Section 1.3: Resonance and Filters #

You’ve just learned that inductive reactance climbs with frequency while capacitive reactance falls. In a simple ideal series LC circuit, the inductive and capacitive reactances are equal at one frequency, and these opposite reactances cancel each other completely. This special frequency transforms ordinary LC circuits into powerful frequency selectors—one foundation for the filters you’ll encounter in radio.

Resonance is the principle that lets your antenna “ring” at exactly the right frequency, enables your radio to ignore thousands of unwanted signals, and allows that narrow CW filter to slice through interference like a surgeon’s scalpel.

Why Resonance Matters in Amateur Radio #

At resonance in an LC circuit, inductive reactance and capacitive reactance are equal ( $X_L = X_C$ ) and cancel each other. Depending on the connection, an LC circuit’s impedance at resonance can be much lower or higher than at nearby frequencies. This selectivity is precisely what we need to:

Tune into specific stations
Reject interference
Generate stable oscillator frequencies
Limit the range of frequencies we transmit

Changing either the inductance or the capacitance changes the resonant frequency. With the other value unchanged, increasing either one lowers the resonant frequency; decreasing either one raises it.

Let’s see how resonance works in practical circuit configurations.

Series and Parallel Resonance: Two Critical Circuit Behaviors #

There are two fundamental ways to connect inductors and capacitors in resonant circuits, and they behave quite differently:

Two circuits compare an inductor and capacitor in series and in parallel. In the series circuit, current follows one path through both components. In the parallel circuit, the inductor and capacitor form separate branches between the same two terminals. Under each circuit, a graph shows frequency increasing to the right and impedance increasing upward. The series curve dips to its minimum at resonance, then rises again. The parallel curve peaks at resonance and falls on either side. These are simplified responses; real component losses limit the minimum and maximum. — Each dashed center line marks the resonant frequency on the horizontal axis. Series resonance gives minimum impedance; parallel resonance gives maximum impedance in these simple circuits. Real components limit both responses.

Series Resonant Circuit: When L and C are in series, their reactances cancel at resonance, leaving only the resistance to limit current flow. This creates minimum impedance at the resonant frequency, allowing maximum current flow.
Application: Placed in line with the signal, a series resonant circuit can form a band-pass filter that selects a specific frequency range.
Parallel Resonant Circuit (Tank Circuit): When L and C are in parallel, the opposite occurs—impedance is maximum at resonance. The inductor and capacitor currents cancel at the external connection, creating a high-impedance path at resonance even while current circulates between the two components.
The tank analogy fits: energy sloshes back and forth between the inductor’s magnetic field and the capacitor’s electric field—like water sloshing in a tank—creating an oscillating current. In a real circuit, losses make that oscillation fade unless a source replaces the lost energy.

Key Information: The inductance and capacitance in the tank circuit determine the frequency of an LC oscillator.

Practical Note: While many modern transceivers use digital frequency synthesis for tuning, they may still contain tuned circuits. Understanding these resonant circuits remains relevant for antenna tuners, filters, and many homebrew projects.

Filters: Controlling the Flow of Signals #

Filters are circuits that pass some frequencies while rejecting others. The range a filter is designed to pass is its passband. As you move into General class operating, you’ll encounter several types:

Four graphs show filter output as frequency increases from left to right; a higher curve means more output. The low-pass curve stays high at low frequencies, then falls at higher frequencies. The high-pass curve does the reverse. The band-pass curve rises for a middle range of frequencies and falls on both sides. The notch curve stays high except for a narrow dip around one frequency. The sloping transitions show that these filters do not change abruptly between passing and rejecting a signal. — The curves show which frequencies each filter passes or reduces. The notch is narrow so it can reduce one interfering tone while preserving most of the surrounding signal.

Low-Pass Filters: Pass frequencies below a cutoff point
- Application: Reduce harmonics from your transmitter output
- Example: A transmitter low-pass filter that reduces harmonic interference, or a telephone filter that passes voice while rejecting RF
High-Pass Filters: Pass frequencies above a cutoff point
- Application: Reduce low-frequency noise
- Example: A suitable high-pass filter at a television antenna input that reduces lower-frequency HF interference
Band-Pass Filters: Pass a specific range of frequencies
- Application: Select your operating band
- Example: Receiver front-end filters
Band-Stop (Notch) Filters: Block specific frequencies
- Application: Reduce a narrow interfering signal
- Example: Notch filters in modern transceivers

Key Filter Specifications You Should Know #

Whether you’re evaluating equipment or building your own circuits, understanding these specifications will help you make informed decisions:

Cutoff Frequency #

Key Information: The cutoff frequency of a low-pass filter is the frequency above which its output power is less than half the input power.

This “half-power” point corresponds to a 3 dB reduction in power. When you see filter specifications mentioning “-3 dB points,” they’re referring to these cutoff frequencies.

Filter Bandwidth #

Key Information: You measure a band-pass filter’s bandwidth between its upper and lower half-power (-3 dB) points.

Typical receiver-filter settings vary by mode and by the signal you receive:

CW: 250-500 Hz
SSB: 2.4-2.8 kHz
AM: 6 kHz
FM: about 10-16 kHz for common voice signals, depending on deviation

Operating Tip: Using a wider filter than necessary reduces your signal-to-noise ratio, while using one that’s too narrow can distort the received signal. Modern transceivers allow you to select appropriate filter bandwidths for different modes.

Q Factor and Selectivity #

A resonant circuit’s Q factor (quality factor) describes the sharpness of its response. Higher Q means narrower bandwidth and more selective filtering—exactly what you want when trying to pick out a weak signal from interference. Lower Q means broader bandwidth but less selectivity.

Lower loss generally gives a higher Q. When you adjust your radio’s filter from “wide” to “narrow,” you may be selecting another filter or changing digital calculations, rather than changing an LC circuit’s Q.

Insertion Loss #

Key Information: Insertion loss specifies a filter’s attenuation inside its passband.

Ideally, a filter would pass signals at the desired frequencies without weakening them, but real-world components always introduce some loss. Lower insertion loss preserves more of the wanted signal; bandwidth and rejection still matter too.

For example, a filter with 1 dB insertion loss passes about 80% of the input power within its passband.

Ultimate Rejection #

Key Information: Ultimate rejection specifies a filter’s maximum ability to reject signals outside its passband.

A higher value (measured in dB) means better filtering of interference. A filter with 60 dB ultimate rejection reduces unwanted signals to one-millionth of their original power. The response curve shows where that rejection applies; it need not hold at every frequency outside the passband.

Impedance Matching with Filters #

Some filters serve double duty by matching impedances as well as selecting frequencies. Other devices can match impedances too:

Key Information: Transformers, Pi-networks, and lengths of transmission line can all be used for impedance matching at radio frequencies.

A matching network changes the voltage-to-current relationship seen at its input, so a different load can look like the impedance the equipment needs. Common examples include:

Transformers: Change voltage and current in opposite ratios; the next section follows this in detail.
Pi-networks: The name comes from their resemblance to the Greek letter π in schematic form (capacitor-inductor-capacitor). Antenna tuners and amplifier output circuits often use these networks.
L-networks: Simpler than Pi-networks, using just two components (one series and one parallel), these are common in antenna matching applications.
Quarter-wave transformers: Special sections of transmission line that transform impedance based on their characteristic impedance.

Filter Technologies in Your Radio #

Modern amateur radio equipment employs various filter technologies:

LC Filters: Traditional combinations of inductors and capacitors
Crystal Filters: Use quartz crystals for precise, narrow filtering
Mechanical Filters: Use mechanical resonant elements; appear mostly in older equipment
Digital Signal Processing (DSP) Filters: Use calculations to filter a signal after an analog-to-digital converter turns measurements of its voltage into numbers. The filtering happens in the digital domain: it works on those numbers. A digital-to-analog converter can then turn the result back into an analog signal, such as audio for a speaker.

Your Filter Toolkit Is Ready #

You now understand how resonance transforms simple LC circuits into powerful frequency selectors. Your receiver’s roofing filter limits the signals reaching later stages and may use crystal resonators rather than an LC tank. The notch filter that reduces an annoying carrier could use an analog circuit or digital processing. Your antenna tuner is a matching network that changes the impedance your transmitter sees.

When you turn your radio’s filter knob from “wide” to “narrow,” you’re choosing a smaller frequency range. A 500 Hz CW filter can reject noise and interference outside that range while passing the signal you want. Even your antenna acts as a resonant filter, naturally favoring the frequencies it’s cut for.

But filtering and resonance are only part of the power transfer puzzle. Next, we’ll explore how transformers move energy between circuits while offering impedance matching, possible electrical isolation, and the ability to step voltages up or down.