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20160812192002overview__rc_filter_design__final_fall_2012_2_.pptx

20160812192006msu_mobile_studio_project_5__rc_circuit_and_time_constant_fall_2012_1_.pdf

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Overview RC Filter Circuit Design
Dr. Yacob Astatke
Fall 2010
Overview: RC Filter Circuit Design
 Definition: “A filter is a circuit that passes certain
frequencies and rejects other frequencies.”
 The importance of filters cannot be over
emphasized because they are used everywhere.
 Power supply filters are useful for obtaining a DC signal
from a sine-wave signal.
 When you tune a radio, you usually vary the capacitance
in a resonant circuit.
 Line filters are used to prevent power line spikes from
damaging the PC and are used to prevent high frequency
interference that emanates from the PC.
Overview: RC Filter Circuit Design
 For example: a low pass filter passes low
frequencies and rejects high frequencies.
 For example: a High pass filter passes high
frequencies and rejects low frequencies.
 We will build both types of filter circuits in this lab
and identify the cut-off frequency (Fc)for each circuit.
Let’s try to predict which circuit is the HP or LP ?
Overview: RC Filter Circuit Design
 Here are examples of 4 types of filter outputs
Lab #9: RC Filter Circuit Design
 Here are examples of Low Pass filter outputs
 The cut-off frequency can be obtained by looking at
the ratio between the output and input voltages or
powers.
Lab #9: RC Filter Circuit Design
 Here are examples of High Pass filter outputs
 The cut-off frequency can be obtained by looking at
the ratio between the output and input voltages or
powers.
Overview: RC Filter Circuit Design
 Here are examples of 1st and 2nd order filter circuits
Fc = 1/(2ΠRC)
Blue Curve: 1st order system
Purple Curve: 2nd order system
Overview: RC Filter Circuit Design
 Let’s analyze the circuit below in the frequency
domain to find out if it is a high pass or low pass
filter.
 Let’s write the equation of the voltage across
node B using voltage division.
Overview: RC Filter Circuit Design
Overview: RC Filter Circuit Design
Lab #9: RC Filter Circuit Design
 Let’s analyze the circuit below in the frequency
domain to find out if it is a high pass or low pass
filter.
 Let’s write the equation of the voltage across
node B using voltage division.
Overview: RC Filter Circuit Design
Overview: RC Filter Circuit Design
Overview: RC Filter Circuit Design
Department of Electrical and Computer Engineering
Morgan State University
EEGR 202 – Electric Circuits
Prof. Yacob Astatke
Mobile Studio (MS) Project#5 – RC Circuits and Time Constant
1. Mobile Studio and Instrumentation Board
MS is a technology-based new learning tool comprising a tablet PC (or any PC) and an
instrumentation board, which replaces most of the lab equipment. Therefore, MS allows a
small foot print, mobile laboratory experiments any place any time. The measurement by
MS is possible by a Windows-based software, Mobile Studio Desktop, which is already
installed in the tablet PCs. The icon for the Mobile Studio Desktop is illustrated below.
The opening window when you double click the icon above would be like this:
As you see in the above picture, the instrumentation board is USB connected to the tablet
PC.
The instrumentation board can function as :
(a) scope, (b) DMM, (c) Power supply, and (d) Function generator.
There are, however, important limitations in using the Red board:
(1) No direct measurement of current — You get current indirectly (by measuring voltage
across a resistor, etc)
(2) No direct measurement of resistance — You get it indirectly (You may still need a
DMM for resistance measurement)
(3) There is no variable voltage unless you use a variable resistor. There are fixed
voltages generated from the power supply sources.
The picture and Pin Layout for the Red Board is shown .You need to follow the Pin
numbers correctly in order to use the I/O board for measurements.
Created by: Yacob Astatke
-1-
Fall 2012
Department of Electrical and Computer Engineering
Morgan State University
Mobile Studio (MS) Project#5 – RC Circuits and Time Constant
Objective:
The goal of this Mobile Studio experiment is to investigate the frequency response of
RC circuits with varying RC values and their effects on the time constant.
Directions:
Build the circuit shown in Figure #1 below on your breadboard and connect it to your
mobile studio board. The circuit will be used to test two important features of RC
circuits:
 Identify the type of filter circuit you have based on the position of the R and C. Is
the circuit in Figure#1 a High Pass or Low Pass filter ? Why ? Justify your answer.
Figure 1: Simple RC Circuit
Part#1: Identify the type of filter circuit

Assume Vs(t) in Figure#1is a sine wave with Vin = 1.41 Vpeak. If R=1 Kohm and
C = 0.1 uF , use the correct equation to compute and predict the theoretical CutOff frequency for the circuit.
Step#1: Build the circuit shown in Figure#1. Increase the frequency of the source
from F=100Hz up to F=2KHz, by steps of 100Hz. Measure and record the voltage
Vout=Vbc at each frequency step. Make sure to identify the correct cut-off
frequency and measure the corresponding output voltage.
Step#2: Switch the place of the R and C in figure #1. First, indicate the type of
filter it represents. Build the new circuit, and repeat step#1.
Step#3: Design a new High-Pass or Low-Pass filter with a cut-off frequency of
Fc=1KHz by choosing the appropriate R and C values. Build the new filter circuit
and take measurements by repeating step#1.
Created by: Yacob Astatke
-2-
Fall 2012
Department of Electrical and Computer Engineering
Morgan State University
Analysis of Results:

Plot the results of Vout=Vbc (y-axis) versus frequency (x-axis) for steps#1, #2,
#3. Observe and explain what happens to the output of the circuit Vout when
the frequency is varied in steps#1,and #2.
Observe and explain what happens to the output of the circuit Vout when the
frequency is varied in steps#1, and#2,after the location of the capacitor and the
resistor have been switched.
How could each of these circuits (in steps#1 and #2) be used in real applications?
Please give an example of practical application of the circuits shown in Figure#1.
Part#2: Effect of the values of R and C on the time Constant
Definition: “The time constant of a circuit is defined as the time required for the
response to decay by a factor of 1/e (1/e= 0.3678) of its initial value”. This implies that
the time constant is the time required for the response to decay to 37% of the initial
value”. We can make the assumption that after 5 time constants (e-5= 0.00674) the
stored voltage in the capacitor is fully discharged because its final value is less than 1%
of this initial value  this is known as the “5 tau rule”.
Figure 1a: Simple RC Circuit

Step#1: Build the circuit shown in Figure#1a, with the resistor R replaced by a
variable resistor (1Kom Potentiometer) and C = 1 uF . Assume the source is a
square wave with a peak voltage of Vp = 0.75 Vac and a frequency = 250 Hz.
Step#2: start varying the value of R using the potentiometer such that your
picture looks like the one shown in Figure#2. Next, capture and save the output
observed at node B, with channel#1 showing Vin (square wave) and channel#2
showing Vout (across the capacitor). Your screen capture should look similar to
that shown in Figure#2.
Analysis of Results:
We will complete the following steps to predict the value of R
Created by: Yacob Astatke
-3-
Fall 2012
Department of Electrical and Computer Engineering
Morgan State University

Step#3: Look at your screen capture for the capacitor voltage Vout: how long
does it take for the capacitor to fully discharge ? You can do this by measuring
the time on the X-axis.
Step#4: Use the time you measured to compute the time constant of your
circuit. Don’t forget to use the “5 tau rule”.
Step#5: Use the calculated value of the time constant to predict the value of the
variable resistor R.
touching the wiper handle) and measure the actual value of the resistor using a
DMM.
Step#7: Compare the predicted value and the measured value of R. How close
are the two values?
Step#8: Replace the C = 1 uF capacitorin Figure#1, by a new C = 0.47 uF
capacitor and repeat all the steps listed in step#3- steps#7.
Write a discussion based on your observations of the results in steps#3 to
steps#8.
Figure 2: Response of RC Circuit to a square wave
Extra-Credit

Step#9: Keep the circuit in step#8 and replace the source Vs from a squarewave to a sine-wave. What do you expect the output voltage Vout to look like ?
Created by: Yacob Astatke
-4-
Fall 2012
Department of Electrical and Computer Engineering
Morgan State University
(a) What was most frustrating in the class and the use of the MStudio Board?
(b) What was most interesting in the class and the use of the MStudio Board?
(c) How much more do you understand the function and use of RC circuits, and time
Choose one :
1. Not Confident
2. Fairly Confident
3. Confident
4. Extremely Confident
(d) How much more do you understand the function and use of RC circuits as Filter
Choose one :
1. Not Confident
2. Fairly Confident
3. Confident
4. Extremely Confident
(d) How much are you comfortable with measuring voltage using the instrumentation
board and tablet PC?
Choose one :
1. Not Confident
2. Fairly Confident
3. Confident
4. Extremely Confident
(e) Was mobile studio pedagogy a helper (with your understanding and practice of circuit
theory) or a distracter/nuisance ?
Choose one :
1. Did not help at all(distracter/nuisance)
2. Helped a little
3. Helped
4. Helped a lot
(f) Did you get your needed help from the discussion with your team member?
(g) Did you get your needed help from the instructor/TA? Satisfied?
Created by: Yacob Astatke
-5-
Fall 2012