Download Band pass filtration and amplification

Band pass filtration and amplification
Final Draft
Group Members: Gerald Warchol, Sergio Guzman, Wing Leung, Steven Vaccaro,
Scott Weiss, Chitwant Singh. Group 1
Abstract:
Our objective is to design a band pass filter to separate three different
frequencies from each other. Once separated, the signal at a certain frequency will pulse a
common 120-volt AC outlet. The primary focus of this project will be to learn about
filtration and some of the unique things we can do with the individual signals. Once
completed, any normal 120-volt light source can become an indicator lamp for when the
signal uses a specific frequency. The purpose for the signal is to light three different
colors of lights each at different frequencies creating a very interesting and fascinating
effect to demonstrate some of the different properties of signals we hear everyday.
During this project, our group will learn a lot about different types of filtration, how to tie
different filters together, manipulation of signals, and many fun things to do with them
helping us gain a good grasp on signals and the systems they travel through.
CHAPTER 1: (INTRODUCITON)
Frequency filtration is widely used in the market today. We rely on frequency
filtration in a lot of the electronic devices we use on a daily basis. The most common
types of frequency filters are the Low Pass, High pass, and Band Pass filters. These
filters eliminate unwanted frequencies, which cause distortion at the output of a system.
One example could be the cell phone, which relies on these types of filters to eliminate
distortion at the output of the system.
There are three common types of filters. One type is the Low Pass filter. This
type of filter is a circuit offering easy passage to low frequency signals and difficult
passage to high frequency signals. One example is an inductive low pass filter circuit.
Here you have and inductor in series with a resistor. The impedance in the
inductor increases as the frequency increases therefore not letting signal reach the load
resistance if the impedance is too high. Another example of a low pass filter circuit is the
capacitive low pass filter.
Here the high frequency decreases the capacitors impedance. Then the circuit is
shorted out through the capacitor therefore not letting the signal to reach the load resistor.
There are also high pass filters. These filters eliminate the low frequencies in a
signal so they will not reach the load resistance. One example is the capacitive high pass
filter.
Here as the frequency increases the impedance of the capacitor decreases
therefore allowing more current through. Basically this circuit only allows the signal to
get thorough if the frequency is high enough. Another simple circuit for a high pass filter
is the inductive high pass filter.
Here the frequency also needs to be high otherwise the low impedance of the
inductor tends to short out the low frequency signals and not being able to reach the load
resistance.
The final filter circuit that is widely used if a band pass filter. This is a circuit that
allows signals between two specific frequencies to pass, but doesn’t let through signals of
other frequencies. One example is the capacitive band pass filter.
Band pass filters are widely used in wireless transmitters and receivers. Basically
a band pass filter is a combination of low pass and high pass filters. This wraps up what
are the three most common types of filters, their function and how each one does its job
in eliminating unwanted frequencies. There filter circuits will be analyzed more in depth
in later chapters.
CHAPTER 2: (Active Filters)
Active filters are filters, which use operational amplifiers along with resistors and
capacitors. They have one component that they lack that makes them unique, inductors.
Since they do not use inductors they become less inexpensive and easier to design.
“They are usually easier to design than passive filters”(Lacanette 15). The most
important aspect of active filters, however, is that they can provide a gain where as
passive filters can’t. In this chapter, the three basic first-order active filters, low, high,
and band pass, will be discussed to get a better understanding of these circuits.
Active low pass filters are just like passive low pass filters because they allow low
frequencies to pass while higher frequencies do not. In the graph shown, the circuit
allows all frequencies to pass, which are lower than fc, the cut off frequency, while it cuts
off anything greater in frequency. The cut off frequency for both high and low pass
filters is = 1/2RC. There is something an active circuit gives to the output that passive
circuits do not and that is gain, denoted Av. Av = the integral of (1/RC Vi dt).
High pass active filters use the same theory as low pass filters do except that the
positions of the resistors and capacitors are switched, and the circuit allows high
frequencies to pass and low frequencies to be cut off. The graph below shows how it
allows frequencies above the cut off frequency to pass.
A band pass filter, in simplest form, is the combination of a high and low pass
filter. It allows for a certain range of frequencies to pass while all the other frequencies
outside of this range are clipped off. The range of frequencies is determined by
subtracting the two cutoff frequencies, which gives the bandwidth, or BW. In the graph
shown BW = fh –fl. In the circuit below is a simple band pass filter. It has a capacitor
and resistor in series before the input to the operational amplifier, and it has a capacitor
and resistor in parallel connecting the input and output of the operational amplifier. The
values of these components can change which brings about the size and proportion of the
bandwidth.
CHAPTER 3: (Our Design)
The down-loadable .sch files are available on site second draft page.
When you download the files, make sure to save them as .sch. PSPICE
will then recognize the file and it can be opened up with the schematics
utility.
Low-Pass section of our design:
In our design proposal for the team project we have low pass, high pass and band pass
filter implementation. The figure below is representation of low pass filter in our design.
It is Sallen-Key second order butterworth low pass configuration. It is also know as unity
gain and non-inverting low pass filter. This filter is also referred to as a positive feedback
filter since the output feeds back into the positive terminal of the op amp. The circuit
consists of four passive elements (two resistor and two capacitors) and one active element
(op-amp).
For the low pass filter, the band pass contains region from dc (0hz) to cut-off frequency.
Frequencies above cut-off frequencies fall in stop band region.
For our design proposal we have chosen 500 Hz to be cut-off frequency for low pass
filter. To solve of the values of the components (resistors and capacitors) following
equation were used.
Fc  500Hz
R  4.7K
3
R1  R
R2  R1
C1 
R  4.7  10 
3
R1  4.7  10 
1.414
2  Fc R
.7071
C2 
2  Fc R
F 
1
2  R1 R2 C1 C2
F  500.04 Hz
3
R2  4.7  10 
8
C1  9.576  10
F
8
C2  4.789  10
F
High-pass section of our design:
In our schematic, the High-Pass Filter is in Butterworth type with 2nd order configuration
(See Figure 1), which is also called Unity-Gain Sallen-Key High Pass Filter. It is a twopole filter topology and is used to block direct current and lower frequencies, and allows
higher frequencies to pass above a selected crossover frequency (See Figure 2a and 2b).
Figure 1) the circuit of High-Pass Filter in Butterworth type with 2nd order.
| H (f)|
| H (f)|
Stop
Pass band
band
Band
Cutoff frequency, fc
Pass
Cutoff frequency, fc
Frequency
Frequency
Fig. 2a) Ideal High Pass Filter
Figure 2b) Practical High Pass Filter
To simplify the circuit we designed, some information we have to know:
1) Unity-gain, α = 1
2) C = 4.7nF and 10nF
3) RA = 0.0701/ (2πfcC)
4) RB = 1.414/ (2πfcC)
5) fc = 1/√(2π*RA*RB*C*C)
6) |H(f)| = 1/√[1 +( fc/f)4
We choose 1.5 kHz for the cutoff frequency, and 4.7nF for the capacitors, so the values
of the other components are shown as below:
RA
= 0.0701 / [2π (1.5k) (4.7n)]
= 16kΩ
RB
= 1.414 / [2π (1.5k) (4.7n)]
= 32kΩ
fc
= 1 / √ [2π (16k) (32k) (4.7n)2]
= 1.5kHz
Figure 3) Active high pass filter with calculated parameters
Figure 4) the frequency response of the circuit (Voltage vs. Frequency)
Figure 5) the frequency response of the circuit (dB vs. Frequency)
Band-pass section of our design:
The band pass filter, which is used, will consist of the combination of a high and
low pass filter. What it does is filter out the frequencies higher than 1.5k hertz and lower
than 500 hertz. This is done by finding the fo which is the center frequency, fo=1/2RC,
and then calculating the values of the capacitors and resistors which will filter out these
frequencies. The center frequency was 1k hertz because 1.5k – 500 is 1k. The low and
high pass filters used different equations to find these components, however. The high
pass filter has the following equations:
C1 = C2 = C where C was calculated from fo.
R1 = 1.414R where R was calculated from fo.
R2 = .707R where R was calculated from fo.
And the low pass filter has the following equations:
C1 = C where C was calculated from fo.
C2 = 2C “
“ “
“
“ “.
R1 = R2 = .707R “ R “ “
“ “.
The combination of these two make a band pass filter.
CHAPTER 4 : (Conclusion)
As seen, we integrated many filter devices into our project design allowing it to
perform properly. Our goal was to design a device that flashed certain lights depending
on a desired signal frequency from music. For this we utilized low pass filters, high pass
filters, and band pass filters to filter out the frequencies passing through the device. We
have these three types of filters feeding the signal to a series of two op-amps per filter.
The op-amps intensified the signal to our desired 120-volt output, which was respectively
low output, high output, and band output. The 120-volt low output was utilized to power
certain lights. The band-pass and high output were used for the same purpose but were
powering other lights.
Basically as the signal frequency from music passed through our device, the
filters then did their task into filtering out the frequencies and sending it to different opamps. Then the op-amps intensified the signal and gave power to the different colored
light. This allowed us to see what was the range in frequency that was most present in a
certain sound or in music. It can be seen that the design was not very complicated
therefore meaning that it would be cost efficient. Musicians may be interested in a device
like this for it allows for a simple and easy was of knowing what frequencies are most
present in music they are producing.
REFERENCES:
Kuphaldt, T. R. (2003). All about circuits. Retrieved (2005, February 10) from
http://www.allaboutcircuits.com
Lacanette, K. (1991). A basic introduction to filters; Active, passive, and switched
capacitor. Retrieved (2005, March 8) from http://www.national.com/an/AN/AN-779.pdf
Frequency response and active filters. (n.d.). Retrieved (2005, March 7) from
http://www.swarthmore.edu/NatSci/echeeve1/Ref/FilterBkgrnd/Filters.html
Johnson, David. (2002). Low Pass Active Filters. Retrieved (2005, March 10) from
http://www.imagineeringezine.com/PDF-FILES/lowpass.pdf.
Sallen-Key Low-Pass Filter. (n.d). Retrieved (2005, March 8) from
http://www.ecircuitcenter.com/Circuits/opsalkey1/opsalkey1.htm
Sedra, A.S., & Smity, K.C. (2004). Microelectronic Circuits. Oxford University Press.