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Resonance and Q: Characteristics of Resonant Circuits, Series and Parallel Resonance

Learn about resonance in electronic circuits, including the characteristics of resonant circuits, series and parallel resonance, Q factor, half-power bandwidth, and phase relationships in reactive circuits.

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Resonance and Q: Characteristics of Resonant Circuits, Series and Parallel Resonance

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  1. WELCOME

  2. E5 E5A – Resonance and Q: characteristics of resonant circuits; series and parallel resonance; Q; half-power bandwidth; phase relationships in reactive circuits Resonance is one of the coolest things in electronics. Resonant circuits are what makes radio, as we know it, possible.

  3. Resonance and Q What is resonance? Well, a circuit is said to be resonant when the inductive reactance and capacitive reactance are equal to one another. That is to say, when 2πfL = 1/2πfC where L is the inductance in henries and C is the capacitance in farads. For a given L and a given C, this happens at only one frequency: f = 1/2π√(LC)

  4. Resonance and Q This frequency is called the resonant frequency. Resonance in an electrical circuit is the frequency at which the capacitive reactance equals the inductive reactance.(E5A02) Let’s calculate a few resonant frequencies, using questions from the Extra question pool as examples:

  5. Resonance and Q The resonant frequency of a series RLC circuit if R is 22 ohms, L is 50 microhenrys and C is 40 picofarads is 3.56 MHz. (E5A14) f = 1/2π√(LC) = 1/(6.28 x √(50×10-6 x 40×10-12)) = 1/(2.8 x 10-7) = 3.56 MHz Notice that it really doesn’t matter what the value of the resistance is. The resonant frequency would be the same is R = 220 ohms or 2.2 Mohms.

  6. Resonance and Q The resonant frequency of a parallel RLC circuit if R is 33 ohms, L is 50 microhenrys and C is 10 picofarads is 7.12 MHz. (E5A16) f = 1/2π√(LC) = 1/(6.28x√(50×10-6 x 10×10-12)) = 1/(1.4×10-7) = 7.12 MHz

  7. Resonance and Q When an inductor and a capacitor are connected in series, the impedance of the series circuit at the resonant frequency is zero because the reactances are equal and opposite at that frequency. If there is a resistor in the circuit, that resistor alone contributes to the impedance. Therefore, the magnitude of the impedance of a series RLC circuit at resonance is approximately equal to circuit resistance. (E5A03)

  8. Resonance and Q The magnitude of the current at the input of a series RLC circuit is at maximum as the frequency goes through resonance. (E5A05) The reason for this is that neither the capacitor or inductor adds to the overall circuit impedance at the resonant frequency.

  9. Resonance and Q When the inductor and capacitor are connected in parallel, the impedances are again equal and opposite to one another at the resonant frequency, but because they are in parallel, the circuit is effectively an open circuit. Consequently, the magnitude of the impedance of a circuit with a resistor, an inductor and a capacitor all in parallel, at resonance, is approximately equal to circuit resistance. (E5A04)

  10. Resonance and Q Because a parallel LC circuit is effectively an open circuit at resonance, the magnitude of the current at the input of a parallel RLC circuit at resonance is at minimum. (E5A07) The magnitude of the circulating current within the components of a parallel LC circuit at resonance is at a maximum. (E5A06)  Resonance can cause the voltage across reactances in series to be larger than the voltage applied to them. (E5A01)

  11. Resonance and Q Another consequence of the inductive and capacitive reactances canceling each other is that there is no phase shift at the resonant frequency. The phase relationship between the current through and the voltage across a series resonant circuit at resonance is that the voltage and current are in phase. (E5A08)

  12. Resonance and Q Ideally, a series LC circuit would have zero impedance at the resonant frequency, while a parallel LC circuit would have an infinite impedance at the resonant frequency. In the real world, of course, resonant circuits don’t act this way. To describe how closely a circuit behaves like an ideal resonant circuit, we use the quality factor, or Q. Because the inductive reactance equals the capacitive reactance at the resonant frequency, the Q of an RLC parallel circuit is the resistance divided by the reactance of either the inductance or capacitance(E5A09): Q = R/XL or R/XC

  13. Resonance and Q The Q of an RLC series resonant circuit is the reactance of either the inductance or capacitance divided by the resistance (E5A10): Q = XL/R or XC/R

  14. Resonance and Q Basically, the higher the Q, the more a resonant circuit behaves like an ideal resonant circuit,and the higher the Q, the lower the resistive losses in a circuit. Lower losses can increase Q for inductors and capacitors. (E5A15) An effect of increasing Q in a resonant circuit is that internal voltages and circulating currents increase. (E5A13) Q is an important parameter when designing impedance-matching circuits. The result of increasing the Q of an impedance-matching circuit is that matching bandwidth is decreased. (E5A17) A circuit with a lower Q will yield a wider bandwidth, but at the cost of increased losses.

  15. Resonance and Q A parameter of a resonant circuit that is related to Q is the half-power bandwidth. The half-power bandwidth is the bandwidth over which a series resonant circuit will pass half the power of the input signal and over which a parallel resonant circuit will reject half the power of an input signal. We can use the Q of a circuit to calculate the half-power bandwidth: BW = f/Q

  16. Resonance and Q The half-power bandwidth of a parallel resonant circuit that has a resonant frequency of 7.1 MHz and a Q of 150 is 47.3 kHz. (E5A11) BW = f/Q = 7.1 x 106/150 = 47.3 x 103 = 47.3 kHz What is the half-power bandwidth of a parallel resonant circuit that has a resonant frequency of 3.7 MHz and a Q of 118 is 31.4 kHz. (E5A12) BW = f/Q = 3.5 x 106/118 = 31.4 x 103 = 31.4 kHz

  17. E5A01 | What can cause the voltage across reactances in seriesto be larger than the voltage applied to them? A. Resonance B. Capacitance C. Conductance D. Resistance

  18. E5A01 (A) | What can cause the voltage across reactances inseries to be larger than the voltage applied to them? A. Resonance B. Capacitance C. Conductance D. Resistance

  19. E5A02 | What is resonance in an electrical circuit? A. The highest frequency that will pass current B. The lowest frequency that will pass current C. The frequency at which the capacitive reactance equals the inductivereactance D. The frequency at which the reactive impedance equals the resistiveimpedance

  20. E5A02 (C) | What is resonance in an electrical circuit? A. The highest frequency that will pass current B. The lowest frequency that will pass current C. The frequency at which the capacitive reactance equals theinductive reactance D. The frequency at which the reactive impedance equals the resistiveimpedance

  21. E5A03 | What is the magnitude of the impedance of a seriesRLC circuit at resonance? A. High, as compared to the circuit resistance B. Approximately equal to capacitive reactance C. Approximately equal to inductive reactance D. Approximately equal to circuit resistance

  22. E5A03 (D) | What is the magnitude of the impedance of a seriesRLC circuit at resonance? A. High, as compared to the circuit resistance B. Approximately equal to capacitive reactance C. Approximately equal to inductive reactance D. Approximately equal to circuit resistance

  23. E5A04 | What is the magnitude of the impedance of a circuitwith a resistor, an inductor and a capacitor all in parallel, atresonance? A. Approximately equal to circuit resistance B. Approximately equal to inductive reactance C. Low, as compared to the circuit resistance D. Approximately equal to capacitive reactance

  24. E5A04 (A) | What is the magnitude of the impedance of a circuitwith a resistor, an inductor and a capacitor all in parallel, atresonance? A. Approximately equal to circuit resistance B. Approximately equal to inductive reactance C. Low, as compared to the circuit resistance D. Approximately equal to capacitive reactance

  25. E5A05 | What is the magnitude of the current at the input of aseries RLC circuit as the frequency goes through resonance? A. Minimum B. Maximum C. R/L D. L/R

  26. E5A05 (B) | What is the magnitude of the current at the inputof a series RLC circuit as the frequency goes throughresonance? A. Minimum B. Maximum C. R/L D. L/R

  27. E5A06 | What is the magnitude of the circulating current withinthe components of a parallel LC circuit at resonance? A. It is at a minimum B. It is at a maximum C. It equals 1 divided by the quantity 2 times Pi, multiplied by the squareroot of inductance L multiplied by capacitance C D. It equals 2 multiplied by Pi, multiplied by frequency, multiplied byinductance

  28. E5A06 (B) | What is the magnitude of the circulating currentwithin the components of a parallel LC circuit at resonance? A. It is at a minimum B. It is at a maximum C. It equals 1 divided by the quantity 2 times Pi, multiplied by the squareroot of inductance L multiplied by capacitance C D. It equals 2 multiplied by Pi, multiplied by frequency, multiplied byinductance

  29. E5A07 | What is the magnitude of the current at the input of aparallel RLC circuit at resonance? A. Minimum B. Maximum C. R/L D. L/R

  30. E5A07 (A) | What is the magnitude of the current at the inputof a parallel RLC circuit at resonance? A. Minimum B. Maximum C. R/L D. L/R

  31. E5A08 | What is the phase relationship between the currentthrough and the voltage across a series resonant circuit atresonance? A. The voltage leads the current by 90 degrees B. The current leads the voltage by 90 degrees C. The voltage and current are in phase D. The voltage and current are 180 degrees out of phase

  32. E5A08 (C) | What is the phase relationship between the currentthrough and the voltage across a series resonant circuit atresonance? A. The voltage leads the current by 90 degrees B. The current leads the voltage by 90 degrees C. The voltage and current are in phase D. The voltage and current are 180 degrees out of phase

  33. E5A09 | How is the Q of an RLC parallel resonant circuitcalculated? A. Reactance of either the inductance or capacitance divided by theresistance B. Reactance of either the inductance or capacitance multiplied by theresistance C. Resistance divided by the reactance of either the inductance orcapacitance D. Reactance of the inductance multiplied by the reactance of thecapacitance

  34. E5A09 (C) | How is the Q of an RLC parallel resonant circuitcalculated? A. Reactance of either the inductance or capacitance divided by theresistance B. Reactance of either the inductance or capacitance multiplied by theresistance C. Resistance divided by the reactance of either the inductanceor capacitance D. Reactance of the inductance multiplied by the reactance of thecapacitance

  35. E5A10 | How is the Q of an RLC series resonant circuitcalculated? A. Reactance of either the inductance or capacitance divided by theresistance B. Reactance of either the inductance or capacitance times the resistance C. Resistance divided by the reactance of either the inductance orcapacitance D. Reactance of the inductance times the reactance of the capacitance

  36. E5A10 (A) | How is the Q of an RLC series resonant circuitcalculated? A. Reactance of either the inductance or capacitance divided bythe resistance B. Reactance of either the inductance or capacitance times the resistance C. Resistance divided by the reactance of either the inductance orcapacitance D. Reactance of the inductance times the reactance of the capacitance

  37. E5A11 | What is the half-power bandwidth of a parallel resonant circuit that has a resonant frequency of 7.1 MHz and aQ of 150? A. 157.8 Hz B. 315.6 Hz C. 47.3 kHz D. 23.67 kHz

  38. E5A11 (C) | What is the half-power bandwidth of a parallel resonant circuit that has a resonant frequency of 7.1 MHz and aQ of 150? A. 157.8 Hz B. 315.6 Hz C. 47.3 kHz D. 23.67 kHz

  39. E5A12 | What is the half-power bandwidth of a parallel resonant circuit that has a resonant frequency of 3.7 MHz and aQ of 118? A. 436.6 kHz B. 218.3 kHz C. 31.4 kHz D. 15.7 kHz

  40. E5A12 (C) | What is the half-power bandwidth of a parallel resonant circuit that has a resonant frequency of 3.7 MHz and aQ of 118? A. 436.6 kHz B. 218.3 kHz C. 31.4 kHz D. 15.7 kHz

  41. E5A13 | What is an effect of increasing Q in a resonant circuit? A. Fewer components are needed for the same performance B. Parasitic effects are minimized C. Internal voltages and circulating currents increase D. Phase shift can become uncontrolled

  42. E5A13 (C) | What is an effect of increasing Q in a resonantcircuit? A. Fewer components are needed for the same performance B. Parasitic effects are minimized C. Internal voltages and circulating currents increase D. Phase shift can become uncontrolled

  43. E5A14 | What is the resonant frequency of a series RLC circuit ifR is 22 ohms, L is 50 microhenrys and C is 40 picofarads? A. 44.72 MHz B. 22.36 MHz C. 3.56 MHz D. 1.78 MHz

  44. E5A14 (C) | What is the resonant frequency of a series RLCcircuit if R is 22 ohms, L is 50 microhenrys and C is 40picofarads? A. 44.72 MHz B. 22.36 MHz C. 3.56 MHz D. 1.78 MHz

  45. E5A15 | Which of the following can increase Q for inductors andcapacitors? A. Lower losses B. Lower reactance C. Lower self-resonant frequency D. Higher self-resonant frequency

  46. E5A15 (A) | Which of the following can increase Q for inductorsand capacitors? A. Lower losses B. Lower reactance C. Lower self-resonant frequency D. Higher self-resonant frequency

  47. E5A16 | What is the resonant frequency of a parallel RLC circuitif R is 33 ohms, L is 50 microhenrys and C is 10 picofarads? A. 23.5 MHz B. 23.5 kHz C. 7.12 kHz D. 7.12 MHz

  48. E5A16 (D) | What is the resonant frequency of a parallel RLCcircuit if R is 33 ohms, L is 50 microhenrys and C is 10picofarads? A. 23.5 MHz B. 23.5 kHz C. 7.12 kHz D. 7.12 MHz

  49. E5A17 | What is the result of increasing the Q of an impedance-matching circuit? A. Matching bandwidth is decreased B. Matching bandwidth is increased C. Matching range is increased D. It has no effect on impedance matching

  50. E5A17 (A) | What is the result of increasing the Q of animpedance-matching circuit? A. Matching bandwidth is decreased B. Matching bandwidth is increased C. Matching range is increased D. It has no effect on impedance matching

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