California University of Pennsylvania
Department of Applied Engineering & Technology
Electrical / Computer Engineering Technology
EET 215: Introduction to Instrumentations
Lab No. 2
First Order Passive Low Pass Filter
Names:
1.
2.
3.
Signature:
Date
First Experience with NI-ELVIS
Objective of the Experiment
The main objective of this experiment is to further expand the familiarity with the NI-ELVIS II unit and to
understand low pass filters.
Learning Outcomes
Students will demonstrate:
-
the ability to use some features of the prototyping board of NI-ELVIS
understanding of first order low pass filter (experimentally and theoretically).
the ability to collect data and to analyze it to draw conclusions.
CAUTION: It is imperative that students exercise care when handling the ELVIS unit. Make sure all connections
are correctly made. When in doubt, check with your instructor to verify proper circuit connections.
Introduction
A low pass filter (LPF) is a circuit whose main function is to pass low frequency signals with almost no
attenuation and attenuate (hinder the passage) of higher frequency signal.
Necessary Equations
𝑓𝑐 =
1
2𝜋𝑅𝐶
1
𝐴𝑣 =
2
√1 + ( 𝑓 )
𝑓𝑐
𝑓
𝜃 = −𝑎𝑟𝑐𝑡𝑎𝑛 ( )
𝑓𝑐
𝐴𝑣 =
𝑉𝑜
𝑉𝑖𝑛
Thus,
𝑉𝑜(𝑝𝑘) = |𝐴𝑣 |𝑉𝑖𝑛(𝑝𝑘)
𝐴𝑣𝑑𝐵 = 20 𝐿𝑜𝑔|𝐴𝑣|
Where:
f: input sinusoidal wave’s frequency
fc : Cut-off frequency (3dB point)
𝐴𝑣 : voltage gain
𝜃: phase angle between the input and the output (output lags the input when this angle is negative.)
𝐴𝑣𝑑𝐵 : The gain expressed in decibels.
Components Needed:
0.1uF Capacitor
10KΩ Resistor
A-
Experiment- Set-up (place a check mark in the check box as you complete each step)
Power to the unit if OFF
Obtain the ELVIS II unit. Before powering it up, construct the LPF circuit shown and perform the
following steps. (refer to figure and image below as a reference.) Input and output connections are
explained next.
+
10kΩ
Vin
Vo
0.1µF
i-
Measure and record the actual Resistor and (if possible) the capacitor values:
Rmeasured (KΩ)
ii-
Cmeasured (uF)
Connect the circuit’s input to the function generator terminal using a BNC cable
iiiAlso, connect the input to the DAQ board’s analog input 0 (AI0) (positive side to AI0+ and the
side to AI0-) This will allow us to monitor the input on the scope later on.
iv-
Connect the output (the voltage across the capacitor to the BNC input Ch1)
v-
Calculate the theoretical value of the cut-off frequency using measured components.
fc(expected) =
ground
Hz
This frequency should be near 159.2 Hz. If your result is more than 10% off, verify component values.
Note: In this image I did not have a 10KΩ resistor, thus used 2 – 20KΩ resistors in parallel.
v-
Turn the power to the ELVIS unit ON
vi-
Run the Instrument Launcher (All programs>> National Instruments>>NI ELVISmx>>NI ELVISmx
Instrument Launcher)
vii-
Click on Function Generator and set it to sine wave at 100Hz and 4 V(p-p) with 0-DC offset (do not run
it yet.) Make sure the signal routing is set to FGN BNC.
viii-
Click on the scope in the instrument launcher and set it up as shown below.
ix-
RUN the FGN and the Scope – you should see a similar waveform as show below.
Make sure of the following on the Scope:

Ch0 is set to AI0 and that it is enabled.




-
CH1 is set to Scope CH1 and that it is enabled
The vertical scales (Volts/Div) are set to 500 mV
The timebase scale is set to 1ms/div
The vertical positions are set to 0.
Read:
Note, the vertical and horizontal scales will have to be adjusted later on in the experiment. You have to
make that judgment.
Also, at some point, it may be better to set the Acquisition Mode to Run Once – so that you can better
view the signals.
If all above is working correctly, proceed to perform the experiment. Otherwise, check with lab instructor.
B-
Experiment Data Collection and Analysis
1Change the frequency to correspond with the values in the table below and record your measurements.
Note, the measured voltage gain is found by dividing Vo(p-p) by Vin(p-p). In some cases, you will have to adjust
the output’s vertical scale. Also, record your results for the “measured” phase shift. (see example calculations
for measurements of the phase shift-- below.)
SET Vin = 4V(p-p)
At the frequencies marked “*”, estimate the phase difference from the scope. See an example
below.
Experimental Data
f (Hz)
40*
60
100
159.2*
200
400
1K*
1.592K
2K
4K
10K
20K
Vo(p-p)
(V)
𝐴𝑣 =
Av=
𝑉𝑜(𝑝−𝑝)
|𝑉
𝑖𝑛(𝑝−𝑝)
|
Av(dB)
𝜃
(deg.)
Theoretical Data
1
2
√1 + ( 𝑓 )
𝑓𝑐
Av(dB)
𝜃
(deg.)
Example Snap Shot at f = 40Hz.:
Using the time difference, calculate the phase lag.
𝜃 =? at f= 40Hz.
At a frequency, f= 40Hz, T = 1/f = 25 ms.
𝜃=−
1.22𝑚𝑠
25𝑚𝑠
× 360 = -17.6o
𝜃 𝑇ℎ𝑒𝑜𝑟𝑦= − tan−1 (
40
)
159.2
= -14.1o (obviously the cursors were not placed exactly at the zero crossing.)
2- Frequency Response
Automatically generate the Bode-Plot
A bode plot defines the frequency characteristics of a given circuit. Magnitude response is plotted as circuit gain
in decibels as a function of log frequency. Phase response is plotted as the phase difference between input and
output signals on a linear scale as a function of log frequency. NI ELVIS has a bode analyzer SFP which facilitates
automatic bode plot generation of a given circuit. Complete the following steps to obtain the Magnitude and
Phase response of the RC filter:
Turn the power to the unit OFF, remove the connections to the circuit and
Reconnect the circuit as shown below (drawing and an image:) NO BNC connections
1- Connect the DAQ Analog Input 0 ( AI0 +/- ) to the circuit’s output (voltage across the cap)
2- Connect the Analog Input 1 ( AI1 +/- ) to the circuit’s input.
3- Connect the DAQ FGen output to the circuit. Also, connect the corresponding Ground to the circuit
as shown in image below.
4-
Ensure that the connections are correct and switch the prototype board power to ON position.
5- Launch the Instrument Launcher and click on Bode.
6- Set the parameters to be as shown below
7- Run – you should obtain a similar response as shown below.
8- check the “ Cursor ON” and move it in the Gain and Phase so that the vertical line corresponds to
near the cut-off frequency.
At that point, you should read the Gain to be near -3dB and the phase to be near -45 deg. (As shown
below.)
Verify for correctness with the instructor.
Instructor Approval of Frequency Response:
Challenges (Refer to the Bode plot.)
1- Move the cursor in the Bode plotter to determine the gain corresponding to f = 1.59KHz (or close to
it) What is the Gain in dB and in ratio form (as read from the frequency response) ?
Av(dB) =
Av =
Note: Av(ratio form) Is calculated as follows: 10 𝐴𝑣(𝑑𝐵)/20
2- From your result in (1), when comparing this gain to the gain at f =fc=159Hz, the gain dropped by
approximately: (Chose one)
a- 10 dB
b- 20 dB
c- 30 dB
3- What is the maximum phase lag that this filter produces?
4- What is the Pass - Band for this filter (in Hz)?
5- What is the stop band for this filter (in Hz)?
Instructor approval of experiment completion: