## Description

Lab 4 AC Lab

1

Ve215

Lab 4 AC Lab

I. Goals

1. Learn how to define, calculate, and measure the amplitude of a sinusoidal

signal

2. Learn how to define, calculate, and measure the Rise Time and Fall Time of a

signal

3. Learn how to observe FFT spectra of signal and measure their parameters with

cursors

4. Measure the waveforms and FFT spectra of various signals

5. Compare your theoretical results obtained in the Pre-Lab with your In-Lab

data.

II. Introduction

1. High-Z mode

Here I want to introduce you what is the High-Z mode we have kept emphasizing

during the previous Labs.

You have already learnt Thevenin equivalent of a circuit. You can think the

function generator in terms of its Thevenin equivalent circuit, which includes the

voltage source and VS and the equivalent resistance of 50

as shown below.

When the load RL is 50

, according to voltage division, we know that the VL

measured will be 0.5VS. In this case, we use the 50 OHM mode, in which the

function generator produces voltage VS but displays voltage 0.5VS. In that way, if

you set 2Vppk for the function generator, the actual VS will be 4Vppk to make sure

the load get a voltage of 2Vppk.

Lab 4 AC Lab

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In our lab measurements, the load resistance RL is very high—the input resistance

of the oscilloscope is about 1

M

. The VL measured across RL practically equals

VS. So we use High Z mode, in which the function generator produce voltage VS

and displays VS.

2. The Rise Time and Fall Time of signals

The Rise time is the interval between the moment of the time when the signal

reaches its 10% level and the moment of time when the signal reaches its 90%.

We have already used this concept in our Lab3.

The above two figures illustrate the rise time of a sinusoidal like wave and a

saw-tooth wave. If you do not know what is Vppk, you can refer to part 4 of this

section.

Take the sinusoid wave as an example to calculate the rise time.

sin(2 )

2

Vppk

y ft

Lab 4 AC Lab

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,

2 2

ppk ppk

min max

V V

V V

1 1 0.9 0.1

sin ( ) sin ( )

0.5 0.5

2

min ppk min ppk

ppk ppk RiseTime

V V V V

V V

f

3. Fourier Series Representation of a Signal

Here I am going to give you a general idea of Fourier Series to help you

understand some parts of this lab. You will learn Fourier Series in details in your

math course this semester.

Fourier series is a way to represent a wave-like function as a combination of

simply sine waves. It decomposed and period function into the sum of a (possibly

infinite) set of simple oscillation functions.

Let

xt()

be a periodic signal with fundamental period

T0

. It can be represent by the

following synthesis equation,

0

0

0

( ) , where jk t 2

k

k

x t c e

T

The coefficients

k

c

in the above equation can be calculated by the analysis

equation,

0

0

0

0

1

( ) , 0, 1,…

T

jk t

k

c x t e dt

T

k

Plot[Sum[(−1)^(((? + 1)) ⁄ 2) ∗ 2 ⁄ ((? ∗ Pi) ) Cos[? ∗ Pi ∗ (? +

0.5)], {?, 1,100,2}], {?, −4,4}]

You can use the above Mathematic code to get the feeling of how a series of

sinusoidal waves can form a square wave (actually, any waveform). You can

change the value in the red box, and the larger the value is, the more accurate the

result will be. Here we thank the Vv286 TA for FA2014 Gao Yuan for offering us the source

code.

For value 3, we can get the following result.

Lab 4 AC Lab

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For value 20, we can get the following result,

And for value 100, we get,

4. Four ways to measure the amplitude of a sinusoid

a) Vpeak=Vp=Vpk=V0 is the peak amplitude of the sinusoid measured in V or mV.

b) Vpeak-to-peak=Vppk=Vmax-Vmin=2V0 is the value we often use in the lab to

determine the overall size of the waveform. We have used it many times in the

4 2 2 4

0.6

0.4

0.2

0.2

0.4

0.6

4 2 2 4

0.6

0.4

0.2

0.2

0.4

0.6

4 2 2 4

0.6

0.4

0.2

0.2

0.4

0.6

Lab 4 AC Lab

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previous Labs.

c) VRMS is the Root-Mean-Square, or RMS amplitude of the sinusoid. The

sinusoidal voltage

0 V V sin( ) t

dissipates as much power in the load resistor

as does the DC voltage equals to VRMS

For any periodic function f(t) that has period T, the RMS amplitude is defined as

0

0

2

, ( 1

( ))

t T

t

Amplitude RMS f t dt

T

In the case of sinusoid

0

f t V t ( ) sin( ),

0

2 2 2 2

peak ppk

RMS

V V V

V

d) The above three ways all study the signal in time domain, plotted as voltage vs.

time. In this Lab, we also need to study the frequency domain, when you measure

their spectra displayed as amplitude vs. frequency. In frequency domain, the

oscilloscope measures the amplitude of on a logarithmic scale, using decibels.

10 (dBV) 20 ( log )

1

RMS

RMS

Amp Amplitude i litude in decibe n V

V

ls

Decibels are used to calculate ratios of two amplitudes on a logarithmic scale.

10 , (dB) #2, 20 log

#1,

( ) Amplitudeo Ratio in decibels

Amplitude of signal

f signal RMS

RMS

III. Pre-Lab Assignment

1. Consider a sinusoidal signal at 3Vppk and 10 kHz. Calculate its amplitude in

Vpk, RMS, and dBV.

2. Consider a square wave at 3Vppk and 10 kHz. Calculate the amplitude of its

frequency components—fundamental and harmonics up to the 5th

–in Vpk, VRMS,

and in dBV. Fill the following table.

Lab 4 AC Lab

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Column 1 2 3 4

Frequency

component

Frequency,

kHz

Amplitude in

dBV

Amplitude in

VRMS

Amplitude in

Vpk

Fundamental

1

nd harmonic

2

nd harmonic

3

nd harmonic

4

nd harmonic

5

nd harmonic

3. Consider a sinusoidal signal at 3Vppk and 1kHz, calculate the rise time of this

signal.

IV. In-Lab Procedure

Part I

1. On the function generator, set a sine wave at 1 [kHz] and keep its amplitude

at 3 [Vpp]. The load must be High-Z mode.

2. Record the parameters on the datasheet. Fill the table with the data set on the

function generator and displayed on the oscilloscope.

3. Repeat the Step 2 with a sine wave at 1.5 [kHz] and 5 [Vpp] on the function

generator. The load should remain High-Z mode.

4. In post-report, calculate the rise time in theory and compare it with the values

displayed on the oscilloscope.

5. Reminder:

Part II

1. First, we set a sine wave and a square wave, respectively. The frequency is 1

[kHz] and the amplitude is 3 [Vpp].

2. On the oscilloscope, set 1 [V/div] and 5 [ms/div].

3. Push the “MATH” button and select “FFT” function.

4. Push the “cursor” button and select “trace” mode to trace the spectrum.

5. When the cursor reach a peak of the spectrum, record the Frequency in [kHz]

and the Amplitude in [dBV].

6. Set another sine wave and a square wave. The frequency is 2 [kHz] and the

amplitude is 6 [Vpp]. Repeat the steps above.

7. In post-report, you need to calculate the theoretical amplitude of sine wave in

[dBV]. Besides, you need to calculate the Vpeak of each square wave

measured in Part II. You should give a brief conclusion on what you learn

from this lab.

Lab 4 AC Lab

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8. Reminder: for sine wave.

9. Reminder: for square wave.

V. Reference

Circuits make sense A new Lab Book for introductory Course In Electric Circuits.

Fifth edition. Alexander Ganago.