Resonance

Question 1

What is Resonance?

Answer 1

• Part of the periodic response of RLC (resistor, inductor, capacitor) circuits.
• To achieve, energy storing components (L, C) are required.
• Resonance is when an LC circuit is excited by a periodic source with a frequency equal to the natural frequency.

Question 2

Reactance

Answer 2

• Ratio between voltage and current, purely imaginary.
• The “equivalent” resistance of inductors and capacitors to the alternating current.
  -The unit of reactance is 1 Ohm.

Question 3

Impedance

Answer 3

-When capacitors or inductors are connected in series with a resistor, we can simply add their reactance to the resistance.
- Reactance is imaginary and resistance is real.

Question 4

Impedance if Inductor in Series with Resistor Equation

Answer 4

Z = R + jL𝜔&raquo_space;> (if an inductor is connected in series with a resistor there is a positive Reactance)

Question 5

Impedance if Inductor in Series with Capacitor Equation

Answer 5

Z = R - j(1/C𝜔)&raquo_space;> (If a capacitor is connected in series with a resistor, impedances can be added in the same way as complex numbers)

Question 6

The RX-Plane

Answer 6

• It is convenient to represent impedances as vectors in the complex RX plane.
  R is resistance
  X is Reactance

Question 7

Susceptance

Answer 7

-When inductors and capacitors are connected in parallel to each-other or to resistors it is convenient to work with the inverse of their reactance.
-The unit of susceptance is one Siemens.
- Inverse of Reactance.
- Purely imaginary.
- “Equivalent” conductance of inductors and capacitors to alternating current.

Question 8

Inductive Susceptance Formula

Answer 8

• Inductive susceptance is the inverse of inductive reactance.
• Always negative imaginary.
• The greater the frequency the smaller the susceptance

B(L) = 1/X(L) = 1/(j𝜔) = -j(1/𝜔L)

Question 9

Capacitive Susceptance Formula

Answer 9

• Capacitive susceptance is the inverse of the capacitive reactance.
• Always positive imaginary.
• The greater the frequency the greater the susceptance.

B(C) = 1/X(C) = jC𝜔

Question 10

Admittance

Answer 10

• When capacitors or inductors are connected in parallel with a resistor, we can add their susceptance to the conductance of the resistor.
• Susceptance is imaginary and conductance is real, the result will be a complex number.

Question 11

Admittance if Inductor is in Parallel with resistor Equation

Answer 11

Y(L) = 1/R -j(1/L𝜔)

Question 12

Admittance if Capacitor is in Parallel with a resistor

Answer 12

Y(C) = 1/R + jC𝜔

Question 13

GB-Plane

Answer 13

• It is convenient to represent Admittances as vectors in the complex GB plane.
  G is Conductance (and is always positive)
  B is Susceptance

Question 14

Series Resonance