2.7 Modulation Techniques: AM, FM, and SSB

2.7 Modulation Techniques: AM, FM, and SSB

Modulation is the process of superimposing information-bearing intelligence (such as human speech, telegraphy, or computer data) onto an RF carrier wave. Unmodulated RF carriers contain no information; altering the carrier's amplitude, frequency, or phase creates a modulated signal that can be transmitted through space and decoded at a distant receiver.

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1. Amplitude Modulation (AM) Principles and Calculations

In Amplitude Modulation (AM), the instantaneous amplitude of the RF carrier wave is varied in direct proportion to the instantaneous amplitude of the modulating audio signal, while the carrier frequency remains strictly constant.

Mathematical Expression and Modulation Index ($m$)

The mathematical equation for an AM waveform is:

$e(t) = A_c \left[ 1 + m \cdot m_a(t) \right] \cos(2\pi f_c t)$

Where Modulation Index ($m$) is defined as the ratio of peak modulating audio voltage ($V_{\text{audio}}$) to unmodulated RF carrier voltage ($V_{\text{carrier}}$):

$m = \frac{V_{\text{audio}}}{V_{\text{carrier}}}$

Expressed as a percentage: $\text{Modulation Percentage} = m \times 100\%$

• Under-modulation ($m < 1.0$): Safe operation, but transmitted RF power is underutilised, resulting in weaker recovered audio.
• Full Modulation ($m = 1.0$): $100%$ modulation. Audio peak voltage equals carrier voltage. Maximum linear audio power transmission.
• Over-modulation ($m > 1.0$): Audio voltage exceeds carrier voltage. During negative audio troughs, the RF carrier is cut off entirely to zero amplitude for finite intervals. This causes envelope clipping, creating severe odd-harmonic distortion and generating wideband interference known as splatter across adjacent frequencies.

AM Spectrum and Bandwidth

When a carrier at frequency $f_c$ is amplitude-modulated by a single audio tone at frequency $f_a$, three distinct RF spectral components emerge:

1. Carrier Frequency ($f_c$)
2. Upper Sideband (USB): $f_{\text{USB}} = f_c + f_a$
3. Lower Sideband (LSB): $f_{\text{LSB}} = f_c - f_a$

The total bandwidth occupied by an AM signal is twice the highest modulating audio frequency:

$B_{\text{AM}} = 2 \cdot f_{a(\text{max})}$

ACMA Calculation: If voice audio is filtered to a maximum frequency of $f_{a(\text{max})} = 3\text{ kHz}$, the total occupied AM bandwidth is: $B_{\text{AM}} = 2 \times 3\text{ kHz} = 6\text{ kHz}$

AM Power Distribution

The total power ($P_{\text{total}}$) contained in a $100%$ modulated AM wave is distributed between the carrier and the two sidebands:

$P_{\text{total}} = P_{\text{carrier}} \left( 1 + \frac{m^2}{2} \right)$

At $100%$ modulation ($m = 1.0$): $P_{\text{total}} = P_{\text{carrier}} \left( 1 + \frac{1}{2} \right) = 1.5 \cdot P_{\text{carrier}}$

• Carrier Power: Represents $\frac{1.0}{1.5} = 66.7%$ of total transmitted power.
• Sideband Power (Total): Represents $\frac{0.5}{1.5} = 33.3%$ of total power.
• Each Individual Sideband: Carries only $\frac{0.25}{1.5} = 16.7%$ of total power.

Notice that two-thirds ($66.7%$) of the total RF power is expended on the unmodulated carrier, which carries zero information! Furthermore, the two sidebands carry identical, redundant intelligence.

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2. Double Sideband & Single Sideband (SSB) Generation

To overcome the extreme power and bandwidth inefficiency of standard AM, amateur radio relies heavily on Single Sideband (SSB) transmission.

The Filter Method of SSB Generation

1. Balanced Modulator: Audio speech and an RF carrier ($f_c$) enter a balanced modulator (ring diode bridge or Gilbert cell). The balanced circuit cancels out the carrier signal by $40\text{ dB}$ to $50\text{ dB}$, producing a Double Sideband Suppressed Carrier (DSB-SC) signal containing only the upper and lower sidebands.
2. Sideband Filter: The DSB-SC signal passes through an ultra-sharp quartz crystal ladder filter. The filter selectively passes one sideband (e.g., Upper Sideband) while attenuating the unwanted sideband (Lower Sideband) by $50\text{ dB}$ or more.

$\text{Audio} + \text{Carrier} \longrightarrow \boxed{\text{Balanced Modulator}} \longrightarrow \text{DSB-SC} \longrightarrow \boxed{\text{Crystal Filter}} \longrightarrow \text{SSB}$

ACMA Standard Sideband Band Conventions

Amateur radio operators adhere strictly to national and international sideband band plan conventions:

• Lower Sideband (LSB): Used on all amateur bands below 10 MHz (specifically $160\text{m}$, $80\text{m}$, and $40\text{m}$ bands).
• Upper Sideband (USB): Used on all amateur bands above 10 MHz (specifically $20\text{m}$, $17\text{m}$, $15\text{m}$, $12\text{m}$, $10\text{m}$, and all VHF/UHF/Microwave bands).

Note: The $60\text{m}$ band ($5.3\text{ MHz}$) band (5.3 MHz) is a USB exception overseas. Australian amateurs have no 60 m allocation - the ACMA declined amateur access to 5351.5-5366.5 kHz - so it does not appear in the Australian band plan.

Bandwidth Savings of SSB

Because an SSB signal consists of only a single sideband, its occupied RF bandwidth equals the highest audio frequency transmitted:

$B_{\text{SSB}} = f_{a(\text{max})} \approx 2.4\text{ kHz}$

SSB uses less than half the spectrum space of AM ($2.4\text{ kHz}$ vs $6.0\text{ kHz}$) and concentrates $100%$ of transmitter output power into intelligence-bearing sideband energy, offering a communications advantage of over $9\text{ dB}$ ($8\times$ effective power improvement) over AM.

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3. Frequency Modulation (FM) and Phase Modulation (PM)

In Frequency Modulation (FM), the amplitude of the RF carrier remains strictly constant, while its instantaneous frequency is varied above and below the centre frequency in direct proportion to the modulating audio signal amplitude.

Key FM Terminology

• Peak Frequency Deviation ($\Delta f$): The maximum excursion of the carrier frequency away from its unmodulated centre frequency. In Amateur Narrowband FM (NFM), standard peak deviation is $\Delta f = \pm 5.0\text{ kHz}$ (or $\pm 2.5\text{ kHz}$ on narrow channels).
• Modulation Index ($\beta$): Ratio of peak frequency deviation to highest modulating audio frequency: $\beta = \frac{\Delta f}{f_a}$

Carson's Rule for FM Bandwidth

Unlike AM, an FM signal theoretically generates an infinite number of sideband pairs spaced at multiples of $f_a$ ($f_c \pm f_a, f_c \pm 2f_a, f_c \pm 3f_a, \dots$), described mathematically by Bessel functions.

However, Carson's Rule establishes that $98%$ of total FM signal power is contained within a practical bandwidth defined as:

$B_{\text{FM}} = 2 \cdot (\Delta f + f_{a(\text{max})})$

ACMA Calculation Example: Calculate the total bandwidth of an Australian 2-metre FM amateur transmission using peak deviation $\Delta f = 5\text{ kHz}$ and maximum speech audio frequency $f_{a(\text{max})} = 3\text{ kHz}$.

$B_{\text{FM}} = 2 \times (5\text{ kHz} + 3\text{ kHz}) = 2 \times 8\text{ kHz} = 16\text{ kHz}$

This explains why standard VHF/UHF FM repeater channels require $25\text{ kHz}$ or $12.5\text{ kHz}$ channel spacing.

Phase Modulation (PM)

In Phase Modulation (PM), the instantaneous phase of the carrier is shifted by speech. Because phase change is mathematically the time derivative of frequency, PM is functionally equivalent to FM with a $+6\text{ dB/octave}$ audio pre-emphasis filter applied. Most commercial "FM" VHF hand-held transceivers actually generate Phase Modulation using reactance modulators.