1.2 DC Circuits, Voltage, Current, and Ohm's Law

1.2 DC Circuits, Voltage, Current, and Ohm's Law

Understanding direct current (DC) circuits is the bedrock of radio communications engineering and the starting point for the Australian Communications and Media Authority (ACMA) Standard Recognition Certificate examination. All electronic radio equipment—from low-noise preamplifiers and digital signal processors to high-power RF final amplifiers—relies on stable DC voltages and currents to bias active semiconductor components and establish operating parameters.

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1. Electrical Fundamentals: Charge, Voltage, Current, and Resistance

At the subatomic level, electrical phenomena stem from the movement and interaction of charged subatomic particles. Electrons carry a negative elementary charge of approximately $1.602 \times 10^{-19}$ Coulombs. In conductive materials, such as copper, silver, and aluminium, outer-shell valence electrons are loosely bound to atomic nuclei, forming a "sea" of free electrons capable of drifting through the crystal lattice when exposed to an electric field.

Potential Difference (Voltage, $V$)

Electric potential difference—commonly termed Voltage ($V$) or Electromotive Force (EMF)—is the force or pressure that drives free electrons through a conductor. Voltage represents the work required to move a unit charge between two points against an electric field. The SI unit of potential difference is the Volt (V), named after Alessandro Volta. One Volt is defined as the potential difference across a conductor when a current of one Ampere dissipates one Watt of power ($1\text{ V} = 1\text{ J/C}$).

In radio station equipment, DC operating voltages vary widely:

• $13.8\text{ V DC}$: Standard nominal DC voltage for mobile and desktop transceiver power supplies (matching a charging 12V lead-acid or $\text{LiFePO}_4$ battery).
• $5.0\text{ V}$ & $3.3\text{ V}$: Standard logic levels for microcontrollers, synthesisers, and DSP circuitry.
• $50\text{ V}$ - $3000\text{ V DC}$: Anode/drain voltages found in high-power solid-state or vacuum tube RF linear amplifiers.

Electric Current ($I$)

Current ($I$) is the rate of flow of electric charge past a specified point in a circuit. The SI unit of current is the Ampere (A), named after André-Marie Ampère. One Ampere represents the flow of one Coulomb of charge ($6.242 \times 10^{18}$ electrons) passing a boundary per second ($1\text{ A} = 1\text{ C/s}$).

In DC circuits, current flows in a single continuous direction. It is important for ACMA candidates to distinguish between two conventions:

1. Conventional Current Flow: Assumes positive charge moves from the positive terminal of a voltage source, through the external circuit, to the negative terminal. This convention is standard in circuit diagrams and mathematical calculations.
2. Electron Flow: Reflects the physical movement of negatively charged electrons, which travel from the negative terminal toward the positive terminal.

Common current metric prefixes in amateur radio include:

• Microampere ($\mu\text{A}$): $10^{-6}\text{ A}$ (e.g., receiver AGC bias currents).
• Milliampere ($\text{mA}$): $10^{-3}\text{ A}$ (e.g., small-signal transistor stage biasing).
• Ampere ($\text{A}$): $10^{0}\text{ A}$ (e.g., transmit current drawn by a 100W HF transceiver, typically 18A to 22A at 13.8V).

Electrical Resistance ($R$)

Resistance ($R$) is the opposition a material offers to the flow of electric current. As electrons travel through a conductor, they collide with lattice ions, converting electrical energy into heat. The SI unit of resistance is the Ohm ($\Omega$), named after Georg Simon Ohm.

Materials are categorised by their volumetric resistivity ($\rho$):

• Conductors (e.g., copper, silver): Very low resistivity ($\approx 1.7 \times 10^{-8}\ \Omega\cdot\text{m}$), allowing free electron drift.
• Insulators (e.g., PTFE/Teflon, ceramic, glass, PVC): Extremely high resistivity ($> 10^{12}\ \Omega\cdot\text{m}$), preventing charge movement under normal operating voltages.
• Semiconductors (e.g., silicon, germanium): Intermediate resistivity, which can be precisely controlled by introducing impurity atoms (doping).

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2. Ohm's Law

Ohm's Law states that the current flowing through a conductor between two points is directly proportional to the potential difference across the two points and inversely proportional to the resistance between them, provided temperature remains constant.

$\text{Ohm's Law Formulas: } \quad V = I \times R \quad \vert \quad I = \frac{V}{R} \quad \vert \quad R = \frac{V}{I}$

Where:

• $V$ is potential difference in Volts (V)
• $I$ is current in Amperes (A)
• $R$ is resistance in Ohms ($\Omega$)

Worked Example 1.1: Standard Transceiver Current Draw

An amateur transceiver operating on the 7 MHz (40m) band draws current from a regulated $13.8\text{ V DC}$ power supply. If the internal receiver preamp circuit presents a DC load resistance of $184\ \Omega$, calculate the current drawn by the preamp circuit.

Solution: $I = \frac{V}{R} = \frac{13.8\text{ V}}{184\ \Omega} = 0.075\text{ A} = 75\text{ mA}$

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3. Series Resistor Circuits

In a series circuit, components are connected end-to-end, forming a single continuous loop for current flow.

Key Properties of Series Circuits:

1. Current Conservation: The current ($I$) flowing through every series element is identical: $I_{\text{total}} = I_1 = I_2 = \dots = I_n$.
2. Equivalent Resistance: Total resistance is the sum of all individual resistances: $R_{\text{total}} = R_1 + R_2 + R_3 + \dots + R_n$
3. Voltage Drops: The total applied voltage equals the sum of individual voltage drops across each resistor: $V_{\text{supply}} = V_1 + V_2 + \dots + V_n$.

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4. Parallel Resistor Circuits

In a parallel circuit, components are connected across the same two common nodes, creating multiple independent current branches.

Key Properties of Parallel Circuits:

1. Voltage Equality: The potential difference across every parallel branch is identical: $V_{\text{supply}} = V_1 = V_2 = \dots = V_n$.
2. Current Division: Total supply current equals the sum of currents through each branch: $I_{\text{total}} = I_1 + I_2 + \dots + I_n$.
3. Equivalent Resistance: The reciprocal of equivalent resistance is the sum of reciprocals of branch resistances: $\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n} \implies R_{\text{total}} = \frac{1}{\sum_{i=1}^n \frac{1}{R_i}}$

For two parallel resistors, the simplified "product over sum" formula is: $R_{\text{total}} = \frac{R_1 \times R_2}{R_1 + R_2}$

Note for ACMA Exam: Equivalent resistance of a parallel network is always strictly less than the resistance of the smallest individual resistor in that network.

Worked Example 1.2: Parallel Combination Calculation

Three resistors with values $R_1 = 100\ \Omega$, $R_2 = 200\ \Omega$, and $R_3 = 300\ \Omega$ are connected in parallel across a $12\text{ V DC}$ power source. Calculate:

1. Total equivalent resistance $R_{\text{total}}$.
2. Total current drawn from the supply $I_{\text{total}}$.

Solution: $\frac{1}{R_{\text{total}}} = \frac{1}{100} + \frac{1}{200} + \frac{1}{300} = 0.01 + 0.005 + 0.003333 = 0.018333\ \Omega^{-1}$ $R_{\text{total}} = \frac{1}{0.018333} \approx 54.55\ \Omega$ $I_{\text{total}} = \frac{V}{R_{\text{total}}} = \frac{12\text{ V}}{54.55\ \Omega} \approx 0.220\text{ A} = 220\text{ mA}$

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5. Voltage Dividers & Kirchhoff's Circuit Laws

Unloaded Voltage Divider Rule

A series combination of two resistors acts as a Voltage Divider, scaling down an input voltage to a lower reference value:

$V_{\text{out}} = V_{\text{in}} \times \left( \frac{R_2}{R_1 + R_2} \right)$

Where $V_{\text{out}}$ is taken across $R_2$.

Kirchhoff's Current Law (KCL)

Kirchhoff's First Law states that the algebraic sum of currents entering any circuit node (junction) is zero: $\sum I_{\text{in}} = \sum I_{\text{out}}$ KCL reflects the fundamental physical principle of conservation of electrical charge.

Kirchhoff's Voltage Law (KVL)

Kirchhoff's Second Law states that the algebraic sum of all potential differences (voltage sources and voltage drops) around any closed loop is zero: $\sum V = 0$ KVL reflects the principle of conservation of energy.