mạch điện ac trang bị điện

mạch điệnwdwdw ưdwdwdwdTrong chương này chúng ta sẽ khảo sát qua các loại cổng logic thông dụng trong máy tính, các phương thức hoạt động và các ký hiệu của chúng. Đồng thời ta cũng nghiên cứu về đại số Boole, là đối tượng liên quan khá chặt chẽ đến các cổng. Đại số boole được phát minh bởi nhà toán học George Boole. Trong đại số này các biến chỉ mang một trong hai trạng thái: 0 và 1 (đúng hay sai) và cũng chính vì thế người ta còn gọi đại số boole là đại số lưỡng trạng. Riêng khả năng của nó chính là giải quyết rất tốt các bài toán về các mạch luận lý (logic) như đơn giản hoá mạch, mạch tương đương,… Các mạch này còn được gọi là các cổng luận lý vì ta có thể dùng đại số boole để tính toán chúng. 12.1 Biểu diễn các trạng thái logic 1 và 0 Trong hệ thống mạch logic, các trạng thái logic được biểu diễn bởi các mức điện thế. Với qui ước logic dương, điện thế cao biểu diễn logic “1”, logic âm, điện thế thấp biểu diễn logic “0”. Trong thực tế, mức “1” và “0” tương ứng với một khoảng điện thế xác định và có một khoảng chuyển tiếp giữa mức cao và thấp, ta gọi là khoảng không xác định. Khi điện áp của tín hiệu rơi vào khoảng này, mạch sẽ không nhận ra là mức “0” hay “1”. Khoảng này tùy thuộc vào họ IC sử dụng và được cho trong bảng thông số kỹ thuật của linh kiện. Đa s

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Ho Chi Minh City National University

Ho Chi Minh City University of Technology

Faculty of Mechanics Engineering Department of Mechatronics Engineering

Subject:

Electrical & Electronic Equipment for Industrial Machinery

AC Electric Circuit & Theory

PhD Ngô Hà Quang Thịnh, nhqthinh@hcmut.edu.vn

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▪ Natural Response of a Parallel RLC circuit

▪ Natural Response of a Series RLC circuit

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Introduction

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What are SI units ?

► Abbreviation from French “Système international d'unités”,established in 1960

► The SI Units are based on 7 defined quantities: length (m), mass (kg),time (s), current (A), temperature (K), amount (mol), luminous intensity(cd)

► SI units enable engineers to communicate in a meaningful way aboutquantitative results

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Derived units in SI

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Prefixes to Signify Powers of 10

► Engineers often use powers divisible by 3, and base numbers between

1 and 1,000

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Prefixes to Signify Powers of 10

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Passive Sign Convention

► If the reference current through the element is in the direction of thereference voltage drop across the element, we can use a positive sign inthe i-v relation of the element

► E.g Let the reference current and voltage of the resistor satisfy thepassive sign convention, → we have v = +R x i, though the values of v, ican be >0 or <0

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Generation & Distribution of AC Power

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Residential Wiring

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Single Phase Three-Wire Residential Wiring

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Ground Fault Circuit Interrupter (GFCI)

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What is a Complex Number

► A complex number z is a point (or vector) on a two-dimensional plane,known as the complex plane and represented by C

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Cartesian Coordinates

► The Cartesian coordinates of z are

- x = Re{z}: the real part of z

- y = Im{z}: the imaginary part of z

► The corresponding axes are known as the real and imaginary axes,respectively

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Polar Coordinates

► The polar coordinates of z are

- r = |z|: the modulus or magnitude of z

- θ = z: the angle of z

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Converting Between Coordinates

► The Cartesian coordinate pair (x, y) is also equivalent to the polarcoordinate pair (r, θ) where r is the (non-negative) length of the vectorcorresponding to (x, y) and θ is the angle of the vector relative to positivereal time

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Definition

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What is Alternating Current

► Consider that a machine is constructed to rotate a set of wire coils withthe turning of a shaft in the magnetic field

► In accordance with Faraday’s Law of electromagnetic induction, ACvoltage will be produced across the wire coils when shaft is rotated

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AC Waveform

► Voltage, current or flux signal and

so on are related to time in sine function:

where

Vm: amplitude of voltage [V] ω: angular frequency [rad/s] Ф: initial phase when t = 0 [rad]

► Period T or frequency f of current, voltage are determined in the following:

► Units :

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AC Measurements

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AC Measurements

► Peak amplitude is the height of an AC waveform as measured from

the zero mark to the highest positive or lowest negative point on a graph

► Peak-to-peak amplitude is the total height of an AC waveform as

measured from maximum positive to maximum negative peaks on agraph

► A waveform’s average value is often calculated as the mathematical

mean of all the points’ absolute values or flux signal

►“RMS” stands for Root Mean Square, and is a way of expressing an

AC quantity of voltage or current in terms functionally equivalent to DC

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AC Phase

► The two waves shown

above (A versus B) are of

the same amplitude and

frequency, but they are out

of step with each other In

technical terms, this is called

a phase shift.

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How to Perform AC Current

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Vector and AC Waveform

► Conditions to compare the different phase:

When comparing the error of phase, the signals (sine current or voltage)need to satisfy the following conditions

+ The same frequency of signals+ Both of the signals are performed in sine (or cosine)Consider that there are two sine signals:

If Δφ is the error of phase, then it can be established as following:

Δφ > 0 : V1 leads V2

Δφ < 0 : V2 leads V1

Δφ = 0 : V1 equals V2

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How to Measure the Phase Shift

► Measure the period T between repeat Digital scopes often measure

f = 1 / T automatically

► Measure t d , the smallest time difference between occurrences of the

feature on the two waveforms

► The phase difference is then:

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Vector Phase: Fresnel

► Consider that a point (named

as M) moves around the circle (angular velocity ω, radius R)

► Center point of a circle is named as O

► At t=0, the angle between

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Addition of Two Phasors

► Consider that two signals V1 and V2 are illustrated as following

► Assume that VT is the sum vector of V1 and V2, we can obtain VT inthe following method

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► Consider that two signals V1 and V2 are illustrated as following

► V2 of 30 volts in the reference direction along the horizontal zeroaxis, then it has a horizontal component but no vertical component

► V1 of 20 volts leads V2 by 60o then, it has both horizontal and verticalcomponents (V1 = 10 + j17.32)

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► The resultant voltage, VT is found by adding together the horizontaland vertical components as follows

► VHorizontal = sum of real parts of V1 and V2 =30 + 10 = 40 volts

► VVertical = sum of imaginary parts of V1 and V2 =0 + 17.32 = 17.32volts

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Power of AC Current

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Instantaneous Power

► “Instantaneous” power is the product of the instantaneous terminalvoltage and current

► Positive sign is used if the passive sign convention is satisfied(current is in the direction of voltage drop)

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Sinusoidal Power Formula

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Relation among i(t), v(t), p(t)

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Average Power & Reactive Power

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Relation Among Components of Power

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What is Average Power

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What is Reactive Power

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Power for Resistive Loads

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Power for Inductive Loads

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Power for Capacitive Loads

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Power Factor & Reactive Factor

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Definition of Root-Mean-Square (RMS) Value

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RMS Value of Sinusoidal Function

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Power Formula in terms of RMS Value

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Complex Power

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Complex Power: Example

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Power Calculations

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Power Calculations

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Power Calculations: Example

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Transformers

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► Transformers are essential parts of most power systems to convert electrical energy at one voltage to some other voltage.

► Transformers include two-port circuit element.

V1, N1 and i1: primary voltage, primary turns and primary current

V2, N2 and i2: secondary voltage, secondary turns and secondary current

TS Ngô Hà Quang Thịnh, nhqthinh@hcmut.edu.vn

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a transformer with turns ratio of 13800 / 240 = 57.5

► The transformer, at least in its ideal form, does not consume, produce nor store energy Hence, the sum of power flows into a transformer is identically zero:

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► The transformer also tends to transform impedances as below figure.

► Some impedances are connected to one side of an ideal transformer Find an equivalent impedance viewed from the other side of the transformer.

Then, the ratio between input voltage and current is

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Natural Response of a Series RLC Circuit

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A Series RLC Circuit

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Natural Response of a Parallel RLC Circuit

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A Parallel RLC Circuit

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A Parallel RLC Circuit

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The End

Tiêu đề	AC Electric Circuit & Theory
Tác giả	PhD. Ngô Hà Quang Thịnh
Trường học	Ho Chi Minh City National University
Chuyên ngành	Electrical & Electronic Equipment for Industrial Machinery
Thể loại	thesis
Thành phố	Ho Chi Minh City

Định dạng
Số trang	67
Dung lượng	2,22 MB