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Elektronika (10) Elektronika (10) Presentation Transcript

  • Elektronika
    AgusSetyo Budi, Dr. M.Sc
    Sesion #10
    JurusanFisika
    FakultasMatematikadanIlmuPengetahuanAlam
  • Outline
    18-1: Sine-Wave VC Lags iCby 90o
    18-2: XC and R in Series
    18-3: Impedance ZTriangle
    18-4: RC Phase-Shifter Circuit
    18-5: XC and R in Parallel
    18-6: RF and AF Coupling Capacitors
    18-7: Capacitive Voltage Dividers
    18-8: The General Case of Capacitive Current iC
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    2
    07/01/2011
  • Capacitive Circuits
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    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    3
  • 18-1: Sine-Wave VC Lags iCby 90o
    For any sine wave of applied voltage, the capacitor’s charge and discharge current ic will lead vc by 90°.
    Fig. 18-1: Capacitive current ic leads vc by 90°. (a) Circuit with sine wave VA across C. (b) Waveshapes of ic90° ahead of vc. (c) Phasor diagram of ic leading the horizontal reference vc by a counterclockwise angle of 90°. (d) Phasor diagram with ic as the reference phasor to show vc lagging ic by an angle of −90°.
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    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    4
  • 18-1: Sine-Wave VC Lags iCby 90o
    The value of ic is zero when VA is at its maximum value.
    At its high and low peaks, the voltage has a static value before changing direction. When V is not changing and C is not charging or discharging, the current is zero.
    ic is maximum when vc is zero because at this point the voltage is changing most rapidly.
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    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    5
  • 18-1: Sine-Wave VC Lags iCby 90o
    icand vc are 90° out of phase because the maximum value of one corresponds to the zero value of the other.
    The 90° phase angle results because ic depends on the rate of change of vc. ic has the phase of dv/dt, not the phase of v.
    The 90° phase between vc and ic is true in any sine wave ac circuit. For any XC, its current and voltage are 90° out of phase.
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    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    6
  • 18-1: Sine-Wave VC Lags iCby 90o
    The frequency of vc and ic are always the same.
    The leading phase angle only addresses the voltage across the capacitor. The current is still the same in all parts of a series circuit. In a parallel circuit, the voltage across the generator and capacitor are always the same, but both are 90° out of phase with ic.
    07/01/2011
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    7
  • 18-2: XC and R in Series
    When a capacitor and a resistor are connected in series, the current is limited by both XC and R.
    Each series component has its own series voltage drop equal to IR for the resistance and IXC for the capacitive reactance.
    For any circuit combining XC and R in series, the following points are true:
    The current is labeled I rather than IC, because I flows through all the series components.
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    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    8
  • 18-2: XC and R in Series
    The voltage across XC, labeled VC, can be considered an IXC voltage drop, just as we use VR for an IR voltage drop.
    The current I through XC must lead VC by 90°, because this is the phase angle between the voltage and current for a capacitor.
    The current I through R and its IR voltage drop are in phase. There is no reactance to sine-wave alternating current in any resistance. Therefore, I and IR have a phase angle of 0°.
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    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    9
  • 18-2: XC and R in Series
    Phase Comparisons
    For a circuit combining series resistance and reactance, the following points are true:
    The voltage VC is 90° out of phase with I.
    VRand I are in phase.
    If I is used as the reference, VC is 90° out of phase with VR.
    VC lags VR by 90° just as voltage VC lags the current I by 90°.
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    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    10
  • 18-2: XC and R in Series
    Combining VR and VC ; the Phasor Voltage Triangle
    When voltage wave VR is combined with voltage wave VC the result is the voltage wave of the applied voltage VT.
    Out-of-phase waveforms may be added quickly by using their phasors. Add the tail of one phasor to the arrowhead of another and use the angle to show their relative phase.
    VR2 + VC2
    VT =
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    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    11
  • 18-2: XC and R in Series
    Fig. 18-3: Addition of two voltages 90° out of phase. (a) Phasors for VC and VR are 90° out of phase. (b) Resultant of the two phasors is the hypotenuse of the right triangle for VT.
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    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    12
  • 18-2: XC and R in Series
    VR
    R
    q
    q
    VT
    ZT
    XC
    VC
    Voltage Phasors
    Impedance Phasor
    Phasor Voltage Triangle for Series RC Circuits
    07/01/2011
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    13
  • 18-2: XC and R in Series
    q = 0
    I
    VR
    I
    I
    q = - 90
    VC
    Waveforms and Phasors for a Series RC Circuit
    Note: Since current is constant in a series circuit, the current waveforms and current phasors are shown in the reference positions.
    07/01/2011
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    14
  • 18-3: Impedance Z Triangle
    R and XC may be added using a triangle model as was shown with voltage.
    Adding phasors XC and R results in their total opposition in ohms, called impedance, using symbol ZT.
    Fig. 18-4: Addition of R and XC 90° out of phase in a series RC circuit to find the total impedance ZT.
  • 18-3: Impedance Z Triangle
    R2 + XC2
    ZT =
    XC
    tan ΘZ =

    R
    Z takes into account the 90° phase relationship between R and XC.
    • Phase Angle with Series XC and R
    • The angle betweenthe applied voltage VT and the series current I is the phase angle of the circuit.
    • The phase angle may be calculated from the impedance triangle of a series RC circuit by the formula
    07/01/2011
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    16
  • 18-3: Impedance Z Triangle
    R
    I = 2 A
    XC
    Z
    R = 30 W
    VT = 100
    XC = 40 W
    =
    Z =
    = 50 W
    R2 + XC2
    302 + 402
    100
    VT
    = 2 A
    I =
    =
    50
    Z
    The Impedance of a Series RC Circuit
    The impedance is the total opposition to current flow. It’s the phasor sum of resistance and reactance in a series circuit
    07/01/2011
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    17
  • adjacent
    Θ
    opposite
    negative
    angle
    positive
    angle
    opposite
    Θ
    adjacent
    18-3: Impedance Z Triangle
    The Tangent Function
    07/01/2011
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    18
  • 18-3: Impedance Z Triangle
    I = 2 A
    30 W
    q
    R = 30 W
    VT = 100
    XC = 40 W
    40 W
    50 W
    XC
    40
    -
    Θ = Tan−1
    -
    = Tan−1
    = −53°
    30
    R
    I
    −53°
    VT lags I by 53°
    VC
    VT
    The Phase Angle of a Series RC Circuit
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    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    19
  • 18-3: Impedance Z Triangle
    Θ < 0
    I
    XC < R
    I
    XC = R
    Θ = −45
    VT
    VT
    VT
    I
    I
    XC > R
    Θ < − 45
    VT
    Source Voltage and Current Phasors
    Note: The source voltage lags the current by an amount proportional to the ratio of capacitive reactance to resistance.
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    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    20
  • 18-4: RC Phase-Shifter Circuit
    The RC phase-shift circuit is used to provide a voltage of variable phase to set the conduction time of semiconductors in power control circuits.
    Output can be taken across R or C depending on desired phase shift with respect to VIN.
    VR leads VT by an amount depending on the values of XC and R.
    VC lags VT by an amount depending on the values of XC and R.
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    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    21
  • 18-4: RC Phase-Shifter Circuit
    Fig. 18-5: An RC phase-shifter circuit. (a) Schematic diagram. (b) Phasor triangle with IR, or VR, as the horizontal reference. VR leads VT by 46.7° with R set at 50 kΩ. (c) Phasors shown with VTas the horizontal reference.
    07/01/2011
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    22
  • 18-5: XC and R in Parallel
    The sine-wave ac charge and discharge currents for a capacitor lead the capacitor voltage by 90°.
    The sine-wave ac voltage across a resistor is always in phase with its current.
    The total sine-wave ac current for a parallel RC circuit always leads the applied voltage by an angle between 0° and 90°.
    07/01/2011
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    23
  • 18-5: XC and R in Parallel
    Phasor Current Triangle
    The resistive branch current IR is used as the reference phasor since VA and IR are in phase.
    The capacitive branch current IC is drawn upward at an angle of +90° since IC leads VA and thus IR by 90°.
    Fig. 18-7: Phasor triangle of capacitive and resistive branch currents 90° out of phase in a parallel circuit to find the resultant IT.
  • 18-5: XC and R in Parallel
    Phasor Current Triangle (Continued)
    The sum of the IR and IC phasors is indicated by the phasor for IT, which connects the tail of the IR phasor to the tip of the IC phasor.
    The IT phasor is the hypotenuse of the right triangle.
    The phase angle between IT and IR represent the phase angle of the circuit.
    IR2 + IC2
    IT =
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    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    25
  • 18-5: XC and R in Parallel
    Impedance of XC and R in Parallel
    To calculate the total or equivalent impedance of XC and R in parallel, calculate total line current IT and divide into applied voltage VA:
    VA
    IT
    ZEQ =
    07/01/2011
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    26
  • 18-5: XC and R in Parallel
    3 A
    5 A
    IT = 5 A
    R = 30 W
    XC = 40 W
    VA = 120
    4 A
    120
    VA
    =
    = 24 Ω
    ZEQ =
    IT
    5
    Impedance in a Parallel RC Circuit
    07/01/2011
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    27
  • Phase Angle in Parallel Circuits
    IC
    Tan ΘI =
    IR
    18-5: XC and R in Parallel
    Use the Tangent form to find Θ from the current triangle.
    Tan ΘI = 10/10 = 1
    ΘI = Tan 1
    ΘI = 45°
    Fig. 18-7
  • 18-5: XC and R in Parallel
    Parallel Combinations of XC and R
    The series voltage drops VRand VC have individual values that are 90° out of phase.
    They are added by phasors to equal the applied voltage VT.
    The negative phase angle −ΘZ is between VT and the common series current I.
    The parallel branch currents IR and IC have individual values that are 90° out of phase.
    They are added by phasors to equal IT, the main-line current.
    The positive phase angle ΘI is between the line current IT and the common parallel voltage VA.
    07/01/2011
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    29
  • 18-5: XC and R in Parallel
    • Parallel Combinations of XC and R
    • Resistance (R) in Ohms, Ω
    • Voltage in phase with current.
    • Capacitive Reactance (XC) in Ohms, Ω
    • Voltage lags current by 90°.
    Series circuit impedance (ZT) in Ohms, Ω
    Voltage lags current.
    Becomes more resistive with increasing f.
    Becomes more capacitive with decreasing f.
    Parallel circuit impedance (ZEQ) in Ohms, Ω
    Voltage lags current.
    Becomes more resistive with decreasing f.
    Becomes more capacitive with increasing f.
    07/01/2011
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    30
  • 18-5: XC and R in Parallel
    Summary of Formulas
    Series RC
    Parallel RC
    R2 + XC2
    ZT =
    VA
    VT =
    VR2 + VC2
    IT =
    IR2 + IC2
    1
    1
    ZEQ =
    XC =
    XC =
    IT
    2 πf C
    2 πf C
    XC
    IC
    tan Θ = −
    tan Θ =
    R
    IR
    07/01/2011
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    31
  • 18-6: RF and AF Coupling Capacitors
    • CC is used in the application of a coupling capacitor.
    • The CC’s low reactance allows developing practically all the ac signal voltage across R.
    • Very little of the ac voltage is across CC.
    • The dividing line for CC to be a coupling capacitor at a specific frequency can be taken as XC one-tenth or less of the series R.
    07/01/2011
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    32
  • 18-7: Capacitive Voltage Dividers
    When capacitors are connected in series across a voltage source, the series capacitors serve as a voltage divider.
    Each capacitor has part of the applied voltage.
    The sum of all the series voltage drops equals the source voltage.
    The amount of voltage across each capacitor is inversely proportional to its capacitance.
    07/01/2011
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    33
  • 18-7: Capacitive Voltage Dividers
    Fig. 18-9: Series capacitors divide VT inversely proportional to each C. The smaller C has more V. (a) An ac divider with more XC for the smaller C.
    07/01/2011
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    34
  • 18-7: Capacitive Voltage Dividers
    Fig. 18-9: Series capacitors divide VT inversely proportional to each C. The smaller C has more V. (b) A dc divider.
    07/01/2011
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    35
  • 18-8: The General Case of Capacitive Current iC
    The capacitive charge and discharge current ic is always equal to C(dv/dt).
    A sine wave of voltage variations for vc produces a cosine wave of current i.
    Note that vc and ic have the same waveform, but they are 90° out of phase.
    07/01/2011
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    36
  • 18-8: The General Case of Capacitive Current iC
    XC is generally used for calculations in sine-wave circuits.
    Since XC is 1/(2πfC), the factors that determine the amount of charge and discharge current are included in f and C.
    With a nonsinusoidal waveform for voltage vc, the concept of reactance cannot be used. (Reactance XC applies only to sine waves).
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    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
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