This document discusses resonant circuits and their properties. It covers topics such as series and parallel resonance, resonant frequency, Q factor, bandwidth, tuning, and choosing component values for resonant circuits. Specific examples and equations are provided to illustrate concepts like how inductive and capacitive reactance cancel at resonance, the relationship between resonant frequency and component values, and how Q factor determines bandwidth and voltage magnification. Applications of resonant circuits in radio tuning are also described.

1. ElektronikaAgusSetyo Budi, Dr. M.ScSesion #15JurusanFisikaFakultasMatematikadanIlmuPengetahuanAlam

2. Outline 25-5: Q Magnification Factor of Resonant Circuit25-6: Bandwidth of Resonant Circuit25-7: Tuning25-8: Mistuning25-9: Analysis of Parallel Resonant Circuits25-10: Damping of Parallel Resonant Circuits25-11: Choosing L and C for a Resonant Circuit© 2010 Universitas Negeri Jakarta | www.unj.ac.id |207/01/2011

3. Resonance07/01/2011© 2010 Universitas Negeri Jakarta | www.unj.ac.id |3

4. 25-1: The Resonance EffectInductive 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

5. 25-1: The Resonance EffectThe most common application of resonance in rf circuits is called tuning.

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 ResonanceAt 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 ResonanceCLwhere:fr= resonant frequency in HzL = inductance in henrysC = capacitance in faradsSeries Resonant Circuit07/01/2011© 2010 Universitas Negeri Jakarta | www.unj.ac.id |7

10. 25-2: Series ResonanceFig. 25-2 (b) shows XL and XC equal, resulting in a net reactance of zero ohms.

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 Resonance5 AR = 4 W20 V5 kHzIr= 20/4 = 5 AXC = 31 WXL = 31 WVL = I × XL = 155 VVC = I × XC = 155 VResonant Rise in VL and VCNote: 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 ResonanceQ = 7.8Q = 325 AR = 4 W5 A20 V5 kHz4 W20 V5 kHzL1 mF4 mH0.25 mF1 mHVL = I × XL = 640 VVL = I × XL = 155 VVC = I × XC = 640 VVC = I × XC = 155 V32 × 20 V = 640 V7.8 × 20 V = 155 VQVS = VXResonant Rise in VL and VC07/01/2011© 2010 Universitas Negeri Jakarta | www.unj.ac.id |10

14. 25-2: Series Resonance14 Ω= = 5.03 kHz20 V2 π 1× 10−3× 1× 10−61 μF1 mHf543Current in A21123456789100Frequency in kHzFrequency Response07/01/2011© 2010 Universitas Negeri Jakarta | www.unj.ac.id |11

15. 25-3: Parallel ResonanceWhen 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 ResonanceLC1=fπLCr2Parallel Resonant Circuitwhere:fr= resonant frequency in HzL = inductance in henrysC = capacitance in farads[Ideal; no resistance]07/01/2011© 2010 Universitas Negeri Jakarta | www.unj.ac.id |13

17. 25-3: Parallel ResonanceFig. 25-607/01/2011© 2010 Universitas Negeri Jakarta | www.unj.ac.id |14

18. 25-3: Parallel ResonanceC = 1 mFL = 1 mH20 VR = 1 kWInductiveCapacitive32IT in A1010123456789Frequency in kHzFrequency Response07/01/2011© 2010 Universitas Negeri Jakarta | www.unj.ac.id |15

19. 25-4: Resonant FrequencyThe formula for the resonant frequency is derived from XL = XC. For any series or parallel LC circuit, the fr equal to is the resonant frequency that makes the inductive and capacitive reactances equal.07/01/2011© 2010 Universitas Negeri Jakarta | www.unj.ac.id |16

20. 25-5: Q Magnification Factor of Resonant CircuitThe 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 Circuit20 V5.03 kHzC = 1 mFL = 1 mHrS = 1 WXL31.6==31.6Q =1rSQ 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 Circuit4 W4 W20 V20 V4 mH1 mH1 mF0.25 mF54Half-powerpointQ = 323Current in AQ = 7.821012345678910Frequency in kHzIncreasing the L/C Ratio Raises the Q07/01/2011© 2010 Universitas Negeri Jakarta | www.unj.ac.id |19

23. 25-6: Bandwidth of Resonant CircuitWhen 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 CircuitFig. 25-10: 07/01/2011© 2010 Universitas Negeri Jakarta | www.unj.ac.id |21

25. 25-7: TuningTuning means obtaining resonance at different frequencies by varying either L or C.

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. 25-1207/01/2011© 2010 Universitas Negeri Jakarta | www.unj.ac.id |22

27. 25-7: Tuning Fig. 25-13 illustrates a typical application of resonant circuits in tuning a receiver to the carrier frequency of a desired radio station.

28. The tuning is done by the air capacitor C, which can be varied from 360 pF to 40 pF.Fig. 25-1307/01/2011© 2010 Universitas Negeri Jakarta | www.unj.ac.id |23

29. 25-8: MistuningWhen 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 impedanceThe net reactance off-resonance makes the LC circuit either inductive or capacitive.07/01/2011© 2010 Universitas Negeri Jakarta | www.unj.ac.id |24