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General Course, Module 3: Electricity, Round Two

Covers NCVEC 2023-2027 General Pool, Subelement G5 (Electrical Principles). Three questions on your exam come from this material.

Ray sets an antenna tuner on the bench with its lid off. Inside: two big air-variable capacitors and a fat rotary inductor. "At Technician you learned that this box matches impedances," he says. "Today you learn how. Three ideas: reactance, resonance, and the honest way to measure power. Bring a calculator, and relax. Every formula in this module is multiply, divide, or square."

3.1Reactance, Impedance, and Resonance

Resistance opposes all current equally. AC gets opposed by something extra: reactance, the opposition to alternating current caused by capacitance or inductance. It is measured in ohms, like resistance, and it wears the letter X.

The two flavors pull in opposite directions as frequency changes:

An inductor's reactance increases as frequency increases. The coil fights change, and higher frequency is faster change.
A capacitor's reactance decreases as frequency increases. The faster the alternation, the less time the plates have to charge up and push back.

One goes up while the other comes down, which means for any L and C pair there is exactly one frequency where they meet. That meeting is resonance: the inductive and capacitive reactances cancel. In a series LC circuit, resonance makes the impedance very low, a wide-open door at one frequency. (Its mirror image, the parallel LC circuit, presents a very high impedance at resonance, the tuned circuits from your Technician course.)

Impedance now gets its formal definition: the ratio of voltage to current, the total opposition combining resistance and reactance, in ohms. Its inverse has a name the exam checks: admittance.

And matching impedances, the antenna tuner's job? The rules bless several tools: a transformer, a Pi-network (that capacitor-inductor-capacitor arrangement in Ray's tuner), or even a length of transmission line. All of these. The lidless tuner on the bench is a Pi-network with knobs, and you now know what the knobs move.

Knowledge Check 3.1

Tap an answer. In your own words first, then check yourself.

1. What is reactance?

2. What happens in a series LC circuit at resonance?

3. As frequency increases, an inductor's reactance:

3.2Honest Power: dB, RMS, and PEP

Three measurement ideas separate operators who know their numbers from operators who repeat them.

Decibels carry over from Technician with the same anchor: 3 dB is a factor of two in power, up or down. New precision point: a loss of just 1 dB costs you 20.6 percent of your power. One dB sounds like nothing; a fifth of your power is not nothing. That number is why feed line choices matter.

Power math now runs three formulas instead of one. You know P = I x E. Ohm's Law substitution gives the other two: P = E² / R and P = I² x R. Pick whichever matches the numbers you have:

400 volts DC across an 800-ohm load: P = 400² / 800 = 160,000 / 800 = 200 watts.
A 12-volt bulb drawing 0.2 amps: P = 12 x 0.2 = 2.4 watts.
7.0 milliamps through 1,250 ohms: P = 0.007² x 1250 = about 61 milliwatts.

RMS answers a question you have never thought to ask: when we say "120 volts AC," which voltage do we mean? The wave swings continuously, peaking far above 120. The answer: the RMS (root-mean-square) value, defined as the AC value that produces the same power dissipation in a resistor as a DC voltage of the same value. RMS is the honest average for power purposes, and the wall socket's 120 is an RMS number.

For sine waves, the conversions are fixed gears:

Peak = RMS x 1.414
Peak-to-peak = RMS x 2.828
RMS = Peak x 0.707

Drill them: 120 V RMS is 339.4 V peak-to-peak (yes, the wall socket swings that far). A 17-volt-peak sine wave is 12 V RMS.

PEP, peak envelope power, is the FCC's chosen yardstick from Module 1, so learn to compute it: PEP is the power at the peak of the modulation envelope, calculated from the peak voltage using RMS. The recipe for a sine wave across a load: peak-to-peak, divide by 2 for peak, multiply by 0.707 for RMS, square it, divide by the resistance.

200 V peak-to-peak across 50 ohms: peak = 100, RMS = 70.7, PEP = 70.7² / 50 = 100 watts.
500 V peak-to-peak across 50 ohms: peak = 250, RMS = 176.75, PEP = 176.75² / 50 = 625 watts.

Run it backward too: a dummy load dissipating 1200 watts at 50 ohms has an RMS voltage of the square root of (1200 x 50) = 245 volts.

One conceptual freebie finishes the group: for an unmodulated carrier (a steady tone, key held down), the envelope never varies, so the ratio of PEP to average power is exactly 1.00. Average power 1060 watts means PEP 1060 watts. The distinction between PEP and average only appears when modulation makes the envelope move.

Knowledge Check 3.2

Tap an answer. In your own words first, then check yourself.

1. A 1 dB feed line loss costs approximately what fraction of your power?

2. What is the RMS voltage of household 120 VAC expressed as peak-to-peak?

3. Your amplifier produces an unmodulated carrier with 1060 watts average power. What is the PEP?

3.3Components in Teams, and the Transformer's Secret

At Technician you learned series and parallel circuits. Now the component math that goes with them, and the good news is there are only two patterns, worn by three components.

Resistors and inductors use the same pattern: values add in series, and combine to less than the smallest in parallel.

Inductors in series: 20 mH + 50 mH = 70 mH. Want more inductance? Add an inductor in series.
Inductors in parallel: three 10 mH inductors = 10/3 = 3.3 mH.
Resistors in parallel: 100 and 200 ohms give (100 x 200)/(100 + 200) = 67 ohms. Three resistors of 10, 20, and 50 ohms: add the reciprocals (0.1 + 0.05 + 0.02 = 0.17), flip it: 5.9 ohms.

Capacitors run the pattern backward: they add in parallel, and shrink in series.

In parallel: 5 nF + 5 nF + 750 pF = 10.75 nF (10,750 pF, minding the prefixes from Technician). Want more capacitance? Add a capacitor in parallel.
In series: three 100 µF capacitors = 33.3 µF; a 20 µF and a 50 µF in series = (20 x 50)/(20 + 50) = 14.3 µF.

Ray's memory hook: capacitance is plate area, and paralleling capacitors is just building a bigger plate.

Then the transformer, which earns its own respect. Why does a voltage appear on the secondary at all? Mutual inductance: the primary's changing magnetic field induces voltage in the secondary through the shared core. Everything else is ratios:

Voltage follows the turns ratio. 120 VAC into a 500-turn primary with a 1500-turn secondary: ratio 3, output 360 volts.
The transformer has no idea which side you labeled primary. Feed a signal into the secondary of a 4:1 step-down and it becomes a step-up: the voltage is multiplied by 4.
Current runs opposite to voltage, which is why the low-voltage winding of a step-up transformer uses the larger wire: to carry its higher current.
Impedance follows the turns ratio squared. That square is the transformer's secret, and it is how a small transformer performs impedance magic: matching a 600-ohm antenna feed point to 50-ohm coax needs an impedance ratio of 12, so a turns ratio of the square root of 12, which is about 3.5 to 1.

File that last one next to your EFHW's matching transformer: an end-fed half-wave presents a few thousand ohms, and a 49:1 impedance transformer is just a 7:1 turns ratio doing exactly this arithmetic. The mystery box at the end of your wire has been running Module 3 all along.

Knowledge Check 3.3

Tap an answer. In your own words first, then check yourself.

1. What is the total inductance of a 20 mH and a 50 mH inductor in series?

2. To increase a circuit's capacitance, you add a capacitor:

3. What turns ratio matches a 600-ohm feed point to 50-ohm coax?

Review: every Exam Anchor from this module

G5A Reactance: opposition to AC from capacitance or inductance, measured in ohms, symbol X. Inductive reactance rises with frequency; capacitive reactance falls. Series LC at resonance: very low impedance. Resonance: inductive and capacitive reactance cancel. Impedance: the ratio of voltage to current. Admittance: the inverse of impedance. Impedance matching at RF: transformer, Pi-network, or a transmission line length (all of these).

G5B 3 dB = factor of 2 in power; 1 dB loss = 20.6 percent. Parallel branch currents add to the total. P = E²/R and P = I²R: 400 V into 800 ohms = 200 W; 12 V at 0.2 A = 2.4 W; 7 mA through 1250 ohms = 61 mW. RMS: the AC value dissipating the same power as equal DC. 120 V RMS = 339.4 V peak-to-peak; 17 V peak = 12 V RMS. PEP of 200 V p-p across 50 ohms = 100 W; of 500 V p-p = 625 W. 1200 W in 50 ohms = 245 V RMS. Unmodulated carrier: PEP-to-average ratio is 1.00, so 1060 W average = 1060 W PEP.

G5C Transformer secondary voltage comes from mutual inductance. Inductors add in series (20 + 50 = 70 mH); parallel inductors shrink (three 10 mH = 3.3 mH). Parallel resistors: 100 || 200 = 67 ohms; 10 || 20 || 50 = 5.9 ohms. Capacitors add in parallel (5 nF + 5 nF + 750 pF = 10.75 nF); shrink in series (three 100 µF = 33.3 µF; 20 and 50 µF = 14.3 µF). More capacitance: parallel capacitor. More inductance: series inductor. 500:1500 turns with 120 V in = 360 V out. A reversed 4:1 step-down multiplies by 4. Step-up primary uses larger wire for its higher current. Impedance ratio is turns ratio squared: 600 to 50 ohms = 3.5:1 turns.

Before you move on

The tuner's lid can go back on: you know that its capacitors and inductor form an adjustable matching network, that resonance is reactances cancelling, and that impedance transformation is turns ratios squared. You can also compute power three ways, convert RMS to peak and back, and calculate PEP the way the FCC measures it.

Module 4 restocks the parts bin at General depth: diode threshold voltages, capacitor personalities, MOSFETs, ferrites, and the last few vacuum tubes still worth knowing.