10/30/2014

Low Pass Filter Experiment LabVIEW Graphical Representations

Leether, Cole E., Walkowski, Hubert C., Powers, William A. WENTWORTH INSTITUTE OF TECHNOLOGY

Low Pass Filter Lab

Abstract:

The Low Pass Filter Lab was conducted in order to determine how various

resistance values affect the cut off frequency of the circuit. In order to test the cut

off frequency of the circuits a circuit was constructed with the use of a resistor

and a capacitor. The resistors used to construct the four circuits were 470 ohm,

1k, 4.7k, and 10k. The cut off frequency was first theoretically determined for

each of the circuits then the circuits made on the breadboards were run and the

experimental cut off frequency was measured along with the slope of the cut off.

In the end it was concluded that as the resistor value increased the cut off

frequency decreased and as the resistance increased the rate in which the

capacitor was charged decreased.

Introduction/Synopsis:

A low-pass filter is a filter that passes signals with a frequency lower than a

certain cutoff frequency and attenuates signals with frequencies higher than the

cutoff frequency. The amount of attenuation for each frequency depends on the

filter design. The filter is sometimes called a high-cut filter, or treble cut filter in

audio applications. [1]

The cutoff frequency above which the output voltage falls below 70.7% of

the input voltage. This cutoff percentage of 70.7 is not arbitrary, all though it may

seem so at first glance. In a simple capacitive/resistive low-pass filter, it is the

frequency at which capacitive reactance in ohms equals resistance in ohms. In a

simple capacitive low-pass filter (one resistor, one capacitor), the cutoff

frequency is given as: [2]

By using LabVIEW, it is possible generate a response curve for different resistors through a sweep of frequencies.

Images of Lab Equipment and Apparatus:

The electrical components used in this set up consisted of a breadboard

with connected resistors and capacitor. Four different circuits were constructed

using a 470 ohm, 1k, 4.7k, and a 10k resistor.

The images below express a complete set up of all above components. The

only aspect of the test equipment left out is the computer in which the LabVIEW

program was projected. This program was used to generate the graphics shown in

the graphical results section of the report.

Schematic of Set up:

Equations:

𝑓𝑐 =1

2𝜋𝑅𝐶

𝑤ℎ𝑒𝑟𝑒 𝑓𝑐 = 𝑐𝑢𝑡 𝑜𝑓𝑓 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦, 𝑅 = 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒, 𝐶 = 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑎𝑛𝑐𝑒

Graphical Results:

470 ohm

1k

4.7k

10k

Theoretical vs Calculated Cut Off Frequency Chart

Resistance Theoretical Cut Off

Frequency

Cut off Freq in log Scale (x

value on Graphs)

Converting Log to

Measured Frequency

Measured Cut Off Frequency

470 3.386 kHz 3.4 103.4 2.51 kHz

1k 1.59 kHz 3.133 103.133 1.36 kHz 4.7k 338.6 Hz 2.467 102.467 293 Hz

10k 159 Hz 2.067 102.067 116 Hz

LabVIEW Interface to Calculate Theoretical Cut off Frequency

Discussion of Results:

The trends of the graphs show that the cut off frequency is what was

expected for a low pass filter. For the 470 ohm and 1 k resistors, the amplitude

decreases significantly after the cut off frequency is reached which is in the stop

band of the graph. For the 4.7 k and 10 k resistors, their graphs show a more

gradually decreasing amplitude after the cut off is reached, again in the stop band

of their respective graphs. Based on each graph, comparing the measured cut off

frequencies to theoretical values, it is seen that the frequencies are far off for

each resistor. But, an important thing to notice here is the trend when going from

a 470 ohm resistor to 10 k. The theoretical values show a decreasing frequency

trend which is also shown with the measured values; theoretical cut off

frequencies range from 3.386 kHz to 159 Hz, and the measured cut off

frequencies range from 2.51 kHz to 116 Hz. It is good to see that both show a

decreasing trend, but the values are off due to large error in the experiment.

The main area of error in this experiment has to do with the capacitors

used. Companies who make capacitors generally do so at minimal cost. Because

of this, capacitors tend to be very inaccurate, leading to untrue results. As

explained before, the trend of measured cut off frequencies makes sense, but it is

consistently off from theoretical values due to bad lab hardware. The labelled

value of the capacitor used was 0.1 micro farad but it is estimated that it was truly

0.2 micro farad based on numerical results.

Conclusions:

The results of this lab show the characteristics of a low pass filter. As

resistance in the system decreases, the cut off frequency increases. Obviously,

these two variables have an inverse relationship which is important to know.

Once the cut off frequency is reached, the amplitude decreases until it ceases. In

situations that require a low pass filter and need high accuracy, investment in

quality hardware and instruments is recommended because if cheap material

were used like in this experiment, low accuracy will be produced. If this was done

again with proper equipment, the low pass filter could actually be used in

applications like converting AC to DC where it can smooth out the rippling

waveform of the alternating current2.

Reference Material:

[1] http://en.wikipedia.org/wiki/Low-pass_filter#Acoustics

[2] http://www.allaboutcircuits.com/vol_2/chpt_8/2.html