7.5 Frequency Counter Accuracy, PPM & Harmonics

7.5 Frequency Counter Accuracy, PPM & Harmonics

Quick Answer: Error (Hz) = indicated frequency (Hz) × ppm × 10⁻⁶. So 462.1 MHz at ±1.0 ppm → 462.1 Hz; at ±0.1 ppm → 46.21 Hz. 156.52 MHz at ±1.0 ppm → 156.52 Hz; at ±10 ppm → 1565.20 Hz. Second harmonic = 2 × fundamental: 380 kHz → 760 kHz; 4146 kHz → 8292 kHz.

Sub-topic 3-B-011 (Frequency) is the highest-value single sub-topic in the electrical-math topic for the effort involved. Four of its six pool items are the same calculation with different numbers, and the remaining two are the easiest arithmetic in Element 3.

What a time-base accuracy actually means

A frequency counter measures by counting cycles over a precisely known interval. That interval comes from an internal crystal oscillator—the time base. If the time base is slightly off, the count is proportionally off. So the counter's accuracy specification is a fractional figure, given in parts per million (ppm).

Parts per million means exactly what it says: multiply by 10⁻⁶.

A convenient anchor: 1 ppm of 1 MHz is exactly 1 Hz. Every question in this sub-topic can be scaled from that single fact.

The formula and the four worked pool items

Maximum error (Hz) = indicated frequency (Hz) × ppm ÷ 1,000,000

The shortcut worth learning

Notice the pattern in the middle two rows. At 1.0 ppm, the error in hertz is numerically the frequency expressed in megahertz:

• 462.1 MHz at 1 ppm → 462.1 Hz
• 156.52 MHz at 1 ppm → 156.52 Hz

That is not a coincidence—it falls straight out of 1 ppm of 1 MHz = 1 Hz. Once you see it, the whole sub-topic collapses to: write the frequency in MHz, then scale by the ppm figure.

• ±0.1 ppm → move the decimal one place left: 462.1 → 46.21 Hz
• ±1.0 ppm → the number unchanged: 156.52 → 156.52 Hz
• ±10 ppm → move the decimal one place right: 156.52 → 1565.2 Hz

Three decimal-point moves cover four of the six items in this sub-topic.

Why this matters on the bench

The practical reading of these numbers is: your measurement is only as good as your reference. Two consequences:

1. A counter cannot verify a tolerance tighter than its own time base. If a Part 80 or Part 87 station must hold ±0.0005% (5 ppm) and your counter is ±10 ppm, the instrument cannot prove compliance. You need a counter an order of magnitude better than the tolerance you are checking, or an external reference (a GPS-disciplined oscillator or a rubidium standard).
2. Time-base error scales with frequency. The same ±1 ppm counter is off by 2 Hz at 2 MHz and by 462 Hz at 462 MHz. Errors that are invisible on MF become significant at UHF, which is exactly why the pool's examples use marine VHF (156.52 MHz) and land-mobile UHF (462.1 MHz).

Note also that these are ± figures, so the true frequency lies anywhere in a window twice the stated error wide. The pool asks "the most the actual frequency could differ," which is the one-sided value—do not double it.

Harmonics

The other two items in this sub-topic are trivial once you know the definition. A harmonic is an integer multiple of the fundamental:

The second harmonic of a 380 kHz frequency is 760 kHz. The second harmonic of SSB frequency 4146 kHz is 8292 kHz.

The one trap: the second harmonic is twice the fundamental, not three times. Counting confusion arises because the fundamental is itself the first harmonic, so the "second" is the first additional one. If an option offers 1140 kHz for the second harmonic of 380 kHz, it has counted the fundamental as harmonic zero.

Harmonics matter operationally because a transmitter's output stage is non-linear and always generates them. Harmonic suppression—through low-pass filtering, tuned tank circuits, and push-pull configurations that cancel even harmonics—is what keeps a station legal. Note that 4146 kHz is a real marine HF working frequency, and its second harmonic at 8292 kHz lands in the 8 MHz marine band, so unsuppressed harmonics from one marine transmitter interfere directly with another marine service.