unj fmipa-fisika

1. Elektronika AgusSetyo Budi, Dr. M.Sc Sesion #15 JurusanFisika FakultasMatematikadanIlmuPengetahuanAlam

2. Outline 25-5: Q Magnification Factor of Resonant Circuit 25-6: Bandwidth of Resonant Circuit 25-7: Tuning 25-8: Mistuning 25-9: Analysis of Parallel Resonant Circuits 25-10: Damping of Parallel Resonant Circuits 25-11: Choosing L and C for a Resonant Circuit © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 2 07/01/2011

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

4. 25-1: The Resonance Effect Inductive reactance increases as the frequency is increased, but capacitive reactance decreases with higher frequencies. Because of these opposite characteristics, for any LC combination, there must be a frequency at which the XL equals the XC; one increases while the other decreases. This case of equal and opposite reactances is called resonance, and the ac circuit is then a resonant circuit. The frequency at which XL = XC is the resonant frequency. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 4

6. In Fig. 25-1, the LC circuit is resonant at 1000 kHz.

7. The result is maximum output at 1000 kHz, compared with lower or higher frequencies.Fig. 25-1: 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 5

8. 25-2: Series Resonance At the resonant frequency, the inductive reactance and capacitive reactance are equal. In a series ac circuit, inductive reactance leads by 90°, compared with the zero reference angle of the resistance, and capacitive reactance lags by 90°. XL and XC are 180° out of phase. The opposite reactances cancel each other completely when they are equal. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 6

9. 25-2: Series Resonance C L where: fr= resonant frequency in Hz L = inductance in henrys C = capacitance in farads Series Resonant Circuit 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 7

11. The only opposition to current is the coil resistance rs, which limits how low the series resistance in the circuit can be.Fig. 25-2: 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 8

12. 25-2: Series Resonance 5 A R = 4 W 20 V 5 kHz Ir= 20/4 = 5 A XC = 31 W XL = 31 W VL = I × XL = 155 V VC = I × XC = 155 V Resonant Rise in VL and VC Note: The reactive voltages are phasor opposites and they cancel (VXL+VXC= 0). 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 9

13. 25-2: Series Resonance Q = 7.8 Q = 32 5 A R = 4 W 5 A 20 V 5 kHz 4 W 20 V 5 kHz L 1 mF 4 mH 0.25 mF 1 mH VL = I × XL = 640 V VL = I × XL = 155 V VC = I × XC = 640 V VC = I × XC = 155 V 32 × 20 V = 640 V 7.8 × 20 V = 155 V QVS = VX Resonant Rise in VL and VC 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 10

14. 25-2: Series Resonance 1 4 Ω = = 5.03 kHz 20 V 2 π 1× 10−3× 1× 10−6 1 μF 1 mH f 5 4 3 Current in A 2 1 1 2 3 4 5 6 7 8 9 10 0 Frequency in kHz Frequency Response 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 11

15. 25-3: Parallel Resonance When L and C are in parallel and XL equals XC, the reactive branch currents are equal and opposite at resonance. Then they cancel each other to produce minimum current in the main line. Since the line current is minimum, the impedance is maximum. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 12

16. 25-3: Parallel Resonance L C 1 = f π LC r 2 Parallel Resonant Circuit where: fr= resonant frequency in Hz L = inductance in henrys C = capacitance in farads [Ideal; no resistance] 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 13

17. 25-3: Parallel Resonance Fig. 25-6 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 14

18. 25-3: Parallel Resonance C = 1 mF L = 1 mH 20 V R = 1 kW Inductive Capacitive 3 2 IT in A 1 0 10 1 2 3 4 5 6 7 8 9 Frequency in kHz Frequency Response 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 15

20. 25-5: Q Magnification Factor of Resonant Circuit The quality, or figure of merit, of the resonant circuit, in sharpness of resonance, is indicated by the factor Q. The higher the ratio of the reactance at resonance to the series resistance, the higher the Q and the sharper the resonance effect. The Q of the resonant circuit can be considered a magnification factor that determines how much the voltage across L or C is increased by the resonant rise of current in a series circuit. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 17

21. 25-5: Q Magnification Factor of Resonant Circuit 20 V 5.03 kHz C = 1 mF L = 1 mH rS = 1 W XL 31.6 = = 31.6 Q = 1 rS Q is often established by coil resistance. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 18

22. 25-5: Q Magnification Factor of Resonant Circuit 4 W 4 W 20 V 20 V 4 mH 1 mH 1 mF 0.25 mF 5 4 Half-power point Q = 32 3 Current in A Q = 7.8 2 1 0 1 2 3 4 5 6 7 8 9 10 Frequency in kHz Increasing the L/C Ratio Raises the Q 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 19

23. 25-6: Bandwidth of Resonant Circuit When we say that an LC circuit is resonant at one frequency, this is true for the maximum resonance effect. Other frequencies close to fr also are effective. The width of the resonant band of frequencies centered around fr is called the bandwidth of the tuned circuit. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 20

24. 25-6: Bandwidth ofResonant Circuit Fig. 25-10: 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 21

26. As illustrated in Fig. 25-12, the variable capacitance C can be adjusted to tune the series LC circuit to resonance at any one of five different frequencies.Fig. 25-12 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 22

28. The tuning is done by the air capacitor C, which can be varied from 360 pF to 40 pF.Fig. 25-13 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 23

29. 25-8: Mistuning When the frequency of the input voltage and the resonant frequency of a series LC circuit are not the same, the mistuned circuit has very little output compared with the Q rise in voltage at resonance. Similarly, when a parallel circuit is mistuned, it does not have a high value of impedance The net reactance off-resonance makes the LC circuit either inductive or capacitive. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 24

31. The coil has its series resistance rs in the XL branch, whereas the capacitor has only XC in its branch.

32. For high-Q circuits, we consider rs negligible.Fig. 25-14 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 25

33. 25-9: Analysis of Parallel Resonant Circuits In low-Q circuits, the inductive branch must be analyzed as a complex impedance with XL and rs in series. This impedance is in parallel with XC, as shown in Fig. 25-14. The total impedance ZEQ can then be calculated by using complex numbers. Fig. 25-14 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 26

35. The RP may represent the resistance of the external source driving the parallel resonant circuit, or Rp can be an actual resistor.

36. Using the parallel RP to reduce Q is better than increasing rs.Fig. 25-15 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 27

37. 25-11: Choosing L and C for a Resonant Circuit A known value for either L or C is needed to calculate the other. In some cases, particularly at very high frequencies, C must be the minimum possible value. At medium frequencies, we can choose L for the general case when an XLof 1000 Ω is desirable and can be obtained. For resonance at 159 kHz with a 1-mH L, the required C is 0.001 μF. This value of C can be calculated for an XC of 1000 Ω, equal to XL at the fr of 159 kHz. 07/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 28

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