Asst. Prof. Dr. Prapun Suksompongprapun@siit.tu.ac.th

1

Basic Elec. Engr. Lab ECS 204

Lab 4• AC Circuit• Time-varying Signal • Oscilloscope• Function generator• Capacitor and Inductor

Time-varying periodic signal (voltage)

2

Suppose the period is T.

Instantaneous value at time t:

Average value

RMS value

Peak value

Peak-to-peak value

v t

0

0

1 t T

t

v t v t dtT

0

0

2 21 t T

t

v t v t dtT

0 0

maxt t t T

v t

0 00 0

max mint t t Tt t t T

v t v t

DCV

V

pV

p pV

rmsV In this lab, VDC = 0 makes Vrms = VAC.

Vp-p

T

Vp

Sinusoidal signal (voltage)

3

The period is

Instantaneous value at time t:

Average value

RMS value

Peak value

Peak-to-peak value

0

0

2 21 t T

t

v t v t dtT

0 0

maxt t t T

v t

0 00 0

max mint t t Tt t t T

v t v t

V

pV

p pV

rmsV

1 2Tf

cosv t A t

0

2A

A

2A

t

v(t)

T/2 T0

A

-A

0

0

1 t T

t

v t v t dtT

DCV

12

Steady-State AC Analysis

4

Phasor Domain:

Time Domain:

ZV I

Resistor Inductor Capacitor

Z R Z j L1Z

j C

“CIVIL”

∘

Adding 90∘ to the phase

1 ∘

Removing 90∘ from the phase

Oscilloscope (scope)

5

Draw a graph of a voltage over time as a trace on its screen.

Cathode-ray oscilloscopes (CROs) Electron gun emits a beam of electrons (historically called

“cathode rays”, hence the name) which is deflected according to the signal being measured.

The trace is produced by the electrons striking a phosphor screen, which glows green where they hit.

Demo 1: Cathode-ray oscilloscope (CRO)

6

Cathode-ray tubes: ELECTRON GUN and DEFLECTION SYSTEM.

Caution: An overly bright trace can damage the phosphor of the screen if the dot is moving too slowly.

You may have seen an oscilloscope in use, in the form of a heart-rate monitor (electrocardiogram, or EKG) of the type seen in doctor's offices and hospitals.

Oscilloscope: Display

7

Notice the grid markings on the screen.

These markings create the graticule.

Each vertical and horizontal line constitutes a major division.

The graticule is usually laid out in an 8-by-10 division pattern.

The readout for volts/div and time/div always refer to major divisions.

The tick marks on the center horizontal and vertical graticule lines are called minor divisions.

Dual-channel Oscilloscope: Can handle two signals at once.

time/div

volts/div

Oscilloscope: Sketching Waveform(s)

8

The screen on the scope actually shows MORE than the 8-by-10 grid area.

 

In your sketch, don’t make the mistake of thinking the boundary of the whole screen is the same as the boundary of the provided grid area.

Voltage/Division _________Time/Division _________

1 V/DIV (CH1 & CH2)

0.1 ms/DIV

Oscilloscope Preparation

9

Follow III.3 and III.4.

POWER (1)

INTEN control (2)

FOCUS control (4)

CH1 (15) and CH2 (16)

CH 1’s GND (19) and CH 2’s GND (20)

Front panel

Vertical controls

Display controls

Oscilloscope Preparation

10

Make sure that the TRIGGER MODE (26) is set to ATO mode, otherwise the trace will not be shown.

Use the CH1 and CH2 POSITION controls ((9) and (10)) to align both traces on the center graticule.

Trigger controls

Oscilloscope Preparation

11

Connect the probe tips to the CAL test point (6) of the oscilloscope.

The square wave of the calibrator signal will be displayed on the screen.

VERTICAL:

VOLTS/DIV ((13) and (14)) 1V

COUPLING ((17) and (18)) DC

ALT/CHOP/ADD (12) CHOP or ALT

HORIZONTAL:MODE (22) MAIN

TIME/DIV (21) 0.5ms

TRIGGER:

MODE (26) ATO

SOURCE (29) CH1

COUPLING (28) AC

Make sure that ×1 is selected (not ×10)

Sect

ion

III.4

in th

e m

anua

l.

Function Generator

12

Part A

13

Part C

14

R2100 ohms

Sine-wavegenerator

OscilloscopeCh-1 Ch-2

probe tip

probe tip

ground clip

Ground clip

Z1

Part C.1: Z1 is a resistor

15

R2100 ohms

Sine-wavegenerator

OscilloscopeCh-1 Ch-2

probe tip

probe tip

ground clip

Ground clip

Z1

Ch 1

Ch 2

GND

Cables

16

Select ×1 here

The ×10 mode simply acts as a 10:1 voltage divider for any measured signals. With this, you will see tiny signal on the scope.

Obviously, one use for a ×10 probe is measuring voltages beyond the normal range of an oscilloscope.

For function generator, For oscilloscope,

Demo 2

17

Function Generator

Connect the circuit.

The generator should output a 4 Vp-p

sinusoid. Getting exactly 4 Vp-p

may be difficult to do visually on the oscilloscope. We may use the DMM to help.

R1 100 ohms

R2100 ohms

Sine-wavegenerator

OscilloscopeCh-1 Ch-2

probe tip

probe tip

ground clip

ground clip

DMM in AC mode

18

Demo 2: DMM in AC Mode

19

Similar to the DC Voltage measurement except that the rotary switch is set at the AC mode.

p-p

rms

V 2 4

22V 2 1.414

2 2

A

AA

Demo 2

20

Ch 1: VG

Ch 2: V2

Ch 2 GND

Ch 1 GND

R1

R2

R2100 ohms

Sine-wavegenerator

OscilloscopeCh-1 Ch-2

probe tip

probe tip

ground clip

Ground clip

Z1

Demo 3

21

(Probe) ground clips

The scope’s two “reference” or “ground” clips are electrically common with the oscilloscope’s metal chassis, they are electrically common with each other as well.

It is very likely that the function generator is earth-grounded through its power cord as well.

Wrong measurement of V1

22

Ch 2 GND

Ch 1 GND

Ch 1: VG

Ch 2: V1?R1

R2

An attempt to use CH2 to measure V1.

Function Generator

Wrong measurement of V1

23

Ch 2 GND

Ch 1 GND

Ch 1: VG

Ch 2: V1?R1

R2

Correct measurement of V1

24

Ch 1

Ch 2

Ch 2 GND

Ch 1 GND

R1

R2

CH1 CH2V VUse to measure the voltage across any pair of nodes in the circuit

while still keeping the ground clips together. Differential Measurement

Part C.2

25

R2100 ohms

Sine-wavegenerator

OscilloscopeCh-1 Ch-2

probe tip

probe tip

ground clip

Ground clip

Z1

Part C.3

26

R2100 ohms

Sine-wavegenerator

OscilloscopeCh-1 Ch-2

probe tip

probe tip

ground clip

Ground clip

Z1

Reading Capacitor Code

27

Code Value

102 0.001 F

103 0.01 F

104 0.1 F

473 0.047 F

474 0.47 F

4 4 4

4 6 2

2

6

1 6 6p 10 10 1047 10 F 47 10 F 47 10 F1047 10 10 F 47 10 F

=0.47 F

Measuring C and L

28

We can use DMM to measure capacitance.

Special device (LCR meter) to measure inductance.

Capacitor and Inductor

29

5 mH Inductor

0.47 F capacitor (474) LCR meter