ECEN 3714----Network Analysis
Section 3
Laboratory Manual
LAB 9:- Active Band Pass Filter
Oklahoma State University
School of Electrical and Computer Engineering.
Laboratory manual
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Spring 2016
LAB-9 Active Band-Pass Filter
1. OBJECTIVE
nd
st
The objective of this lab is to construct a 2 -order band-pass filter, in comparison to the previous 1 -order low-pass (or
nd
high-pass) filters. A 2 -order filter can be low-pass, high-pass, band-pass, or band-reject. A band-pass filter passes
frequencies within certain range and rejects (attenuates) frequencies outside that range. This lab enhances your skills and
understanding of the filter for preparing you to complete the final project.
2. INTRODUCTION TO ACTIVE BAND PASS FILTER
A band pass filter passes signals within a certain "band" or range of frequencies between two cut-off or corner frequencies
labeled "lower frequency" (ƒl or f1) and "higher frequency" (ƒh or f2), while attenuating signals outside this range, as shown
in the frequency response in Fig 1. (Question: is the center frequency of a bpf
0 
1  2
2
?)
Figure 1
A Band Pass Filter can be constructed by cascading a Low Pass Filter with a High Pass Filter. The cut-off or corner
frequency of the low pass filter (LPF) must be higher than the cut-off frequency of the high pass filter (HPF), otherwise
nothing may get through. A simple band-pass filter, as is shown in Fig. 2, is composed by using an RC-based 1st-order
high pass filter and a 1st-order low pass filter. The filter shown in Fig. 2 uses an op-amp, but its overall response is loaddependent, why?
Figure 2
Figure 3
A “true active” band pass filter (that means the frequency-response is load-independent) can be constructed by using an
active low-pass filter cascaded with an active high-pass filter as the one shown in Fig. 3. The transfer function is obtained
by multiplying the transfer function of the low pass filter with that of the high pass filter, i.e.;
1


V ( s )  R2
R2C2
H ( s)  0
 
 R1
1
Vi ( s )
s

R2C2



s
  R4
 R3
1
s

R3C3







The lower cut-off frequency of the band-pass filter is the cut-off frequency of the high-pass filter, and the higher cut-off
frequency of the band-pass filter is the cut-off of the low-pass filter, should both the low-pass and high pass filters have
ideal transition bands, in which cases,
1 
Laboratory manual
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1
and  2 
R3C3
R2 C 2
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Spring 2016
However, as the LPF and HPF shown in Fig.3 do not have sharp transition band, and if ω2 is not significantly
greater than ω1, you will find that the gain at the center-frequency is much lower than 1 (if both the HPF and LPF
have a pass-band gain of 1), and the actual cut-off frequencies are not the ones shown above. Why?
Center Frequency: - The band-pass filter has a peak amplitude response at its "center frequency". The center
frequency is the “geometric mean” of the lower and upper cut-off frequencies:
0  12
The "Q" or Quality Factor: - The Q of the band-pass filter is calculated by
, Where
is the band width of
the filter. This Q Factor is a measure of how "selective" or "un-selective" the band pass filter is towards a given spread of
frequencies. The higher the value of the Q factor is, the narrower the bandwidth of the filter is, and consequently the more
"selective" the filter is. The Q value of a BPF is much dependent upon the specific design of the filter-----the specific design
infers to whether the BPF is constructed by cascading a LPF and a HPF or by more advanced design----choosing the
poles of the transfer function.
A “wide-band” band-pass filter may be constructed as the one shown in Figure 4(a), and a “narrow-band” band-pass-filter
may be constructed as the one shown in Figure 4(b).
(a)
(b)
Figure 4
3. PRE-LABORATORY ASSIGNMENT
The pre-lab section helps you to understand the requirements of the lab. The pre-lab assignment MUST be completed
before you perform the hands-on laboratory measurement. The pre-lab worth 40% of the grade of this lab.
3.1 Pre-Lab Assignments:
3.1.1 You can use the circuit in Fig. 3 or another circuit to design a BPF. If you use the circuit other than the one
in Fig. 3, you are responsible for deriving the transfer function of the circuit and using it to figure out the
values of the circuit elements. The requirement of the band pass filter is that
----the cut-off frequency of the HPF-only part is 1.0 KHz ---------------------------------------10%pts
----the cut-off frequency of the LPF-only part is 5.0 KHz, -------------------------------------10%pts
----You can choose R1=R2, and R3=R4. What is the overall pass-band gain of the filter? In order to find
that gain, you need to evaluate the gain at the center frequency of the designed filter, i.e., at the geometric
mean of the higher and lower cut-off frequencies. -----------------------------------------------5% pts.
(List the design values of the elements and justify your results------you will find it easier to choose
the values of the capacitors first, then find the values of the resistors.)
3.1.2 Find the frequency-response (between 0—100KHz) of the circuit using Pspice. --------5%pts
3.1.3 From the PSPICE response, find the frequencies of which the gain is 0.707 of the maximum gain. Are
those still 1.0 KHz and 5.0 KHz? ……---------------------------------------------------------------5%pts
3.1.4 Calculate the Q-factor of your BPF, using bandwidth you found with PSPICE------------5%pts
You will need a flash drive to save the data from the oscilloscope. Check the data saved in the disk before leaving lab as
no credit can be given for lost data.
4. LABORATORY ASSIGNMENT
4.1 Preparation:
 Check the availability of a working op-amp in your took kit along its data sheet. Be prepared that you may see
something unexpected in terms of the actual frequency-response.
Laboratory manual
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4.2 Activities:4.2.1 You will design your BPF like the one in Fig.3 or another design you have chosen in your pre-lab.
Construct the LPF and HPF, but do not connect them together, so they can function separately. Verify that
the cut-off frequency of the LPF is 5.0 KHz, and the cut-off frequency of the HPF is 1.0 KHz, with a
tolerance of 5%. You may need to use potentiometer to adjust the cut-off frequency of the separated LPF
and the HPF.
Measure the amplitude and phase responses of each of the HPF and LPF at the following frequencies:
100Hz, 250Hz, 500Hz, 1KHz, 2.5KHz, 5KHz, 10KHz, 25KHz, 50KHz, 100KHz.
You are going to plot the measured amplitude and phase responses in your lab report using a logarithmic
frequency scale in MATLAB.
4.2.2
Now connect the LPF and HPF to form a BPF (caution: turn off the power first!). Measure the amplitude
and phase responses at the same frequencies as in 4.2.1.
4.2.3
Find the center frequency and the gain at the center frequency. Then find the frequencies at which the
gain is 0.707 (-3dB) of the gain at the center frequency.
4.2.4
If the cut-off frequencies seem to have changed from 1.0 KHz and 5.0 KHz, provide the explanations.
4.3 Laboratory Report:4.3.1 Cover page---------------------------------------------2%
The cover page should include (1) the course name, lab-sections, dates, lab numbers, etc. that indicate the
comprehensive lab information, (2) the names of the group members, and the signatures of the members. The lab
should be the work of the lab-group only, no discussion with other group members is allowed.
4.3.2 Objective of the lab: - ----------------------------------3%
Describe the objective of this laboratory section---what are the expected learning outcomes?
4.3.3. Completed pre-lab (with the signature of TA): ---------------40 %
4.3.4 Results and data analysis---------------------------------40%
Based on the order of the laboratory activities defined in 4.2, organize the estimated and observed responses of the
circuits. This section shall include the following components for each experimental set up of 4.2.2—4.2.4
 The amplitude and phase responses of the HPF-part only------------------10%
 The amplitude and phase responses of the LPF-part only------------------10%
 The amplitude and phase responses of the resulted BPF-------------------15%
 The measured center frequency, the gain (in dB) at the center frequency, and the cut-off frequencies
-------------------5%
 The measured responses are to be plotted in MATLAB, as x---frequency in log scale, y—amplitude in dB
scale or phase in linear scale.
4.3.5 Discussions: -----------10%
4.3.6 Conclusion---------------------------------------5%
Laboratory manual
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Spring 2016