6.1 Harmonic Emissions, Spurious Signals, and Transmitter Filtering

6.1 Harmonic Emissions, Spurious Signals, and Transmitter Filtering

In amateur radio operation, maintaining high spectral purity is both a technical necessity and a regulatory obligation: the amateur class licence requires that a station not cause harmful interference, and transmitters must meet the unwanted-emission limits that apply in Australia. Whenever an amateur radio transmitter generates a signal on its intended operating frequency—known as the fundamental frequency ((f_0))—unwanted energy can also be emitted on other frequencies. These unwanted emissions fall into two main categories: harmonic emissions and non-harmonic spurious signals. Unchecked emissions can cause severe interference to other radio services, including television broadcasting, commercial telecommunications, and aviation navigation.

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1. Fundamentals of Harmonic Emissions

A harmonic is an emission on a frequency that is an exact positive integer multiple of the fundamental operating frequency. Harmonics are designated by their multiplication factor (n):

$\text{Harmonic Frequency } (f_n) = n \times f_0$

Where (f_0) is the fundamental frequency and (n) is an integer ((n = 2, 3, 4, \dots)).

• Fundamental Frequency ((f_0)): The primary frequency to which the transmitter is tuned and intended to radiate.
• Second Harmonic ((2f_0)): Twice the fundamental frequency.
• Third Harmonic ((3f_0)): Three times the fundamental frequency.
• Fourth Harmonic ((4f_0)): Four times the fundamental frequency.

Practical Example of Harmonic Frequencies

Consider an amateur transmitter operating on the 40-metre band at a fundamental frequency of (f_0 = 7.100\text{ MHz}):

• Second Harmonic ((2f_0)): (2 \times 7.100\text{ MHz} = 14.200\text{ MHz}) (falls directly inside the 20-metre amateur band).
• Third Harmonic ((3f_0)): (3 \times 7.100\text{ MHz} = 21.300\text{ MHz}) (falls directly inside the 15-metre amateur band).
• Fourth Harmonic ((4f_0)): (4 \times 7.100\text{ MHz} = 28.400\text{ MHz}) (falls directly inside the 10-metre amateur band).

Similarly, if an amateur station transmits on the 20-metre band at (f_0 = 14.150\text{ MHz}):

• Second Harmonic ((2f_0)): (2 \times 14.150\text{ MHz} = 28.300\text{ MHz}) (10-metre band).
• Third Harmonic ((3f_0)): (3 \times 14.150\text{ MHz} = 42.450\text{ MHz}) (low VHF spectrum).
• Fourth Harmonic ((4f_0)): (4 \times 14.150\text{ MHz} = 56.600\text{ MHz}) (falls just above the Australian 6-metre amateur band, which ends at 54 MHz, and inside the former analogue VHF Television Band I / Channel 1).

Causes of Harmonic Generation

Harmonics are created whenever an RF signal passes through a non-linear circuit element. In an ideal linear amplifier, the output waveform is an exact, amplified replica of the input sine wave. However, real-world RF power amplifiers often introduce non-linearity:

1. Overdriving Amplifier Stages: Driving an RF power amplifier beyond its linear dynamic range pushes the active components (transistors or vacuum tubes) into saturation or cutoff. This clips the top and bottom of the RF sine wave.
2. Class of Operation: Power amplifiers operating in Class B or Class C intentionally cut off during portions of the RF cycle to achieve higher electrical efficiency. According to Fourier analysis, any non-sinusoidal periodic waveform contains rich harmonic energy at integer multiples of the fundamental frequency.
3. Excessive Drive / Improper ALC: In Single Sideband (SSB) transmitters, excessive audio mic gain or inadequate Automatic Level Control (ALC) overdrives the final power amplifier, distorting the envelope and producing both harmonics and intermodulation distortion ("splatter").

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2. Non-Harmonic Spurious Emissions

Spurious emissions (or spurs) are unwanted signals generated in a transmitter at frequencies that are not exact integer multiples of the fundamental frequency. Unlike harmonics, spurious signals can appear at virtually any point across the radio spectrum.

Primary Sources of Spurious Signals

• Mixer Products: Superheterodyne transmitters combine local oscillator (LO) frequencies and intermediate frequencies (IF) in a mixer stage to produce the desired output. Imperfect filtering allows unwanted sum and difference mix products ((|f_{\text{LO}} \pm f_{\text{IF}}|)) to reach the power amplifier and radiate.
• Parasitic Oscillations: Self-oscillation in high-gain RF amplifier stages caused by stray inductive or capacitive feedback loops at unexpected frequencies (often VHF or UHF frequencies). Parasitic oscillations waste power, heat components, and radiate illegal broadband signals.
• Synthesiser Phase Noise & Reference Spurs: Modern digital transmitters utilising Phase-Locked Loop (PLL) or Direct Digital Synthesis (DDS) frequency synthesisers can generate sideband phase noise and reference clock spurs adjacent to the operating carrier.
• Intermodulation Distortion (IMD): When two signals (such as two audio tones in an SSB transmitter) are processed by a non-linear amplifier, they combine to form spurious intermodulation products at (2f_1 - f_2), (2f_2 - f_1), etc.

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3. Transmitter RF Output Filtering

To prevent harmonics and spurious emissions from leaving the transceiver and reaching the antenna, transmitters rely on specialised RF filter networks.

Low-Pass Filters (LPF)

A Low-Pass Filter (LPF) is the primary defence against transmitter harmonic interference. Installed directly in the 50-ohm coaxial transmission line between the HF transmitter output (or linear amplifier) and the antenna tuner/feedline:

• It allows all desired HF fundamental signals (1.8 MHz to 30 MHz) to pass with negligible attenuation (insertion loss < 0.5 dB).
• It heavily attenuates all frequencies above its cutoff frequency ((f_c)), effectively neutralising second, third, and higher-order harmonics before they reach the antenna.
• A standard HF Low-Pass Filter has a cutoff frequency around 32–35 MHz, ensuring full coverage of the 10-metre band (28–29.7 MHz) while providing 60 dB or more attenuation at 50 MHz (6-metre / TV Band I) and 174 MHz (VHF TV Band III).

High-Pass Filters (HPF) on Consumer Receivers

When an amateur HF transmitter causes interference to a nearby television receiver, the cause is often not transmitter harmonics, but rather the TV's front-end receiver being overloaded by the strong fundamental HF signal. A High-Pass Filter (HPF) installed directly at the TV antenna input passes high-frequency television signals (e.g., above 50 MHz) while blocking the strong HF signals (1.8–30 MHz) from overloading the TV's tuner.

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4. Filter Cutoff Frequency and Attenuation Specifications

Understanding filter specifications is essential when designing or selecting filters for an amateur station:

1. Cutoff Frequency ((f_c)): The frequency at which the filter's power output drops by 3 dB (50% power point) relative to its passband level.
2. Passband Insertion Loss: The small amount of signal power lost when the fundamental frequency passes through the filter. High-quality filters exhibit insertion loss under 0.2 to 0.5 dB. Excessive insertion loss converts RF power into heat inside the filter, potentially damaging components under high power.
3. Stopband Attenuation (Roll-off Rate): The rate at which attenuation increases beyond the cutoff frequency, measured in decibels per octave (doubling of frequency) or decibels per decade (10-fold increase in frequency). Multi-element LC filter designs (e.g., 7-pole or 9-pole Chebyshev/Elliptic filters) provide steep roll-off curves.

$\text{Attenuation (dB)} = 10 \log_{10} \left( \frac{P_{\text{in}}}{P_{\text{out}}} \right)$

For example, an attenuation of 60 dB reduces unwanted harmonic power by a factor of 1,000,000 (one millionth of the fundamental power).

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5. ACMA Regulatory Spurious Emission Limits

Australian radio amateurs must not cause harmful interference, and their transmitters must meet the unwanted-emission limits set by the Radiocommunications (Unwanted Emissions - Spurious Domain) Standard. Transmitters must not generate spurious or harmonic emissions that exceed defined limits relative to the mean power of the fundamental transmission.

ACMA Technical Standards for Transmitters Below 30 MHz (HF)

For amateur stations operating on frequencies below 30 MHz:

• Spurious emissions (including harmonics) must be attenuated by at least:

$\text{Minimum Attenuation} = 43 + 10 \log_{10} (P_{\text{PEP}}) \text{ dB}$

Or 50 dB, whichever represents the lesser attenuation (where (P_{\text{PEP}}) is the Peak Envelope Power in watts).

• For standard equipment operating at typical power levels (e.g., 100 W PEP):
  • (43 + 10 \log_{10}(100) = 43 + 20 = 63\text{ dB}).
  • Applying the 50 dB ceiling rule, spurious emissions must be at least 50 dB down below the fundamental carrier level.
• Above 30 MHz, Australian unwanted-emission limits come from the same source - the ITU-R SM.329 spurious-domain limits given legal effect by the Radiocommunications (Unwanted Emissions - Spurious Domain) Standard. There is no separate Australian '60 dBc' amateur figure. Numerical emission limits are examined in the regulations paper, not the theory paper.

Radio amateurs are held strictly responsible for ensuring their equipment complies with ACMA spectral standards at all times to protect primary radiocommunication services, emergency channels, and consumer electronics.