple-Feedback Band-Pass Filter
XBP1
XFG1
IN OUT
10nF
C1
100kΩ
R2
741
3
Vo
6
Vin 1kΩ 2 10kΩ
10nF
R1 RL
C2
Figure 4-2 shows a second-order (two-pole) Sallen-Key notch filter. The expected center
frequency (fO) can be calculated from
At this frequency (fo), the feedback signal returns with the correct amplitude and phase to
attenuate the input. This causes the output to be attenuated at the center frequency.
The notch filter in Figure 4-2 has a passband voltage gain
and a quality factor
8. The voltage gain of a Sallen-Key notch filter must be less than 2 and the circuit Q must be less
than 10 to avoid oscillation.
Figure 4-2 Two pole Sallen-Key Notch Filter
XBP1
XFG1 IN OUT
27kΩ
27kΩ
R52
R/2
50nF 50nF
0.05µF 3
0.05µF
C3 C
Vin C C 6
2 741 Vo
RL
54kΩ 54kΩ 10kΩ
54kΩ 54kΩ
R3 R
R R 0
R2
100nF
2C R1 10kΩ
13kΩ
0
0
9. PROCEDURE
Active Band-Pass Filter
Step 1 Open circuit file FIG 4-1. Make sure that the following Bode plotter settings are
selected. Magnitude, Vertical (Log, F = 40 dB, I = 10 dB), Horizontal (Log, F =
10 kHz, I = 100 Hz)
Step 2 Run the simulation. Notice that the voltage gain has been plotted between the
frequencies of 100 Hz and 10 kHz. Draw the curve plot in the space provided.
Next, move the cursor to the center of the curve. Measure the center frequency
(fo) and the voltage gain in dB. Record the dB gain and center frequency (fo) on
the curve plot.
fo = 1.572 kHz
AdB = 33.906 dB
AdB
40dB
10 dB f
100 Hz 10 kHz
Question: Is the frequency response curve that of a band-pass filters? Explain why.
Yes, the frequency response is a band-pass filter. The filter only allows the
frequencies lying within the band which is from 100.219 Hz to 10 kHz.
Moreover, the frequency response shows the highest gain at the center
frequency.
Step 3 Based on the dB voltage gain at the center frequency, calculate the actual voltage
gain (AV)
AV = 49.58
10. Step 4 Based on the circuit component values, calculate the expected voltage gain (AV)
at the center frequency (fo)
AV = 50
Question: How did the measured voltage gain at the center frequency compare with the
voltage gain calculated from the circuit values?
There is only a 0.84% difference between the measured and the calculated
values of voltage gain. And also, the measured and calculated values have a
difference of 0.42.
Step 5 Move the cursor as close as possible to a point on the left of the curve that is 3 dB
down from the dB gain at the center frequency (fo). Record the frequency (low-
cutoff frequency, fC1) on the curve plot. Next, move the cursor as close as possible
to a point on the right side of the curve that is 3 dB down from the center
frequency (fo). Record the frequency (high-cutoff frequency, fC2) on the curve
plot.
fC1 = 1.415 kHz
fC2 = 1.746 kHz
Step 6 Based on the measured values of fC1 and fC2, calculate the bandwidth (BW) of the
band-pass filter.
BW = 0.331 kHz
Step 7 Based on the circuit component values, calculate the expected center frequency
(fo)
fo = 1.592 kHz
Question: How did the calculated value of the center frequency compare with the measured
value?
Their values are close. The percentage difference of the calculated value and
the measured center frequency is 1.27%. There is a difference is 0.02.
Step 8 Based on the measured center frequency (fo) and the bandwidth (BW), calculate
the quality factor (Q) of the band-pass filter.
Q = 4.75
11. Step 9 Based on the component values, calculate the expected quality factor (Q) of the
band-pass filter.
Q=5
Question: How did your calculated value of Q based on the component values compare with
the value of Q determined from the measured fo and BW?
The two values are almost alike. The calculated and measured quality factor
differs with only 0.25. It is 5.26% difference between the expected and the
measured quality factor of the band-pass filter.
Step 10 Click Phase on the Bode plotter to plot the phase curve. Change the vertical initial
value (I) to -270o and the final value (F) to +270o. Run the simulation again. You
are looking at the phase difference (θ) between the filter input and output wave
shapes as a function of frequency (f). Draw the curve plot in the space provided.
θ
o
270
o
-270 f
100 Hz 10 kHz
Step 11 Move the cursor as close as possible to the curve center frequency (fo), recorded
on the curve plot in Step 2. Record the frequency (fo) and the phase (θ) on the
phase curve plot.
fo = 1.572 kHz
θ = 173.987o
Question: What does this result tell you about the relationship between the filter output and
input at the center frequency?
The phase shows that the relationship between the filters output is 173.987o or
almost 180o out of phase compared to input.
12. Active Band-Pass (Notch) Filter
Step 12 Open circuit file FIG 4-2. Make sure that the following Bode plotter settings are
selected. Magnitude, Vertical (Log, F = 10 dB, I = -20 dB), Horizontal (Log, F =
500 Hz, I = 2 Hz)
Step 13 Run the simulation. Notice that the voltage gain has been plotted between the
frequencies of 2 Hz and 500 Hz. Draw the curve plot in the space provided. Next,
move the cursor to the center of the curve at its center point. Measure the center
frequency (fo) and record it on the curve plot. Next, move the cursor to the flat
part of the curve in the passband. Measure the voltage gain in dB and record the
dB gain on the curve plot.
fo = 58.649 Hz
AdB AdB = 4. dB
10 dB
-20 dB f (Hz)
2 Hz 500 Hz
Question: Is the frequency response curve that of a band-pass filters? Explain why.
Yes, the frequency response is that of a band-stop filter. The filter only allows
the frequencies outside the band and rejects all frequencies lying within the
band which. And also, the center frequency is at the lowest voltage gain.
Step 14 Based on the dB voltage gain at the center frequency, calculate the actual voltage
gain (AV)
AV = 1.77
Step 15 Based on the circuit component values, calculate the expected voltage gain in the
passband.
AV = 1.77
13. Question: How did the measured voltage gain in the passband compare with the voltage gain
calculated from the circuit values?
They have the same values. The measured and expected voltage gain has no
difference.
Step 16 Move the cursor as close as possible to a point on the left of the curve that is 3 dB
down from the dB gain in the bandpass Record the frequency (low-cutoff
frequency, fC1) on the curve plot. Next, move the cursor as close as possible to a
point on the right side of the curve that is 3 dB down from dB gain in the
passband. Record the frequency (high-cutoff frequency, fC2) on the curve plot.
fC1 = 46.743 Hz
fC2 = 73.588 Hz
Step 17 Based on the measured values of fC1 and fC2, calculate the bandwidth (BW) of the
notch filter.
BW = 26.845 Hz
Step 18 Based on the circuit component values, calculate the expected center frequency
(fo)
fo = 58.95Hz
Question How did the calculated value of the center frequency compare with the measured
value?
There is a 0.51% difference between the expected and measured value of the
center frequency. They are almost equal.
Step 19 Based on the measured center frequency (fo) and bandwidth (BW), calculate the
quality factor (Q) of the notch filter.
Q = 2.18
Step 20 Based on the calculated passband voltage gain (Av), calculate the expected quality
factor (Q) of the notch filter.
Q = 2.17
Question: How did your calculated value of Q based on the passband voltage gain compare
with the value of Q determined from the measured fo and BW?
The values are almost equal. The difference between the calculated and
measure quality factor is 0.01. The calculated only differs 0.46% compared to
the measured value.
14. CONCLUSION
After plotting the gain-frequency response curve of each filter, I conclude that the
response of active filter is the same as the response of a passive filter. Active band pass filters are
simply filters constructed by using operational amplifiers as active devices combined with
passive elements. Still, active band-pass filter passes frequencies within a certain range and
rejects frequencies outside that range. The active band-stop filter is its counterpart which passes
the frequencies outside the band and attenuates the frequencies lying within that band.
Furthermore, the center frequency is the geometric mean of the low and high cutoff. I
notice that the center frequency of a band pass filter is the peak of the mountain like response
where it achieves its highest gain. On the other hand, the center frequency of a band-stop filter is
where the filter achieves its lowest gain.
The cutoff frequency is where the gain decreased by 3 dB. The bandwidth of the response
curve is the difference between the high cutoff frequency and the low-cutoff frequency.
Moreover, for a two-pole active band-pass filter, the output is 180o out of phase with its input.
Lastly, the quality factor indicates the selectivity of the filter. It is inversely proportional
to the bandwidth. If Q is less than one it is considered to be wide-band filter and if Q is greater
than ten it is considered as narrow-band filter. For Sallen-Key Notch Filter’s quality factor
should be less than 10.
