1. Core Concept and Resonance Condition
The essence of resonance is that the inductive reactance (Xₗ) and capacitive reactance (X꜀) in a circuit cancel each other out at a specific frequency, causing the circuit to behave purely resistively. This specific frequency is the resonant frequency (f₀). For both series and parallel circuits, it is calculated using the same formula:
f₀ = 1 / (2π√LC)
This means that as long as the values of the inductor (L) and capacitor (C) are fixed, their resonant frequency is fixed.
2. Characteristics of Series Resonance
A series resonant circuit connects a resistor (R), inductor (L), and capacitor (C) end-to-end in series with a power source.
1)Impedance and Current: At the moment of resonance, the inductive and capacitive reactances are equal in magnitude but opposite in phase, completely canceling each other out. The total impedance of the circuit reaches its minimum value, theoretically equal to just the resistance R (Z = R). According to Ohm's Law (I = V / Z), when the source voltage is constant, the total current in the circuit reaches its maximum value.
2)Voltage Relationship: This is the most remarkable phenomenon of series resonance. Although the voltages across the inductor (L) and capacitor (C) cancel each other out, the voltage across each individual component is not small. In fact, the voltage across each component can be much larger than the source voltage. The amplification factor is the circuit's Quality Factor (Q value). The higher the Q value, the more significant the amplification effect. Therefore, series resonance is often called "voltage resonance." If the circuit resistance is very small (high Q value), it can cause "overvoltage" and damage equipment in power systems, but in radio frequency applications, this is the key principle used to amplify weak signals.
3)Phase: At resonance, the total current is in phase with the source voltage.
3. Characteristics of Parallel Resonance
A parallel resonant circuit typically involves an inductor L (which usually includes its inherent parasitic resistance R) and a capacitor C connected in parallel with each other, and then connected to the power source.
1)Impedance and Voltage: At resonance, the currents in the inductive branch and the capacitive branch are nearly equal in magnitude but almost opposite in phase. This creates a large circulating current between the L and C branches, and these currents compensate for and effectively "cancel" each other from the perspective of the external source. The result is that the total impedance of the circuit, as seen from the input terminals, reaches its maximum value. If the power source provides a constant current, then the output voltage across the circuit reaches its maximum value.
2)Current Relationship: Corresponding to series resonance, in parallel resonance, the circulating current between the inductor (L) and capacitor (C) can be much larger than the total current drawn from the power source. The amplification factor is similarly the Quality Factor (Q value). Therefore, parallel resonance is often called "current resonance."
3)Phase: At resonance, the total voltage across the circuit is in phase with the current from the source.
4. Summary of Core Differences and Applications
You can understand it vividly with these analogies:
Series Resonance is like a choir. At the correct pitch (resonant frequency), everyone's voice (the voltages across L and C) works in unison, producing the loudest and clearest effect (maximum current), but each singer is using a lot of effort individually (high local voltages).
Parallel Resonance is like a traffic roundabout. During rush hour (resonant frequency), the traffic flow within the roundabout (the current in L and C) is very large and circulates smoothly, but the traffic flow on the main road entering and exiting the roundabout (the total current) is very small, making it seem very clear (very high impedance).
Based on these completely different characteristics, their applications are also entirely different:
Series Resonance is used in scenarios where a specific frequency signal needs to pass through easily. For example, it's used in radio tuning circuits. By adjusting the capacitor to change the resonant frequency, only when a radio station's frequency matches the resonant frequency does the circuit current maximize, thus selecting and amplifying that station's signal while suppressing others.
Parallel Resonance is used in scenarios where a specific frequency signal needs to be strongly blocked. Examples include band-stop (notch) filters or frequency-selective networks in oscillators. At resonance, it presents a very high impedance to the target frequency, thereby preventing that frequency signal from passing through.