The Parallel LC Topology: Nodes, Currents, and the Tank Effect
When you wire an inductor and capacitor in parallel, you create what is universally known in RF and analog design as a "tank circuit." The topology is straightforward: both components share the exact same two electrical nodes. Let's define them as Node A (the top junction where the signal or voltage source connects) and Node B (the bottom junction, typically tied to circuit ground).
Unlike a series configuration where current must flow through both components sequentially, a parallel LC topology allows current to divide. At DC, the inductor acts as a short circuit (limited only by its wire resistance) while the capacitor acts as an open circuit. But as AC frequency increases, the inductor's impedance rises ($X_L = 2\pi fL$) while the capacitor's impedance falls ($X_C = \frac{1}{2\pi fC}$).
At one specific frequency—the resonant frequency ($f_r$)—the reactive currents through the inductor and capacitor become equal in magnitude but exactly 180 degrees out of phase. They cancel each other out from the perspective of the source. Energy continuously "sloshes" back and forth between the inductor's magnetic field and the capacitor's electric field, which is why it's called a tank. The resonant frequency is calculated as:
$f_r = \frac{1}{2\pi\sqrt{LC}}$
At this exact frequency, the ideal impedance of the parallel combination approaches infinity. In the real world, parasitic resistance limits this peak, but it remains the defining characteristic of the topology.
Parallel vs. Series LC: Why Choose the Tank Configuration?
Why use an inductor and capacitor in parallel instead of wiring them in series? The choice dictates whether your circuit blocks or passes the resonant frequency. A series LC circuit drops to near-zero impedance at resonance, making it ideal for band-pass filters. A parallel LC circuit spikes to maximum impedance at resonance, making it the standard choice for band-stop (notch) filters, oscillator frequency-determining networks, and RF amplifier loads.
| Characteristic | Parallel LC (Tank) | Series LC |
|---|---|---|
| Impedance at Resonance | Maximum (Ideally Infinite) | Minimum (Ideally Zero) |
| Primary Use Case | Notch filters, oscillator tanks, RF tuning | Band-pass filters, impedance matching |
| Circulating Current | High internal current loops between L and C | High current flows from source through both |
| Failure: Shorting L | Entire circuit becomes a short (0Ω) | Circuit becomes just a capacitor (blocks DC) |
| Failure: Opening C | Circuit becomes just an inductor (passes DC) | Entire circuit becomes an open (infinite Ω) |
The Failure Mode Contrast: What breaks at the extremes? If your inductor fails short in a parallel topology, Node A is directly shorted to Node B, potentially destroying your driving source. If the capacitor fails open, you lose resonance entirely, and the circuit defaults to a simple inductor, passing low frequencies and DC. In a series circuit, an open failure in either component kills the entire signal path, which is why series LC circuits are rarely used in safety-critical DC blocking paths without a parallel bleed resistor.
Design Walkthrough: Building a 100 kHz Parallel Resonant Circuit
Let's move from theory to the workbench. We will design a parallel tank circuit targeting a resonant frequency of 100 kHz. According to Electronics Tutorials, selecting standard component values requires iterating on the math to match available inventory.
1. Select the Inductor (L):
We need an inductor with low DC Resistance (DCR) to maintain a high Quality factor (Q). Let's choose a 1 mH (1000 µH) through-hole radial inductor. A solid bench choice is the Bourns 78FR1M-RC. It has a 10% tolerance and a low DCR of roughly 0.4Ω, which is critical for keeping parasitic losses low.
2. Calculate the Capacitor (C):
Rearranging the resonance formula to solve for C:
$C = \frac{1}{(2\pi f_r)^2 L}$
$C = \frac{1}{(2\pi \times 100,000)^2 \times 0.001} = 2.53 \text{ nF}$
3. Select the Capacitor:
2.53 nF isn't a standard E12/E24 value. We can use a 2.7 nF capacitor. For resonant circuits, dielectric absorption and voltage coefficient matter. Never use X7R or Y5V ceramics here; their capacitance shifts wildly with applied voltage and temperature. Use a C0G/NP0 dielectric. We will spec the Kemet C315C272J1G5TA (2.7 nF, 100V, C0G, 5% tolerance).
4. Verify Actual Resonance:
Using our real-world values (1 mH and 2.7 nF):
$f_r = \frac{1}{2\pi\sqrt{0.001 \times 2.7 \times 10^{-9}}} \approx 96.86 \text{ kHz}$
This is close enough to our 100 kHz target for most oscillator and filter applications, easily trimmable with a small parallel trimmer capacitor if exact precision is required.
A standard solderless breadboard adds roughly 2 pF to 5 pF of stray capacitance between adjacent rows. At 100 kHz, 5 pF is negligible compared to our 2,700 pF (2.7 nF) capacitor. However, if you were designing this same topology for 10 MHz, that 5 pF of breadboard parasitance would severely detune your circuit. For VHF and above, parallel LC circuits must be built on dead-bug prototypes or custom PCBs with controlled ground planes.
Step-by-Step Breadboard Testing and Verification
The most common mistake hobbyists make when testing an inductor and capacitor in parallel is connecting a function generator directly across the tank. Function generators typically have a 50Ω output impedance. If your tank circuit has a resonant impedance of 5,000Ω, that 50Ω source resistance is effectively in parallel with it, dragging the peak impedance down to ~49.5Ω and completely flattening the resonance curve. You must isolate the source.
Tools Required: Function generator (e.g., Siglent SDG1032X), Oscilloscope (e.g., Rigol DS1054Z), two 10x passive probes, 1kΩ series feed resistor.
- Build the Tank: Insert the Bourns 1 mH inductor and Kemet 2.7 nF capacitor onto the breadboard so both of their left legs share a common row (Node A) and both right legs share a common row (Node B). Tie Node B to the breadboard's ground rail.
- Add the Feed Resistor: Insert a 1kΩ resistor. Connect one end to Node A, and leave the other end in an isolated row. This resistor converts your low-impedance voltage source into a higher-impedance current source, allowing the tank's parallel resonance to manifest as a measurable voltage peak.
- Connect the Source and Scope: Connect the function generator's BNC-to-alligator lead to the isolated end of the 1kΩ resistor. Connect the generator's ground to Node B. Clip your oscilloscope's Channel 1 probe directly across Node A and Node B.
- Set the Sweep: Set the function generator to output a 1Vpp sine wave. Configure a frequency sweep (or manually step) from 50 kHz to 150 kHz.
- Observe the Peak: Watch the oscilloscope. As you approach 96.8 kHz, the voltage amplitude on Node A will spike dramatically, potentially reaching several volts peak-to-peak due to the Q-factor voltage magnification. Past 96.8 kHz, the voltage will sharply drop off as the capacitor begins to dominate and shunt the signal to ground.
Frequently Asked Questions
What happens to the impedance when an inductor and capacitor are in parallel at resonance?
At the exact resonant frequency, the reactive currents cancel out, and the impedance of the parallel LC combination reaches its maximum value. In an ideal, lossless circuit, this impedance would be infinite. In physical circuits, the impedance peak is limited by the inductor's DC wire resistance (DCR), the capacitor's Equivalent Series Resistance (ESR), and core losses. This peak impedance is often referred to as the dynamic resistance ($R_d$) of the tank, calculated roughly as $R_d = \frac{L}{C \times R_s}$, where $R_s$ is the total series parasitic resistance.
How does parasitic resistance affect an inductor and capacitor in parallel?
Parasitic resistance is the enemy of a high-Q tank circuit. The inductor's DCR is usually the dominant factor. This resistance dissipates energy as heat during every cycle of the current sloshing between the L and C. The higher the parasitic resistance, the lower the Quality factor (Q), which results in a wider, flatter, and lower-amplitude resonance peak. If you need a sharp notch filter or a stable oscillator, you must select inductors with the lowest possible DCR and capacitors with low ESR, such as C0G/NP0 ceramics or polystyrene film capacitors.
Can I use an inductor and capacitor in parallel for DC filtering?
No, a parallel LC circuit is ineffective for pure DC filtering. At 0 Hz (DC), the capacitor is an open circuit and the inductor is a short circuit. If placed across a DC power rail, the inductor will simply draw massive DC current, likely saturating its core, overheating, and tripping your power supply's overcurrent protection. For DC filtering, you use a capacitor in parallel with the load (to shunt AC ripple to ground) and an inductor in series with the load (to block AC ripple), forming an LC low-pass "pi" or "L" filter network, not a pure parallel tank.
Why does my parallel LC circuit oscillate on its own when connected to a power supply?
If your parallel LC circuit begins to oscillate continuously when connected to a DC source, you have inadvertently built a relaxation or negative-resistance oscillator. This usually happens if the power supply has a negative incremental resistance characteristic, or if the inductor is saturating and introducing non-linear switching transients that the capacitor stores and releases. To stop unintended oscillation in power delivery networks, engineers add a small series damping resistor (snubber) or ensure the power supply's output impedance is strictly positive and heavily decoupled with bulk electrolytic capacitance. For deeper insights into unintended oscillations, refer to application notes on LC oscillator design and stability.
