Resonance circuit are electrical circuits in which inductive and capacitive elements interact in such a way that their reactive effects cancel each other at a particular frequency, known as the resonant frequency. At this frequency, the circuit can exhibit special characteristics, depending on its configuration. Resonance circuits are typically classified into two types:
1. Series Resonance Circuit:
In a series resonance circuit, a resistor (R), an inductor (L), and a capacitor (C) are connected in series.
In RLC series electrical circuit.
Net Impedance, Z = R + j (XL-XC)
o Z = Squrt ((R^2 + (XL-XC)^2)
At a frequency where XL=XC, Z=R.
Resonance occurs when the inductive reactance (XL=2πfL) equals the capacitive reactance (XC=1/2πfC) so they cancel each other out, making the total impedance purely resistive at the resonant frequency.
o Resonant Frequency (fr)=1/2π*squrt LC, 𝛚0 (resonant frequency) = 𝟏/ squrt(𝐋𝐂) 𝐫𝐚𝐝 /𝐬𝐞𝐜
At resonance, impedance is minimized (equal to the resistance RRR).Current is maximized at the resonant frequency. The circuit behaves like a pure resistor, and the phase angle between voltage and current is zero.
𝑰 𝐦𝐚𝐱 = 𝑽 /𝑹 𝑨𝒎𝒑𝒆𝒓𝒆𝒔
𝑷(𝑷𝒆𝒂𝒌) = 𝑽^𝟐 /𝑹 𝑾𝒂𝒕𝒕𝒔 ,Power is max. in case of resonance. Power factor is unity under resonance condition.
Bandwidth
| The difference between the two half power frequencies is called Bandwidth. i.e., 𝐁. 𝐖. (𝛃) = 𝐟𝟐 – 𝐟𝟏 𝐨𝐫 𝛚𝟐 – 𝛚𝟏 |
The ratio of resonant frequency to the bandwidth is called quality factor.
i.e., 𝑄 = 𝜔𝑂/ 𝛽
𝑸 = 𝟏 /𝝎𝑶*𝑪*𝑹=𝝎𝑶*𝑳/ 𝑹=1/R* squrt(L/C)
o Derivation of Half power frequencies
Key Applications of Series Resonance Circuit:
Tuning Circuits (Radio and TV Receivers) :
Purpose: Series resonance circuits are widely used in radio and TV receivers to select a specific frequency (radio station or TV channel) from many different frequencies available in the air.
How it Works: When the resonant frequency of the circuit matches the desired broadcast frequency, the circuit “tunes” to that frequency, allowing maximum current to pass through, effectively picking up the signal.
Example: The tuning knob of a radio is often used to adjust the capacitance or inductance, so the circuit resonates at the frequency of a specific radio station.
Signal Filtering (Band-Pass Filters):
Purpose: Series resonance circuits can be used in band-pass filters, which allow only signals within a specific frequency range to pass through while blocking others.
How it Works: The circuit is designed to resonate at the desired frequency. Signals at this frequency will pass with minimal impedance, while signals at other frequencies will be blocked or attenuated due to higher impedance.
Example: In communication systems, series resonant circuits are used to isolate desired frequencies and eliminate unwanted ones in both transmission and reception.
Impedance Matching in Transmission Lines:
Purpose: Series resonance circuits are used in impedance matching to maximize power transfer between different stages of a circuit or between a source and load.
How it Works: At resonance, the impedance of the circuit becomes purely resistive, which is ideal for matching the load to the source. This minimizes reflection and maximizes the power transferred.
Example: Impedance matching is important in antennas, audio systems, and radio-frequency (RF) communication systems to prevent signal loss and distortion.
Oscillators and Frequency Generators:
Purpose: Series resonance circuits are essential components in oscillators, which generate stable signals at a particular frequency.
How it Works: The resonant frequency of the series circuit determines the frequency of oscillation. When the circuit is excited, it generates oscillations at this specific frequency.
Example: Quartz crystal oscillators, which are commonly used in clocks, watches, and microcontrollers, use series resonance to generate precise frequencies.
Induction Heating:
Purpose: In induction heating, series resonance circuits are used to create high-frequency alternating currents for heating conductive materials.
How it Works: The resonant frequency is set to the required heating frequency, and the circuit generates a large amount of current at that frequency. This current is used to induce heat in the material through electromagnetic induction.
Example: Induction stoves and industrial furnaces use series resonance circuits for efficient and controlled heating.
Resonant Transformers:
Purpose: Series resonance circuits are also used in resonant transformers, where they help to achieve high voltage outputs at specific frequencies.
How it Works: By resonating the primary or secondary winding of a transformer, high voltages can be generated. This principle is used in applications such as Tesla coils or high-frequency switching power supplies.
Example: Tesla coils use series resonance to generate high-voltage, high-frequency electrical discharges.
Audio Systems (Crossover Networks):
Purpose: In audio systems, series resonant circuits are used in crossover networks to direct different frequency bands to specific speakers, such as tweeters, midrange, and woofers.
How it Works: Series resonant circuits can be used to allow only certain frequency ranges to pass to each speaker, ensuring that each speaker handles the frequencies it’s designed for.
Example: A tweeter receives only high frequencies, while a woofer gets low frequencies, optimizing sound quality in audio systems.
2.Parallel Resonance Circuit
In a parallel resonance circuit, the inductor (L) and capacitor (C) and a resistor (R) are connected in parallel. R-L-C parallel circuit is similar to the series circuit, parallel circuits also exhibits the resonance condition, when the circuit is excited by an AC source.
In parallel circuit, the resonance is a phenomenon at which :
1. Voltage and currents are in phase
2. Net susceptance is equal to zero (Imaginary part of admittance)
3. Power factor is unity
4. Maximum impedance and minimum current
5.The circuit behaves like an open circuit at the resonant frequency.
For parallel RLC resonance, the current through the inductor and the capacitor are equal in magnitude but opposite in phase, causing them to cancel out.
At resonance net susceptance is equal to zero :
1 /𝑋𝐿 – 1 /𝑋𝐶 = 0
The formula is the same as for series resonance: fr=1/2π * Squrt (L*C)
Bandwidth:𝒇𝟐 – 𝒇𝟏 = 𝒇𝒐/𝑸
• Relation between resonant frequency to the half power frequencies:𝒇𝒐 = Squrt (𝒇𝟏*𝒇𝟐)
• Quality factor(Current Magnification factor):𝑸 = 𝑹/ 𝝎𝒐*𝑳 = 𝝎𝒐*𝑪*𝑹 = 𝟏/ 𝑹 Squrt (𝑪 /𝑳)
Applications of Parallel Resonance Circuits:
- Tuned Circuits in Radio Receivers: Parallel resonant circuits are used to select specific frequencies while rejecting others.
- Filters: They can be used in band-stop or notch filters to reject a specific frequency and allow others to pass.
- Oscillators: In oscillatory circuits, parallel resonance is often used to generate signals at a precise frequency.