5.2 RF Power and SWR Measurement (PEP vs. Average Power)

5.2 RF Power and SWR Measurement (PEP vs. Average Power)

ACMA Exam Focus: Australian amateur power limits are expressed as peak envelope power (pX) for emission modes J3E and R3E, and as mean power (pY) for all other emission modes. Candidates must understand the difference between PEP and average power, know how to calculate VSWR from directional power readings, and master oscilloscope monitoring of RF envelopes.

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1. Peak Envelope Power (PEP) vs. Average Power

In Radio Frequency (RF) power measurements, a fundamental distinction exists between Average Power and Peak Envelope Power (PEP).

Definition of PEP

Peak Envelope Power (PEP) is defined as the average power supplied to the transmission line by a transmitter during one radio frequency cycle at the highest crest of the modulation envelope under normal operating conditions.

Mathematically, if $V_{rms,max}$ is the peak RMS voltage across a non-inductive matched load resistance $R$ (typically $50\ \Omega$) at the crest of the modulation envelope: $\text{PEP} = \frac{V_{rms,max}^2}{R} = \frac{V_{pk}^2}{2 R}$

where $V_{pk}$ is the peak instantaneous voltage ($V_{pk} = \sqrt{2} \times V_{rms}$).

Definition of Average Power

Average Power ($P_{avg}$) is the total RF energy delivered to the load averaged over a relatively long period of time (e.g., several modulation cycles or speech intervals).

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2. Power Relationships Across Modulation Modes

The relationship between PEP and Average Power depends entirely on the modulation scheme being transmitted:

Frequency Modulation (FM) and Continuous Wave (CW Key-Down)

In FM and unkeyed/constant-amplitude CW key-down transmissions, the amplitude of the RF envelope remains completely constant over time. $\text{PEP} = P_{avg} = P_{carrier}$ A standard thermal or average-reading wattmeter will indicate the true PEP of an FM or CW transmitter.

Single Sideband (SSB) Voice Modulation

In SSB suppressed-carrier transmissions, no RF power is emitted when there is no voice input. When an operator speaks into the microphone, complex audio speech waveforms create rapidly changing RF envelope peaks.

• For typical human speech, the average power indicated on a standard slow-responding wattmeter is only 30% to 40% of the actual peak envelope power (a ratio of roughly 1:2.5 to 1:3).
• If a standard average wattmeter reads $35\text{ W}$ on SSB speech, the actual transmitter PEP is approximately $100\text{ W}$.
• To measure true SSB PEP directly, a wattmeter must incorporate active electronic peak-detecting circuits with a storage capacitor to hold the voltage peak long enough for the meter needle or display to register.

Amplitude Modulation (AM)

A standard double-sideband full-carrier AM signal consists of a continuous carrier plus upper and lower sidebands.

• Unmodulated AM Carrier: $\text{PEP} = P_{carrier} = P_{avg}$.
• 100% Modulated AM (Sine Wave): At 100% modulation, the peak envelope voltage doubles ($V_{pk} = 2 \times V_{carrier}$), which quadruples the peak power: $\text{PEP}_{AM} = 4 \times P_{carrier}$ The average power of a 100% sine-wave modulated AM signal increases by 50% ($P_{avg} = 1.5 \times P_{carrier}$), where 67% of the total average power remains in the unmodulated carrier and 33% is distributed between the two sidebands.

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3. Directional RF Wattmeters & Inline Couplers

Transmitter output power and impedance matching are measured using an inline directional RF wattmeter (such as the classic Bird Model 43) placed in series with the $50\ \Omega$ coaxial transmission line.

Principle of Operation

Directional wattmeters utilise an internal directional coupler or inductive/capacitive sampling element inserted into a rigid transmission line section.

• Forward Power ($P_{fwd}$): When the sampling element is rotated facing toward the transmitter source, it senses only the electromagnetic wave traveling from the transmitter toward the load, displaying Forward Power in Watts.
• Reflected Power ($P_{ref}$): When the element is rotated 180 degrees facing toward the antenna load, it senses only the reflected wave traveling back toward the transmitter, displaying Reflected Power in Watts.

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4. Voltage Standing Wave Ratio (VSWR) Calculation

When an antenna's feedpoint impedance matches the characteristic impedance ($Z_0$) of the coaxial cable (typically $50\ \Omega$), all forward power is absorbed by the load ($P_{ref} = 0\text{ W}$).

If an impedance mismatch exists, a portion of the forward wave is reflected back. The interaction of forward and reflected waves creates a stationary pattern of voltage maxima ($V_{max}$) and minima ($V_{min}$) along the line, defined as the Voltage Standing Wave Ratio (VSWR): $\text{VSWR} = \frac{V_{max}}{V_{min}}$

Calculating VSWR from RF Power Readings

Directional wattmeters allow precise calculation of SWR using measured forward power ($P_{fwd}$) and reflected power ($P_{ref}$):

$\text{VSWR} = \frac{1 + \sqrt{\frac{P_{ref}}{P_{fwd}}}}{1 - \sqrt{\frac{P_{ref}}{P_{fwd}}}}$

Worked Examples for ACMA Exam

Example A: Perfect Match

• Measured: $P_{fwd} = 100\text{ W}$, $P_{ref} = 0\text{ W}$.
• Calculation: $\sqrt{0 / 100} = 0 \implies \text{VSWR} = \frac{1 + 0}{1 - 0} = \mathbf{1.0 : 1}$ (Ideal matched load).

Example B: Moderate Mismatch (SWR 1.5:1)

• Measured: $P_{fwd} = 100\text{ W}$, $P_{ref} = 4\text{ W}$.
• Calculation: $\sqrt{4 / 100} = \sqrt{0.04} = 0.2$.
• $\text{VSWR} = \frac{1 + 0.2}{1 - 0.2} = \frac{1.2}{0.8} = \mathbf{1.5 : 1}$.

Example C: Severe Mismatch (SWR 2.0:1)

• Measured: $P_{fwd} = 100\text{ W}$, $P_{ref} = 11.1\text{ W}$.
• Calculation: $\sqrt{11.1 / 100} = \sqrt{0.1111} = 0.333$.
• $\text{VSWR} = \frac{1 + 0.333}{1 - 0.333} = \frac{1.333}{0.667} = \mathbf{2.0 : 1}$ (Triggers automatic transmitter power foldback in modern transceivers).

Example D: Total Reflection (Open or Short Circuit)

• Measured: $P_{fwd} = 100\text{ W}$, $P_{ref} = 100\text{ W}$.
• Calculation: $\sqrt{100 / 100} = 1 \implies \text{VSWR} = \frac{1 + 1}{1 - 1} = \frac{2}{0} = \boldsymbol{\infty : 1}$ (Total reflection).

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5. Oscilloscope RF Envelope Measurement

An oscilloscope connected across a high-frequency RF sampler/pickup tap provides a direct visual time-domain representation of the RF modulation envelope.

Monitoring SSB Linearity & Overmodulation

• Linear SSB Envelope: A two-tone audio test signal (e.g., 700 Hz and 1900 Hz non-harmonic tones) injected into an SSB transmitter should display smooth, symmetrical sine-wave cross-over shapes meeting cleanly at the zero line without flat-topping.
• Flat-Topping (Splatter): Overdriving an SSB power amplifier or misadjusting Speech Processing causes clipping of the RF voltage peaks. This "flat-topping" generates severe non-linear intermodulation distortion (IMD), resulting in wideband adjacent-channel interference known as splatter.

Trapezoidal Test Pattern

By feeding the modulated RF output envelope to the vertical deflection plates and the transmitter audio modulating signal to the horizontal input of an oscilloscope, an X-Y trapezoidal pattern is produced:

• A perfectly straight-sided trapezoid indicates linear 100% AM modulation.
• Curvature along the sides indicates non-linear amplifier distortion.
• A baseline tail extension beyond the triangle apex indicates overmodulation (>100%).