Section 5: Basic Electronics and Theory Canadian Amateur Radio Basic Qualification (B-005)

5.1 Unit Conversions B-005-001

Electronics uses an enormous range of values -- from picofarads (trillionths of a farad) to gigahertz (billions of hertz). The metric prefix system lets us express these values without writing out long strings of zeros. You must be able to convert between units quickly on the exam, because many problems bury a unit conversion inside a larger calculation.

Metric Prefix Reference Table

How to Convert

The conversion rule is simple: each step between neighbouring prefixes is a factor of 1,000 (three decimal places).

• Going to a smaller unit (e.g., MHz to kHz): Multiply by 1,000. The number gets bigger because you are counting in smaller pieces.
• Going to a larger unit (e.g., Hz to kHz): Divide by 1,000. The number shrinks because each piece is bigger.

A quick sanity check: if your answer seems absurdly large or small, you probably multiplied when you should have divided, or vice versa.

Worked Examples

A few more facts the exam expects you to know:

• A kilohm is 1,000 ohms.
• One quarter ampere = 0.25 A = 250 milliamperes.
• 2 volts = 2,000 millivolts.
• To convert megahertz to gigahertz, divide by 1,000.
• 10,000 microhenries = 10 millihenries (divide by 1,000).

5.2 Conductors and Insulators B-005-002

Every material in the universe falls somewhere on a spectrum from perfect conductor to perfect insulator. Understanding where common materials land on that spectrum -- and the vocabulary the exam uses to describe it -- is essential.

Conductors

A conductor is a material that readily allows the flow of electric current. Metals are the best conductors because their atoms share free electrons that can drift through the material when voltage is applied. Think of the water analogy: a conductor is a wide-open pipe.

On the exam, when asked "What is the best conductor among silicon, aluminum, copper, and carbon?" the answer is always copper. Silver is technically better but is rarely listed as a choice. The exam also asks you to identify groups of three good conductors -- gold, silver, and aluminum is a valid trio.

Insulators

An insulator resists the flow of electric current. In the water analogy, an insulator is a sealed cap on the pipe -- no flow gets through. Good insulators include glass, air, and porcelain, as well as rubber, plastic, Teflon, and mica. Note that wood and carbon are not good insulators (carbon actually conducts to some degree).

Key Electrical Properties

The exam tests several vocabulary terms related to conductors and insulators:

• The flow of electric charge in a circuit is called current.
• The letter "R" is the symbol for resistance.
• An object conducts electricity well when it has low resistance.
• Conductance is the inverse of resistance -- high conductance means low resistance.
• A voltage drop is the loss of voltage caused by the flow of current through a circuit.
• The resistance of a conductor changes with temperature.
• Polarity describes the direction of current in a DC circuit.

5.3 Basic Electrical Concepts B-005-003

Power

Power is the rate at which electrical energy is used. The faster energy is consumed, the higher the power. The unit of power is the watt. A 100-watt light bulb consumes electrical energy at a higher rate than a 40-watt bulb -- so if you are asked which bulb among 40W, 50W, 60W, and 100W consumes energy at the highest rate, the answer is always the 100-watt bulb.

The fundamental power formula ties voltage and current together:

This means that to find power, you multiply the two quantities voltage and current. Equivalently, multiplying volts and amperes gives watts.

Circuit Malfunctions

Two kinds of circuit malfunctions come up repeatedly on the exam: open circuits and short circuits. They are opposites of each other.

  OPEN CIRCUIT                    SHORT CIRCUIT
  (broken wire)                   (bypass path)

   +--++--[R]--+                  +--[R]--+
   |  gap      |                  |       |
  [V]         [V]                [V]  +---+  <-- short
   |           |                  |   |       across R
   +-----------+                  +---+

  No current flows.              Excessive current flows.
  Fuse does NOT blow.            Fuse BLOWS.

• Open circuit: A break in the path. No current flows at all. If a battery and resistor form a circuit and the wire breaks, no current is drawn from the battery -- that is an open circuit.
• Short circuit: An unintended low-resistance bypass that draws excessive current. When you connect a transceiver to a power supply and the fuse blows immediately, a short circuit is the cause.
• When a resistor gets very hot and starts to burn, it is dissipating too much power (not voltage, current, or resistance -- power is the rate of energy release as heat).
• Continuity means the circuit is a closed (complete) circuit -- there are no breaks in the path.

5.4 Ohm's Law B-005-004

Ohm's Law is the single most important formula in electronics and the foundation for most calculations on the exam. It describes the relationship between voltage, current, and resistance in any circuit. If you know any two of these three quantities, you can always find the third.

The variable E (for electromotive force) is sometimes used instead of V for voltage. On the exam you may see \(R = E / I\) -- this is identical to \(R = V / I\).

         THE OHM'S LAW TRIANGLE

              +-----+
             /   V   \        Cover the quantity you want:
            /---------\
           /  I  |  R  \       Want V? See I x R
          /______|______\      Want I? See V / R
                                Want R? See V / I

   V = Voltage (volts)    Also written as E (electromotive force)
   I = Current (amperes)
   R = Resistance (ohms)

Worked Examples

5.5 Series and Parallel Resistors B-005-005

Real circuits rarely have just one resistor. When you combine resistors, the arrangement determines how they share voltage and current. There are two fundamental arrangements: series and parallel.

Series Circuits

In a series circuit, resistors are connected end-to-end so that current has only one path to follow. The same current flows through every resistor, while voltage divides among them.

  SERIES CIRCUIT: Current has only ONE path

    +--[R1]--[R2]--[R3]--+
    |                     |
   [V]                    |
    |                     |
    +---------------------+

  Same current flows through ALL resistors.
  Voltage DIVIDES among the resistors.
  R_total = R1 + R2 + R3 + ...

The total resistance is simply the sum: \(R_{total} = R_1 + R_2 + R_3 + \ldots\). This means the total resistance of resistors in series is always greater than the resistance of any single resistor. For example, five 10-ohm resistors in series give \(5 \times 10 = 50\;\Omega\).

Parallel Circuits

In a parallel circuit, resistors are connected across each other so that current has multiple paths. The same voltage appears across every resistor, while current divides among the branches. The total current equals the sum of all branch currents.

  PARALLEL CIRCUIT: Current has MULTIPLE paths

         +--[R1]--+
         |        |
    +----+--[R2]--+----+
    |    |        |    |
   [V]   +--[R3]--+    |
    |                  |
    +------------------+

  Same voltage across ALL resistors.
  Current DIVIDES among the branches.
  1/R_total = 1/R1 + 1/R2 + 1/R3 + ...

Equal-Value Shortcut

For \(n\) equal resistors of value \(R\) in parallel, the formula simplifies to \(R_{total} = R / n\). This shortcut is heavily tested. For example, four 68-ohm resistors in parallel give \(68/4 = 17\;\Omega\). Ten equal resistors of value R in parallel give \(R/10\).

Two-Resistor Shortcut

For exactly two resistors in parallel: \(R_{total} = \frac{R_1 \times R_2}{R_1 + R_2}\).

Worked Examples

An important conceptual point: if two resistors are in parallel and resistor "A" carries twice the current of "B," then by Ohm's Law (since both see the same voltage), "A" must have half the resistance of "B."

5.6 Power Calculations B-005-006

Power is the rate at which electrical energy is consumed or dissipated. You already know \(P = V \times I\). By substituting Ohm's Law into that formula, you get two additional forms that let you calculate power from any two known quantities:

         THE POWER FORMULA WHEEL

                  P
                / | \
              V   |   I         P = V x I
             /    |    \        V = P / I
            I     R     V      I = P / V
           /      |      \
          R       V       R    P = I² x R     P = V² / R

Power Ratings and Physical Size

A physically larger resistor can dissipate more heat without burning up. That is why a large-size resistor would be used instead of a smaller one of the same resistance -- for greater power dissipation. Resistor wattage ratings are determined by their heat dissipation qualities.

When two resistors are combined (series or parallel), each one can still handle its rated power. Two 1-watt resistors can handle a total of 2 watts, whether they are in series or parallel.

Worked Examples

Replacing a single 50-ohm resistor with two 100-ohm resistors in parallel gives the same resistance but greater power rating, because each resistor handles its own rated power and the total capacity doubles.

5.7 AC Theory B-005-007

Everything discussed so far applies to direct current (DC), where current flows in one direction. In alternating current (AC), the direction of current reverses many times per second. Most radio signals are AC, and household electricity is AC, so understanding these concepts is essential.

Frequency and Wavelength

Frequency is the number of times per second an AC signal completes a full cycle (from positive peak to negative peak and back). It is measured in hertz (Hz). For example, 60 Hz means 60 complete cycles per second -- this is the North American AC power frequency.

Wavelength is the distance a signal travels during one complete cycle. Frequency and wavelength are linked by the speed of light:

This gives us a critical relationship: as frequency increases, wavelength decreases, and vice versa. They are inversely proportional. If a signal's wavelength gets shorter, its frequency is increasing.

Audio Frequencies

The approximate range of frequencies most humans can hear is 20 Hz to 20,000 Hz (20 Hz to 20 kHz). This range is called "audio frequencies" because the human ear can sense sound in this range.

Frequency Bands

The exam will test whether you can place a frequency into its band. For example, 7125 kHz = 7.125 MHz, which falls in the HF range (3-30 MHz).

Other AC Terms

• Sine wave (sinusoidal): The shape of household AC electricity.
• Phase: The timing difference between two AC waveforms of the same frequency that do not begin at the same instant.
• Harmonic: A signal at a whole-number multiple of the fundamental frequency. If the fundamental is 2 kHz, the 4 kHz component is the second harmonic (also simply called a "harmonic").

5.8 Decibels (dB) B-005-008

The decibel (dB) is used to measure the ratio between two signal levels. Rather than saying "the signal is 10 times stronger," we say "the signal is 10 dB stronger." This logarithmic scale compresses huge power ratios into manageable numbers. The formula is:

You do not need to calculate logarithms on the exam. Instead, you need to memorize a small table of dB-to-power-ratio conversions and combine them.

Essential dB Reference Table

S-Meter Readings

S-meter readings on a receiver are often expressed as "dB over S9." When the received power changes, you can calculate the new S-meter reading by converting the power ratio to dB. For example, if power is reduced to one-tenth (a factor of 10), the S-meter drops by 10 dB. If reduced to one-hundredth, it drops by 20 dB.

Worked Examples

5.9 Inductors and Capacitors B-005-009

Resistors dissipate energy as heat. Inductors and capacitors, by contrast, store energy temporarily and release it. They are the building blocks of filters, tuned circuits, and power supplies.

Inductors in Series and Parallel

Inductors combine exactly like resistors:

For two equal inductors: in series the total is twice the value of one; in parallel it is half the value of one.

Capacitors in Series and Parallel

Capacitors combine opposite to resistors. This is the single most common source of confusion on this topic, so pay close attention:

For two equal capacitors: in parallel the total is twice the value of one (they add); in series the total is half the value of one (they use the reciprocal formula).

Component Construction

The exam asks what physical parameters determine inductance and capacitance:

• Air-core inductor: Inductance depends on coil diameter, coil length, and number of turns of wire.
• Parallel-plate capacitor: Capacitance depends on surface area of the plates and spacing between the plates.

Worked Examples

5.10 Reactance and Impedance B-005-010

In DC circuits, only resistance opposes current. In AC circuits, inductors and capacitors create an additional form of opposition called reactance. Unlike resistance, reactance depends on frequency -- the same inductor or capacitor offers different opposition at different frequencies.

Inductive Reactance

An inductor's opposition to AC current is called inductive reactance, calculated as \(X_L = 2\pi f L\). The key takeaway is straightforward: inductive reactance increases as frequency increases. Think of the flywheel analogy -- the faster things change, the more the flywheel resists. At low frequencies, an inductor is barely an obstacle. At high frequencies, it blocks strongly.

Capacitive Reactance

A capacitor's opposition to AC current is called capacitive reactance, calculated as \(X_C = \frac{1}{2\pi f C}\). Because frequency is in the denominator, the relationship is reversed: capacitive reactance decreases as frequency increases. Conversely, capacitive reactance increases as frequency decreases. At high frequencies, a capacitor lets current flow easily; at low frequencies, it blocks.

Impedance

Impedance (Z) is the total opposition to AC current, combining both resistance and reactance. It is also described as the ratio of AC voltage to AC current in a circuit. The formula is:

Practical Applications: Ferrite Chokes and Bypass Capacitors

The frequency-dependent nature of reactance is exploited in practical filtering components:

Notice how the inductor (choke) and capacitor (bypass) work as a team: the choke blocks RF (high reactance at RF), while the bypass cap shunts RF to ground (low reactance at RF). Together they keep RF out of audio circuits.

5.11 Transformers B-005-011

A transformer transfers electrical energy from one circuit to another through electromagnetic induction, using two coils of wire (windings) wrapped around a shared core. Transformers can step voltage up or down, and they are essential for power supplies and impedance matching in radio equipment.

Turns ratio determines voltage: V_s/V_p = N_s/N_p

Transformer Equations

The voltage ratio follows the turns ratio, while the current ratio is its inverse (because power is conserved):

In an ideal (lossless) transformer, power in equals power out: \(V_p \times I_p = V_s \times I_s\). This means if voltage goes up, current must come down by the same factor, and vice versa. Most exam problems assume an ideal transformer unless stated otherwise.

A transformer can also change impedance by carrying different voltages and currents in each winding. The impedance ratio follows the square of the turns ratio: \(\frac{Z_p}{Z_s} = \left(\frac{N_p}{N_s}\right)^2\).

Worked Examples

Other Transformer Facts

• The strength of the magnetic field around a conductor in air is directly proportional to the current in the conductor.
• Maximum induced voltage in a coil occurs when current is going through its greatest rate of change.
• Coupling (induction) between two wires is maximum when the wires are close and parallel.
• A permanent magnet is most likely made from steel.
• Warm iron laminations in a transformer confirm that energy transfer from primary to secondary is not perfect -- some energy is lost as heat.

5.12 Resonant Circuits B-005-012

When an inductor and capacitor are combined in a circuit, something remarkable happens: at one specific frequency, the inductive reactance and capacitive reactance become equal and cancel each other out. This is resonance, and it is the principle that allows your radio to tune in to a single station out of thousands.

The Resonance Condition

At resonance, \(X_L = X_C\). The two reactances are equal in magnitude and opposite in sign, so they cancel. The frequency at which this occurs is:

Series vs. Parallel Resonance

The behaviour at resonance depends on whether the inductor and capacitor are connected in series or parallel:

  SERIES RESONANT CIRCUIT        PARALLEL RESONANT CIRCUIT

    +--[L]--[C]--+                    +--[L]--+
    |            |                    |       |
   [V]          [R]              +---+       +---+
    |            |               |   +--[C]--+   |
    +------------+              [V]              [R]
                                 |               |
  At resonance:                  +---------------+
  XL = XC, they cancel
  Only R remains               At resonance:
  Z is MINIMUM                 XL = XC
  Current is MAXIMUM           Z is MAXIMUM

Bandwidth and Selectivity

Bandwidth is the range of frequencies around resonance where the effect is still significant. A narrow bandwidth means better selectivity -- the circuit can pick out one station more precisely. The Q factor (quality factor) determines bandwidth: higher Q means narrower bandwidth.

Adding a resistor to a resonant circuit affects Q and bandwidth but does not change the resonant frequency itself, because the resonant frequency depends only on L and C.

Resonant circuits in a receiver are used to select the desired signal frequencies -- this is how tuning works.

5.13 Test Instruments B-005-013

To troubleshoot and measure circuits, you need instruments. The exam tests your knowledge of which instrument to use, how to connect it, and what it looks like to the circuit.

Connecting Instruments

The two most fundamental instruments are the voltmeter and ammeter. They are connected differently because they measure different things:

Voltmeter in PARALLEL (high resistance), Ammeter in SERIES (low resistance)

Why does this matter? A voltmeter must have high resistance so it does not draw significant current from the circuit it is measuring. An ammeter must have low resistance so it does not significantly impede the current it is measuring. When measuring voltage across a circuit component, the voltmeter appears to be a high value resistance (essentially an open circuit). When measuring current, the ammeter appears as a low value resistance.

Types of Instruments

An ammeter is also the correct instrument for measuring the final power amplifier current.

Measurement Quality

Quick Reference Summary