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1. Elektronika AgusSetyo Budi, Dr. M.Sc Sesion #10 JurusanFisika FakultasMatematikadanIlmuPengetahuanAlam

2. 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

3. Capacitive Circuits 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 3

4. 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°. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 4

5. 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. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 5

6. 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. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 6

7. 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

8. 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. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 8

9. 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°. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 9

10. 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°. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 10

11. 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 = 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 11

12. 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. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 12

13. 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

14. 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

15. 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.

17. The angle betweenthe applied voltage VT and the series current I is the phase angle of the circuit.

18. The phase angle may be calculated from the impedance triangle of a series RC circuit by the formula07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 16

19. 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

20. 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

21. 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 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 19

22. 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. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 20

23. 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. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 21

24. 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

25. 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

26. 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.

27. 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 = 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 25

28. 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

29. 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

30. 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

31. 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

33. Resistance (R) in Ohms, Ω

34. Voltage in phase with current.

35. Capacitive Reactance (XC) in Ohms, Ω

36. 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

37. 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

39. The CC’s low reactance allows developing practically all the ac signal voltage across R.

40. Very little of the ac voltage is across CC.

41. 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

42. 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

43. 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

44. 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

45. 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

46. 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). 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 37

47. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 38 TerimaKasih