Download Introduction to Filters

ECE 213
University of Idaho
Lab 10 – An Introduction to Filters
Spring 2015
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Lab 10 – An introduction to Filters
Objective
The objective of this experiment is to determine the characteristics of two simple filters: Low Pass filter
and High Pass Filter.
Theory
Historically, the first filters used extensively were in sound systems such as audio amplifiers, radios, and
telephones. For this reason many of the conventions used in describing filters are based on the
properties of human hearing. The first of these properties is that human hearing is logarithmic. This
makes it possible for us to hear sounds with very low volumes while not being completely overwhelmed
by loud sounds. This also results the average person not being able to recognize small changes in the
power of a sound. The average person will not hear a change in sound until its power has decreased to
half of its original value or doubled. Second, the commonly accepted frequency range for human hearing
is from 20 Hertz to 20 kilo Hertz. This varies from person to person and very few people have this
complete range. Third, people cannot hear a phase change in a sinusoid or in one sinusoid in relation to
another. The effects of these hearing characteristics on the conventions used in filter theory will be
indicated where they show up in the following discussion.
Either a low-pass or a high-pass filter can be constructed using two components: a resistor and a
reactive element. Basically the circuit acts as a voltage divider. Since the impedance of one of the
components is frequency dependent the ratio of the voltage division varies with frequency. The voltage
is divided between the two components. As one voltage in the divider increases, the other decreases.
Consider a series resistive-capacitive filter. If the output potential is taken across the capacitor, the
output impedance and therefore the output voltage will be high at low frequencies and decrease as the
frequency increases. On the other hand if the output is taken across the resistor the output voltage will
be low at low frequencies and will increase as the reactance of the capacitor decreases. The size of the
components will determine the frequency at which the filter becomes effective. In keeping with the
characteristic of the human ear, that it does not recognize a change in sound volume until the power has
been reduced to half of its original value, the term "half-power point" is used to describe the effective
point of a filter. This half-power point has two other commonly used names: the "corner frequency" and
the "3-dB-down point". Because the power can be calculated as:
𝑃=
𝑉2
𝑅
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April 29, 2017
ECE 213
University of Idaho
Lab 10 – An Introduction to Filters
Spring 2015
The voltage at the half-power point is 0.707 times the band-pass voltage. The gain in decibels is given
by:
Gain in Voltage =
𝑉0
𝑉𝑖
𝑉0
Gain in dB = 20𝑙𝑜𝑔10 𝑉𝑖 , Then at the half-power point.
Gain in dB = 20log (0.707) = -3dB. This is usually just called -3 dB or 3 dB down.
The Gain (which is less than or equal to in a passive circuit) is often plotted in the logarithmic units of
decibels(dB). This is reasonable since the ear responds to the volume of sound in a logarithmic way.
If an audio amplifier has a half-power point at 20 Hertz and another at 20 kilo-Hertz, with a band pass
filter in between, it is said to have a bandwidth from 20 Hertz to 20 kilo-Hertz. If the gain is plotted as a
function of frequency on a linear frequency scale to a high enough frequency to show the high end dropoff of the amplifier, both the areas of gain drop-off will be very small and not show much detail. These
are the regions of primary interest. For this reason the frequency-response curve is plotted on a semilog plot, on which the frequency (on the x axis) is plotted on a logarithmic scale. The frequency is plotted
in ether Hertz or radians per second and the gain on a linear scale in decibels. This type of plot is called a
Bode plot after H. W. Bode who developed much of this theory while working for Bell Laboratories.
In addition to the changes in the amplitude caused by these filters there will be a phase shift between
the input and output potentials. The human ear does not hear changes in phase, so the change in
amplitude caused by the filter is of primary importance when dealing with sound. There are areas of
study where both phase shift and gain are important. An example of this would be feedback control
systems. In this case the phase of the feedback can be very important.
Procedure:
In this circuit,
R2= 330Ω
C1=480nF
Write down the measured value below:
R2____________________
C1____________________
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April 29, 2017
ECE 213
University of Idaho
Lab 10 – An Introduction to Filters
Spring 2015
1. Solve symbolically the Vout/Vin for Figure 1 below. Result should in terms of f.
2. Setup the circuit of Figure 1 using a function generator as the sinusoidal source.
3. Connect an oscilloscope to read the voltage at the terminals of the function generator and the
voltage across the capacitor. The voltage at the terminals of the function generator is the input
to the filter. The potential across the capacitor is the filter output. Set the input voltage to a
3Vpeak.
4. Adjust the frequency in figure 1 and record output voltage and phase in Table D-1 on the data
sheet. ***You can use excel to record the measurement if prefer.
(The reason for using the oscilloscope for the amplitude measurements rather than the digital
multimeter since none of the digital multimeters in the laboratory are specified to measure
frequencies over 50,000 Hz.)
i.e. The oscilloscope should be read carefully in ordered to get a good curve.
5. Redraw the circuit below by switching the position of resistor and capacitor. This is the high pass
filter. Specify the input and output.
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April 29, 2017
ECE 213
University of Idaho
Lab 10 – An Introduction to Filters
Spring 2015
6. The circuit drawn above is the High pass filter. Calculate symbolically the |Vout/Vin| of the high
pass filter. Remember if Z=a+jb, |Z|=√(a^2+b^2)
7. Construct the High Pass filter and record the measurement results in D2.
8. Simulate the voltage and phase verse frequency for the Low pass and high pass filter using
PSpice/LTSpice/Cadence/TINA. Simulate in a range from 100Hz to 10000Hz.
Result Analysis
All the measured value for the following tables should be calculated from D1 and D2
Low Pass Filter Analysis
Frequency
(Hz)
Calculated Gain
|Vout/Vin|(V/V)
Low Pass Filter
Measured Gain
20 log of
|Vout/Vin|
measured
(V/V)
Vo/Vi (dB)
Measured
Phase Shift
Degree
Percent Err.
(Calc. Gain Meas. Gain)
100
200
500
1000
2000
5000
10000
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April 29, 2017
ECE 213
University of Idaho
Lab 10 – An Introduction to Filters
Spring 2015
High Pass Filter Analysis
Frequency
(Hz)
Calculated Gain
|Vout/Vin|(V/V)
High Pass Filter
Measured Gain
20 log of
|Vout/Vin|
measured
(V/V)
Vo/Vi (dB)
Measured
Phase Shift
Degree
Percent Err.
(Calc. Gain Meas. Gain)
100
200
500
1000
2000
5000
10000
9. Use the data above, plot the voltage vs frequency in excel for both low pass and high pass filter.
10. Use the data above, plot the phase vs frequency in the excel for both low pass and high pass
filter.
Question:
1. What are the use of low pass filter and the use of high pass filter? Give two examples.
2. Why do engineer in recent year try to use resistor and capacitor and avoid using inductor?
3. What is the maximum gain and lowest gain in voltage of the low pass filter?
4. In Both low pass and high pass circuit, what is the 3dB frequency? 3dB frequency means 3dB
down voltage from maximum gain. You can calculate the Vout using Gain in dB equation.
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April 29, 2017
ECE 213
University of Idaho
Lab 10 – An Introduction to Filters
Spring 2015
Datasheet
Table D1 – Output and phase potential for high pass filter
Approx. Input
Frequency (Hz)
Actual Input
Frequency (Hz)
Output Potential
Scale (1x/10x/100x) Peak to Peak
(so you don’t get
Potential (V)
the wrong voltage)
Phase
Time between Vin and
Vout
100
200
500
1000
2000
5000
10000
Table D2 – Output and phase for the high pass filter
Approx. Input
Frequency (Hz)
Actual Input
Frequency (Hz)
Output Potential
Scale (1x/10x/100x) Vout Peak to
(so you don’t get
Peak
the wrong voltage) Potential (V)
Phase
Time between Vin and
Vout
100
200
500
1000
2000
5000
10000
Write a conclusion.
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April 29, 2017
ECE 213
University of Idaho
Lab 10 – An Introduction to Filters
Spring 2015
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April 29, 2017