A series resonance circuit (or series RLC circuit) is a fundamental AC topology where a resistor, inductor, and capacitor are wired in a single continuous loop. At the resonant frequency, the inductive and capacitive reactances cancel each other out, leaving only the resistance to limit current. This results in a sharp peak in current and a minimum in impedance, making the topology indispensable for bandpass filters, RF tuning networks, and impedance matching.
Unlike theoretical textbook examples that rely on idealized variables, bench reality demands strict attention to component parasitics, dielectric absorption, and probe loading. Below is a complete, table-forward guide to designing, analyzing, and testing a series resonance circuit with real-world component values.
The Series Resonance Circuit Topology and Node Behavior
To analyze the circuit mathematically and practically, we define four distinct nodes in the standard series topology:
- Node A (Source+): The AC input voltage ($V_{in}$) from your function generator or RF source.
- Node B (R-L Junction): The connection point between the resistor and the inductor. Voltage here represents the resistive drop plus the inductive kickback.
- Node C (L-C Junction): The connection between the inductor and capacitor. This node experiences the highest voltage swings due to the Q-factor multiplication effect.
- Node D (Source-/GND): The return path to ground, completing the loop back to the AC source.
The total impedance ($Z$) of the circuit is calculated as $Z = \sqrt{R^2 + (X_L - X_C)^2}$. When the driving frequency ($f$) reaches the resonant frequency ($f_r$), $X_L$ equals $X_C$. The reactive terms subtract to zero, and the impedance collapses to exactly $R$. Current is maximized and perfectly in phase with the applied voltage.
Component Behavior Matrix: What Changes When Values Shift
When tuning a series resonance circuit on the bench, you rarely have the exact calculated component value. You must swap parts from your kit. Understanding how shifting one variable impacts the overall system prevents endless trial-and-error. The table below maps parameter changes to their direct electrical consequences.
| Parameter Changed | Effect on Resonant Freq ($f_r$) | Effect on Q-Factor | Effect on Bandwidth (BW) | Peak Current at $f_r$ |
|---|---|---|---|---|
| Increase Inductance (L) | Decreases | Increases (if R is constant) | Narrows | Unchanged (depends on R) |
| Increase Capacitance (C) | Decreases | Decreases | Widens | Unchanged (depends on R) |
| Increase Resistance (R) | No Change | Decreases | Widens | Decreases |
| Decrease Resistance (R) | No Change | Increases | Narrows | Increases |
| Increase Drive Frequency | N/A (Circuit becomes inductive) | N/A | N/A | Decreases (Impedance rises) |
Series vs. Parallel Resonance: Why Choose Series?
The decision to use a series resonance circuit over a parallel (tank) topology comes down to how you want the circuit to interact with the signal at the target frequency.
| Criteria | Series Resonance Circuit | Parallel Resonance Circuit |
|---|---|---|
| Impedance at $f_r$ | Minimum ($Z = R$) | Maximum ($Z = L / (RC)$) |
| Current at $f_r$ | Maximum | Minimum (line current) |
| Primary Application | Bandpass filters, RF signal routing | Bandstop (notch) filters, oscillator tanks |
| Placement in Circuit | In series with the load (passes $f_r$) | In shunt/parallel to ground (blocks $f_r$) |
Choose the series topology when you need to selectively pass a narrow band of frequencies to a load while rejecting others. Choose the parallel topology when you need to reject a specific interfering frequency (notch filter) or sustain oscillations in an LC tank.
Failure Mode Contrast: What Breaks at the Extremes?
Component failure drastically alters circuit behavior, and the two topologies fail in opposite ways:
- Series Circuit Open (L or C fails open): The entire circuit is broken. Current drops to absolute zero across all frequencies. The filter is completely dead.
- Series Circuit Short (C fails short): The capacitor bypasses, turning the circuit into a simple RL low-pass filter. Resonance is lost, but low-frequency signals still pass to the load.
- Parallel Circuit Open (L or C fails open): The tank loses resonance, but the remaining branch still conducts. If L opens, the circuit becomes a simple capacitive high-pass path. Total failure is rare unless both branches open.
Design Walkthrough: Building a 100 kHz Bandpass Filter
Let's design a series resonance circuit targeting a nominal 100 kHz resonant frequency with a Q-factor of roughly 10. We will select standard, off-the-shelf component values and calculate the exact resulting parameters.
Step 1: Select the Capacitor. We choose $C = 2.2 \text{ nF}$ (a standard E12 value). Critical choice: We must specify a C0G/NP0 ceramic dielectric. Standard X7R or Y5V capacitors exhibit severe voltage coefficients and piezoelectric microphonics that will detune the circuit and introduce distortion under AC drive.
Step 2: Calculate the Inductor. Using the resonance formula $f_r = 1 / (2\pi\sqrt{LC})$, we solve for L:
$L = 1 / (4\pi^2 \cdot f_r^2 \cdot C)$
$L = 1 / (39.478 \cdot 10^{10} \cdot 2.2 \times 10^{-9}) = 1.15 \text{ mH}$.
The closest standard inductor value is 1.2 mH. We select a shielded drum-core inductor to prevent magnetic coupling to nearby breadboard wires.
Step 3: Calculate the Resistor for Target Q. With $L = 1.2 \text{ mH}$ and $C = 2.2 \text{ nF}$, the actual resonant frequency shifts slightly to 97.8 kHz.
At 97.8 kHz, the inductive reactance $X_L = 2\pi \cdot 97800 \cdot 0.0012 = 737 \Omega$.
To achieve $Q = 10$, we need $R = X_L / Q = 737 / 10 = 73.7 \Omega$. We select a standard 75 $\Omega$ metal film resistor (1% tolerance).
| Component | Target Value | Selected Real Value | Example Part Number | Tolerance / Spec |
|---|---|---|---|---|
| Capacitor (C) | 2.2 nF | 2.2 nF | Kemet C315C222J1G5TA | 5%, C0G/NP0, 100V |
| Inductor (L) | 1.15 mH | 1.2 mH | Bourns 78F-1R2K-RC | 10%, Shielded Drum Core |
| Resistor (R) | 73.7 $\Omega$ | 75 $\Omega$ | Vishay MRS25000C7509 | 1%, Metal Film, 0.6W |
According to foundational AC theory outlined by Electronics Tutorials, the final bandwidth (BW) of this circuit will be $f_r / Q = 97.8 \text{ kHz} / 9.8 = 9.97 \text{ kHz}$. The filter will pass signals between roughly 92.8 kHz and 102.8 kHz at the -3dB points.
Breadboard Testing and Extreme Failure Modes
Simulating the circuit in LTspice is only half the battle. Parasitic capacitance from the breadboard (typically 2-5 pF per row) and your oscilloscope probes will alter the physical circuit. Here is the step-by-step procedure to verify your series resonance circuit on the bench.
- Assemble the Loop: Insert the 75 $\Omega$ resistor, 1.2 mH inductor, and 2.2 nF C0G capacitor in a strict series chain on the breadboard. Keep lead lengths as short as possible to minimize stray inductance.
- Connect the Source: Attach your function generator's BNC-to-grabber cable to Node A (Source+) and Node D (GND). Set the output to a 2V peak-to-peak sine wave with zero DC offset.
- Probe the Output: Connect a 10x oscilloscope probe across the 75 $\Omega$ resistor (Node B to Node D). This measures the current flowing through the circuit ($V = IR$).
- Sweep the Frequency: Start your function generator at 50 kHz. Slowly increase the frequency while watching the oscilloscope's peak-to-peak voltage across the resistor.
- Identify the Peak: The voltage across the resistor will climb, peak sharply, and then fall. The frequency at the absolute peak is your physical $f_r$. Expect it to read between 96 kHz and 99 kHz due to breadboard parasitics and the 10% tolerance on the drum-core inductor.
Testing the Extremes (Fault Injection)
To understand the circuit's robustness, intentionally inject faults while monitoring the resistor voltage at the established 97.8 kHz peak:
- Short the Capacitor: Place a jumper wire across the 2.2 nF capacitor. The resonant peak will instantly vanish. The voltage across the resistor will drop significantly and will no longer peak as you sweep frequencies, confirming the circuit has degraded into a broadband RL low-pass filter.
- Open the Inductor: Pull one leg of the inductor out of the breadboard. The signal on the oscilloscope will drop to the noise floor (zero current). This confirms that a single open component in a series topology acts as a hard kill-switch for the entire signal path.
By mapping the theoretical math to physical component tolerances and understanding the exact failure modes, you transition from simply memorizing formulas to actively engineering reliable AC networks. For deeper mathematical derivations on Q-factor and impedance matching, the All About Circuits AC textbook provides excellent supplementary reading on the calculus behind the resonance curve.
