chap5 2015 [호환 모드] - HANSUNG · 2015-09-23 · Dept. of Information and Communication Eng....

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Lab. 5 Oscilloscope와 AC Circuit의 기초

Dept. of Information and Communication Eng. 2

이 실험의 목표

AC Circuit의 기초 Capacitor의 기본 회로 특성 이해

Inductor의 기본 회로 특성 이해

Lissajous 도형이란?

Oscilloscope의 동작 특성 이해 Oscilloscope의 사용법

Oscilloscope를 이용한 정현파 표현


Alternating Current and Voltage

In alternating current (AC) circuits, the voltage source is sinusoidal. “Sinusoidal” is related to “Sine”. When the sinusoidal voltage source (Vs ) is applied to a resistive circuit,

an alternating sinusoidal current results. A sine wave changes polarity at its zero value, it alternates between

positive and negative values. When the voltage source changes polarity, the current correspondingly

changes direction as well. The combination positive and negative alternations make up one cycle

of a sine wave.



Period of a Sine Wave A sine wave varies with time ( t ) in a definable manner. The time required for a given sine wave to complete one full

cycle is called the period ( T ) A sine wave continues to repeat itself in identical cycles



or 1 1f TT f

Frequency of a Sine Wave Frequency is the number of cycles that a sine wave completes in

one second. The more cycles completed in one second, the higher the

frequency.

Frequency ( f ) is measured in units of hertz (Hz). Relationship of Frequency and Period:

(2Hz) (4Hz)



Phase of a Sine Wave When a sine wave is shifted left or right with respect to this

reference, there is a phase shift. The sine wave repeats every radians phase shift.2



siny A

Expression for Phase-Shifted in Sine Wave When a sine wave is shifted to the right of the reference (lags)

by a certain angle , the general expression is

Graphically, it is to rotate the phasor by clockwise. Vice verse for sine wave shifted to the left (leads).



Phasor and Phasor Diagram At any given instant, the magnitude of a sine wave can be

described by the values of the phase angle and the amplitude. Such expression is a phasor quantity

Having both magnitude and direction (phase angle)

A phasor quantity is represented graphically as an arrow that rotates around a fixed point.

The length of a sine wave phasor is the peak value and its angular position as it rotates is the phase angle.



45sin(45 ) Im Im 45jv V Ve V

Example of a phasor diagram Length of the phasor = V = peak voltage Angular position = The instant value, v , of the sine wave at this point is related to

both length and angular position of the phasor. Also applies to the AC currents.

45



Peak Values of Sine Waves The peak value of a sine wave is the value of voltage or current at the

positive or negative maximum with respect to zero Peak values (AMPLITUDE) are represented as: Vp and Ip

Peak-to-Peak Values The peak-to-peak value of a sine wave is the voltage or current from

the positive peak to the negative peak The peak-to-peak values are represented as: Vpp = 2Vp and Ipp = 2Ip

RMS Value of a Sine Wave The rms (root mean square) value of a sinusoidal voltage is Vrms =

0.707Vp , Irms = 0.707Ip

Average Value of a Sine Wave The average value is Vavg = 0.637Vp , Iavg = 0.637Ip

dttvT

VT

2

0rms

1


Capacitor

The capacitor is a device that can store electrical charge. The measure of the charge-storing ability is called capacitance

(C) A simple capacitor is constructed of two parallel conductive

plates separated by an insulating material called the dielectric, connecting leads are attached to the parallel plates.


Capacitor

Capacitors in DC Circuits In the neutral state, both places have an equal number of free

electrons. When the capacitor is connected to a DC voltage source

through a resistor, electrons are removed from plate A, and an equal number are deposited on plate B. Plate A becomes positive with respect to plate B.

During charging, electrons flow only through the connecting leads and the source No electrons flow through the insulating dielectric.

(b) When connected to a voltage source, electrons flow from plate A to plate B as the capacitor charges.

(a) Neutral (uncharged) capacitor(same charge on both plates)


Capacitor

The movement of electrons ceases (stops) when the voltage across the capacitor equals the source voltage.

If the capacitor is disconnected from the source, it retains the stored charge for a period of time. A charged capacitor can act as a temporary battery.

(c) After the capacitor charges to Vs, no electrons flow.

(d) Ideally, the capacitor retains charge when disconnected from the voltage source.


Capacitor

Charging of a capacitor does not take place instantaneously, it occurs over a period of time determined by the components of the network the period of charging is called the transient period

(a) Charging curve with percentages of the final voltage.

(b) Discharging curve with percentages of the initial voltage.

Dept. of Information and Communication Eng.

Capacitance (C) is a measure of a capacitor’s ability to store charge. The more charge per unit of voltage that a capacitor can store,

the greater its capacitance

where C is capacitance, Q is charge, and V is voltage Unit: farad (F)

One farad is the amount of capacitance when one coulomb of charge is stored with one volt across the plates

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Capacitor

or QC Q CVV


Capacitor


Capacitor

Capacitor Measurement An LCR meter (LCR =

inductance, capacitance, and resistance) can be used to check the value of a capacitor


Capacitor

Capacitor Labeling Capacitors use several labeling

methods. Small capacitors values are

frequently stamped on them such as .001 or .01, which have implied units of microfarads

Electrolytic capacitors (which are polarized) have larger values, so are read as mF.

The unit is usually stamped as mF, but some older ones may be shown as MF or MMF

0.022 Fm 47 mF


Capacitor

A label with digits only, such as 103 or 104 is read respectively as

Third digit is the multiplier Units are picofarads

Example: capacitance of the capacitor is pF

3 4or10 10 10,000 pF 10 10 100,000 pF


Capacitor


Capacitor

sin , cosCC m C m

dvv V t i C CV tdt

iC leads VC by 90o

Capacitors in AC Circuits

Impedance of a capacitor:

Sinusoidal response of capacitor:

,j t CC m C C

dVV V e I C j CVdt

(Ohm’s law for capacitor)1C

CC

VZI j C


Capacitor

Fig. : Current in a capacitive circuit. (a) The 4-μF capacitor allows enough current I to light the bulb brightly. (b) Less current with smaller capacitor causes dim light. (c) Bulb cannot light with DC voltage applied because a capacitor blocks the direct current.

With a 4-μF capacitor, the bulb lights brightly.

The smaller capacitor has more opposition to AC and the bulb is dim.

The capacitor blocks dc and the bulb cannot light.


A capacitor blocks constant DC, after it charged up, no current flows

A capacitor passes AC with an amount of opposition, called capacitive reactance , that depends on the frequency of the AC

The equation for capacitive reactance is

Unit: ohm ( ), where f is the frequency of the AC source in hertz C is the capacitance in farad

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Capacitor

CX

12CX

fC


Inductor

When a length of wire is formed into a coil, it becomes a basic inductor. When there is current in the

inductor, a three-dimensional magnetic field is created.

A change in current (AC current) causes the magnetic field to change. This in turn induces a voltage

across the inductor that opposes the original change in current.


Inductor

Inductance (L) is a measure of a coil’s ability to establish an induced voltage as a result of a change in its current.

The unit is henry (H). One henry (H) is when a current,

changing at a rate of one ampere per second, induces one volt across the coil (in an opposite direction to the current).

The effect of inductance is greatly magnified by adding turns and winding them on a magnetic material.

Large inductors and transformers are wound on a core to increase the inductance.


Inductor

Typical Inductors ( )H


Lenz’s Law Voltage is induced in a direction to oppose the change. The induced voltage is linearly proportional to the rate of

change of current. Induced voltage is given by

The larger the change in current, the larger the induced voltage.

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Inductor

( )( ) dI tV t Ldt


Inductor

Inductors in DC Circuits

When there is constant current in an inductor, there is no induced voltage.

There is a voltage drop in the circuit due to the winding resistance of the coil. But, practically inductance itself appears as a short to DC.


Inductor

When sine-wave variations of current produce an induced voltage, the current lags its induced voltage by exactly 90°, as shown in Figure

The phasors in Fig. (c) show the 90° phase angle between iL and vL. The 90° phase relationship between iL and vL is true in any sine-

wave AC circuit, whether L is in series or parallel.

Inductors in AC Circuits


Reactance of Inductor ( XL ) For AC circuits

Reactance: Voltage leads current by At low frequency (small ), inductor short-circuit At high frequency (large ), inductor open-circuit

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Inductor

LX L

LL

L

VZ j LI

(Impedance of a Inductor)

90

,j tL m

LL L

I I edIV L j LIdt


Inductor

In Fig. (a), there is no inductance, and the AC voltage source causes the bulb to light with full brilliance.

In Fig. (b), a coil is connected in series with the bulb.

The coil has a negligible DC resistance of 1 Ω, but a reactance of 1000 Ω.

Now, I is 120 V / 1000 Ω, approximately 0.12 A. This is not enough to light the bulb.

In Fig. (c), the coil is also in series with the bulb, but the battery voltage produces a steady DC.

Without any current variations, there is no XL and the bulb lights with full brilliance.


Lissajous

Normally the scope will plot a voltage signal with respect to time. In a Lissajous figure, two voltage signals are plotted against each other.

t

( ) sinyV t A t ( ) sinyV t A t

Normal operation of scope ( ) cosxV t B t

Generating Lissajous figures


Lissajous

( ) sin 0yV t A t

( ) sin 0xV t B t

0t 1t 2t

3t 4t 0 2 4, ,t t t

1t

3t

0t 1t 2t

3t 4tB

A

B

A

B

A

time x y

t0 0 0

t1 B A

t2 0 0

t3 -B -A

t4 0 0


Lissajous

( ) sin 0yV t A t

( ) sin / 2xV t B t

0t 1t 2t

3t 4t 0 4,t t

1t

2t

0t 1t 2t

3t 4tB

A

B

A

B

A3t

time x y

t0 B 0

t1 0 A

t2 -B 0

t3 0 -A

t4 B 0

Circle if A=B !


Lissajous ( ) sin 0yV t A t

( ) sin 2 0xV t B t

0 4 8, ,t t t

1t

7t

0t 1t 2t 3t 4t

B

A

B

A

B

A

5t 6t 7t 8t

0t 1t 2t 3t 4t 5t 6t 7t 8t

2t

3t

5t

6ttime x y

T0 0 0

t1 B 0.7A

t2 0 A

t3 -B 0.7A

t4 0 0

t5 B -0.7A

t6 0 -A

t7 -B -0.7A

t8 0 0

Circle if A=B !


Lissajous


Lissajous

Time

1.0ms 1.2ms 1.4ms 1.6ms 1.8ms 2.0msV(200) V(300)

-1.0V

0V

1.0V

AB

1sin BA


Lissajous


Oscilloscope 기능 이해

(Taktronix 4-Channel Model)



기능 검사 Oscilloscope가 올바르게 작동하는지 확인하는 과정


Display 영역

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Display 영역

45



Display 영역

46




Example:


Oscilloscope의 기능 이해

What is Trigger?


Oscilloscope의 사용법


Passive Probe

대부분의 수동 프로브는 1X나 10X 등의 감쇠율을 가지고 있다.

10X 감쇠 프로브는 부하 효과를 줄여주고, 일반 목적으로서 훌륭한 수동프로브입니다. 부하효과는 특히 주파수가 높아질수록 현저히 나타나므로, 5kHz 이상의 신호 측정시는 10x 프로브를 사용해야 한다.

10X 프로브는 측정의 정확도를 높여주지만, 화면에 나타나는 신호의 크기는 1/10로 줄어든다. 그래서 10X 감쇠 프로브는 10mV 보다 작은 신호는보기가 어렵다.

1X 프로브는 10X 감쇠 프로브와 유사하지만 감쇠 회로가 없다.

감쇠회로가 없으므로 회로를 테스트할 때 더 많은 간섭이 일어나게 된다.

그러므로, 표준 프로브로 10X 감쇠 프로브를 사용하고, 미약한 신호를 위해서는 1X 프로브를 사용하면 편리하다.

chap5 2015 [호환 모드] - HANSUNG · 2015-09-23 · Dept. of Information and Communication Eng....

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Transcript of chap5 2015 [호환 모드] - HANSUNG · 2015-09-23 · Dept. of Information and Communication Eng....