## Description

Lab 5 Filter Lab

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VE215

Lab 5: Filter Lab

I. Goals

Learn about four types of filters – Low-Pass, High-Pass, Band-Pass, and

Band-reject.

Learn about transfer functions.

Predict the theoretical result and make comparison with lab data.

II. Introduction

Filter

Filters are everywhere in our lives. The circuits built to operate on signals usually

apply filters. For example, telephone lines pass the sounds at frequencies

between about 100Hz and 3kHz and practically blocks all other frequencies.

Transfer function

Mathematically, the transfer function is used to analyze what the circuit did to

the signal:

Transfer function =

?????? ??????

????? ??????

This function can also be expressed as

?(ω) =

????(ω)

???(ω)

The magnitude of the transfer function is called “voltage gain”, often measured

as the ratio of the peak-to-peak (ppk) voltages:

|?(ω)| = �

????(ω)

???(ω) � = ????, ???(ω)

???, ???(ω)

It is convenient to express and plot the magnitude of the transfer function on the

logarithmic scale using decibels:

|?(ω)|?? = 20 ∙ log10 �

????, ???(ω)

???, ???(ω) �

Since both ppk voltages are always positive, the transfer function magnitude is

positive and thus can always be converted to decibels. The use of decibels allows us

to review data over a broad range.

Lab 5 Filter Lab

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Types of filters

In the figure above are the four main families of filters:

(1): Low-Pass; (2): High-Pass; (3): Band-Pass; (4): Band-reject (also called

band-stop or notch)

Filter circuits, which you are going to build in this lab, contain resistors,

capacitors, and inductors. They are all passive filters.

High-Pass filter

The high-pass filter we are going to build uses a capacitor and a resistor.

For the high-pass filter, ?(ω) =

????(ω)

???(ω) = ?

?+ 1

?ω?

= ?ω??

1+?ω?? .

Note that H(0) = 0, H(∞) = 1. Hence, it would only let high frequency pass.

Lab 5 Filter Lab

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Low-Pass filter

The low-pass filter we are going to build uses a capacitor and a resistor.

For the low-pass filter, ?(ω) =

????(ω)

???(ω) =

1

?ω?

?+ 1

?ω?

= 1

1+?ω?? .

Note that H(0) = 1, H(∞) = 0. It would only let low frequency pass.

Band-Pass filter

The band-pass filter we are going to build uses a capacitor, an inductor and a

resistor.

For the band-pass filter, ?(ω) =

????(ω)

???(ω) = ?

?+?(ω?− 1

ω?)

.

Note that H(0) = 0, H(∞) = 0. The band-pass filter passes a band of frequencies

centered on the center frequency ω0, which is given by ω0 = 1/√??.

Lab 5 Filter Lab

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Band-Stop filter

The band-stop filter we are going to build uses a capacitor, an inductor and a

resistor.

For the band-stop filter, ?(ω) =

????(ω)

???(ω) = ?(ω?− 1

ω?)

?+?(ω?− 1

ω?)

.

Note that H(0) = 0, H(∞) = 0. The band-stop filter rejects a band of frequencies

centered on the center frequency ω0, which is given by ω0 = 1/√??.

III. Pre-lab assignment

1. What is decibel value? (You may give a typical example to help your explanation.)

What is the advantage of dB scale?

2. How to calculate the band width of rejection of a band-reject filter? (You may

refer to Chapter 14.7 of the textbook.)

3. Predict the theoretical result of this lab. You need to estimate the Expected

transfer function magnitude |?(ω)| and Expected transfer function magnitude in

dB |?(ω)|?? of all of the four types of filter. Fill in the tables in the Data Sheet

to show the expected results (which will not be collected during the lab). Also,

make a table for each type of filter to show the respected results (which will not

Lab 5 Filter Lab

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collected during the lab as pre-lab assignment). We are using Resister of R =

982Ω; Capacitor of C = 0.1μF; Inductor of L = 1mH.

e.g. For high-pass filter

Frequency 1MHz 100kHz 50kHz 10kHz 5kHz 1kHz

|?(ω)|

|?(ω)|??

Tip: You may use MATLAB or Mathematica program to help you calculate this

result.

References:

[1]. Circuits Make Sense, Alexander Ganago, Department of Electrical Engineering

and Computer Science, University of Michigan, Ann Arbor.

[2]. Clarles K. Alexander, Matthew N.O. Sadiku. Fundamentals of Electirc Circuits. New

York: McGraw-Hill, 2013. Print.