LPF and HPF

7/23/2019 LPF and HPF

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ELECTRICAL SYSTEMS 2 - LABORATORY

REPORT:

PASSIVE LOW-PASS FILTER AND PASSIVE HIGH-PASS FILTER

Name: Samuel Pereira

Student Number: D14128558

Course: DT081Year 2

Submission Date: 12/10/2015


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INTRODUCTION

Filters of some sort are essential to the operation of most electronic circuits. An electrical

filter is a circuit that can be designed to modify, reshape or reject all unwanted frequencies

of an electrical signal and accept (or pass) only those signals wanted by the circuitsdesigner. To do so, a filter might change the amplitude and/or phase characteristics of a

signal with respect to frequency. In other words, they filter-out unwanted signals and an

ideal filter will separate and pass sinusoidal input signals based upon their frequency.

Filters in general can be separated in two categories: the active filters and the passive

ones. The first kind uses active devices such as operational amplifiers and transistors,

but the topic of this report specific sort of the second kind, which just uses, basically,

resistors, capacitors and inductors. To be more specific, this report will be about passive

high-pass filters and passive low-pass filters.


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PASSIVE LOW-PASS FILTER

A basic low pass filter can be constructed with a basic RC circuit, which means that the

output level is always less than the input - it has no signal gain because there is no

amplifying elements.

The circuit can be seen in the figure below.

Figure 1Low-pass filter circuit

It consists of a resistor in series with a capacitor and it is important to mention that the

output voltage should be measured across the second component. The Virepresents the

input signal and Vorepresents the output signal.

This circuit was constructed in the laboratory of Electrical Systems 2. The resistor and the

capacitor used had, respectively, the values of 5 kand 3.3 nF and the input signal was

sinusoidal with Vrms = 4 V.

The objective of the experiment was to analyze the behavior of the output signal for

different frequency values in the input signal through the variation of gain, which is the

relationship between the output and input voltages. It is measured in dB and is given by

the following expression.

The values were analyzed especially near to the cut off frequency, which is the point

where this gain drops below 3 dB and can be calculated as:


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According to the values of resistance and capacitance in the circuit, this frequency is

9,645.58 Hz.

The equipment used was a power supply, a 3 MHz function generator a digital multimeter

and a digital oscilloscope.

The following table shows the results of the experiment.

Vin(Vrms) Vout(Vrms) f (kHz) Vout/Vin 20log10(Vout/Vin) (dB) log10(f)

4.02 3.99 1 0.99254 -0.065063148 3

4 3.92 2 0.98 -0.175478486 3.30103

4.02 3.845 3 0.95647 -0.386594179 3.47712

4.01 3.73 4 0.93017 -0.628710816 3.60206

4 3.582 5 0.8955 -0.958688196 3.69897

4.01 3.45 6 0.86035 -1.306505551 3.778154 3.283 7 0.82075 -1.715782172 3.8451

3.99 3.126 8 0.78346 -2.11967844 3.90309

3.99 2.968 9 0.74386 -2.570179982 3.95424

4.01 2.843 10 0.70898 -2.987350259 4

3.99 2.691 11 0.67444 -3.421183958 4.04139

4 2.57 12 0.6425 -3.84253736 4.07918

3.98 2.433 13 0.61131 -4.274819263 4.11394

4.02 2.35 14 0.58458 -4.663163816 4.14613

4 2.227 15 0.55675 -5.086795486 4.17609

3.99 2.13 16 0.53383 -5.451865845 4.204123.98 2.028 17 0.50955 -5.856302428 4.23045

Table 1Results (LPF)

In order to clarify the results, two graphs was constructed. Both show show the frequency

and gain relation, but in the first one the frequency is in linear scale and, in the second, it

is in logarithmic scale.


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Graph 1Frequency x gain (LPF)

Graph 2Gain x log10(f) (LPF)

-7

-6

-5

-4

-3

-2

-1

0

0 2 4 6 8 10 12 14 16 18

Gain

(dB)

frequency (kHz)

Low pass filter

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

-7 -6 -5 -4 -3 -2 -1 0

log10(f)

Gain (dB)

Bode plot - LPF


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PASSIVE HIGH-PASS FILTER

The circuit in this case is similar to the first one, as the figure below. The only difference

is in the output voltage: this it is measured in the resistor.

Figure 1Low-pass filter circuit

The whole process was repeated and the values for input voltage, resistance and

capacitance used was the same as in the low-pass filter (Vi= 4 R = 5 kand C = 3.3 nF).

Furthermore, the cut off frequency was also the same (fc= 9,645.58 Hz).

The results are shows in the table below.


4.01 0.408 1 0.101746 -19.84968419 3

4.03 0.815 2 0.202233 -13.88294875 3.30103

4 1.181 3 0.29525 -10.59620187 3.477121

4.01 1.527 4 0.380798 -8.386106711 3.60206

4.03 1.839 5 0.456328 -6.814466338 3.69897

3.99 2.104 6 0.527318 -5.558543204 3.778151

3.99 2.319 7 0.581203 -4.713442941 3.845098

3.99 2.553 8 0.63985 -3.878441618 3.90309

4 2.743 9 0.68575 -3.276683674 3.954243

3.97 2.869 10 0.72267 -2.82119917 4

3.97 2.992 11 0.753652 -2.456578351 4.041393

3.98 3.129 12 0.786181 -2.089550179 4.079181

3.97 3.215 13 0.809824 -1.83219059 4.113943


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4 3.327 14 0.83175 -1.600143809 4.146128

3.99 3.391 15 0.849875 -1.412902118 4.176091

3.98 3.448 16 0.866332 -1.246316298 4.20412

3.99 3.514 17 0.880702 -1.103422771 4.230449Table 2Results (HPF)

The two graphs was also constructed.

Graph 3Frequency x gain (HPF)

-25

-20

-15

-10

-5

0

0 2 4 6 8 10 12 14 16 18

Gain

(dB)

frequency (KHz)

High pass filter)


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Graph 4Gain x log10(f) (HPF)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

-25 -20 -15 -10 -5 0

log10(f)

Gain (dB)

Bode plot - HPF


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CONCLUSION

The experiment achieved its goal once changes in the behavior of the output signal could

be noticed. In the passive low-pass filter high frequencies were blocked while low

frequencies passed and, in the passive high-pass filter, the opposite occurred highfrequencies passed and low frequencies were blocked. In addition, this analysis could be

predicted through the calculation of the cut off frequency, which represents the limit

between passand block.

This experiment is important to show that useful tools can be constructed through simple

componentssuch as resistors and capacitors -, and knowing how they work can be the

entrance to understand more complex systems.

Documents

LPF and HPF