# General/Chapter 4 Study Guide

### From charlesreid1

## Contents

# Chapter 4: Components and Circuits

## Section 4.1: Current, Voltage, Power

- an increase in power of 2x is equal to 3 dB
- in a purely resistive parallel circuit, the total amount of current is the sum of each branch current
- if 400 V dc is supplied to an 800 ohm load, use the formula
- if a 12 V DC light bulb draws 0.2 A, use the formula
- if 7 mA flows through 1.25 kOhm load, the amount of power dissipated can be found using
- a power transmission line loss of 1 dB: to find percent power loss, use the formula , which rearranges to so the power is 79.4% of what it was. This corresponds to a loss of or 20.6%

## Section 4.2: AC Power

- oscilloscope measures 200 V peak-to-peak across 50 Ohm dummy load. What is PEP output?
- AC signal producing same power dissipation in a resistor as a DC signal of the same voltage is the AC signal with an RMS voltage equal to the DC voltage:
- A sine wave with a peak voltage has an RMS voltage of
- For an unmodulated carrier, PEP = average power
- The RMS voltage across a 50 Ohm dummy load dissipating 1200 W is so
- If average power is measured as 1060 watts for an unmodulated carrier, its PEP output is 1060 watts. For unmodulated signals, PEP = average power
- If oscilloscope measures 500 V peak-to-peak across 50 ohm load, PEP is

## Section 4.3: Basic Components

(Fill in)

Resistors

- The change in resistance is a function of the resistor's temperature coefficient
- Inductive resistors can affect RF circuits and change signals (contain metal winding)
- Use non-inductive resistors in RF circuits

Inductors:

- Double lines in symbol mean metal core
- Inductors store an amount of magnetic energy, from the current flowing through it
- Higher inductance means more magnetic energy stored
- Higher permeability of core increases inductance
- Mutual inductance - current generated from a shared magnetic core
- To avoid mutual inductance, use torroidal inductors, or place inductors at right angles
- Inductor material can be optimized for particular frequencies

Capacitors:

- Basic structure: two conductors separated by a dielectric, which stores electrical energy while preventing DC current flow
- The closer the surfaces, the larger the SA, the larger the dielectric energy storage, the higher the capacitance
- Rolled up capacitors have significant parasitic inductance
- Ceramic capacitors are more common at higher frequencies
- Electrolytic capacitors use electrolyte gel/paste, pack higher capacitance into smaller volume
- Polarized capacitors - current can only flow in 1 direction
- Voltage rating of capacitors is the voltage above which the dielectric insulation will break down
- Blocking capacitors l- block DC signals, but not AC signals
- Bypass capacitors - low impedance path across high impedance circuit
- Filter capacitors - smooth out rectified AC into DC power
- Suppressor capacitors - absorb transient voltage spikes
- Tuning capacitors - varying resonant circuit frequencies

Components in series/parallel:

- series resistance is additive: ----R1----R2----R3---- R1+R2+R3
- series inductance is additive: L1+L2+L3
- series capacitance is reciprocal of reciprocals 1 / ( 1/C1 + 1/C2 + 1/C3 )
- parallel resistances are reciprocal of reciprocals
- parallel inductors are reciprocal of reciprocal
- parallel capacitors are additive

Transformers:

- Transformers utilize mutual inductance (shared magnetic core)
- Inductors are called windings
- Power applied to primary winding
- Power extracted from secondary winding
- Changing number of windings changes current (power is conserved)
- significant changes between primary/secondary voltages requires changes in wire size
- Step-up transformer: primary winding has higher current, so wound with larger diameter wire
- Relation between voltage and number of windings:

## Section 4.4: Reactance and Impedance

Reactance:

- capacitors and inductors respond differently to AC and DC
- resistance to AC is called reactance X (measured in ohms)
- Reactance occurs because capacitors and inductors store energy

Capacitive reactance:

- When DC applied to capacitor:
- Current rushes in
- Capacitor begins to store energy
- Voltage in capacitor rises
- Decrease in voltage leads to decrease in delta V, driving force of current
- the more energy stored in capacitor, the lower the current that flows
- eventually, current stops
- Capacitor in DC circuit:
- Capacitor initially looks like a short circuit (closed circuit)
- After capacitor is charged, looks like an open circuit
- Capacitors block DC current

- When AC applied to capacitor:
- At low frequencies, AC behaves like DC
- Capacitor has enough time to charge, stop current
- If AC voltage is higher frequency, capacitor never fully charges to reduce current very much
- Capacitors block DC current, resist low frequency AC and pass high frequency AC

- Opposition to AC current from stored energy is called capacitive reactance and changes with frequency

Inductive reactance:

- Inductors resist current in a complementary way to capacitors
- When DC voltage applied to inductor:
- Current rushes through coil and magnetic energy begins to fill the core
- THe change in the magnetic field resists current initially, gradually lets more through
- When inductor dielectric material is "fully charged," current can pass through it
- WHen voltage first applied, inductor looks like an open circuit
- AFfter time, inductor looks like closed circuit

- Inductor treats DC in an opposite way from capacitor
- If AC voltage applied to inductor:
- Magnetic field perpetually changing
- Current always opposed
- If low-frequency AC, inductor's magnetic core has time to change nad let current pass through
- An inductor blocks high-frequency AC, passes low-frequency AC currents, and acts as a short circuit for DC currents

- Inductive reactance is opposition to AC current flow from stored energy and is denoted

In summary:

**Capacitors oppose changes in voltage.**

**Inductors oppose changes in current.**

Impedance:

- General term for the opposition to current flow in an AC circuit, caused by reactance, resistance, or any combination
- Impedance denoted Z (ohms)
- Impedance is the ratio of voltage to current
- Resistance is independent of frequency
- Reactance is a function of frequency

Resonance:

- Condition in which match between (frequency at which circuit or antenna naturally responds) and the (frequency of applied signal)
- In a circuit with inductive/capacitive reactances, resonance means effects of inductor/capacitor on AC current cancel out
- Resonant circuit: inductive reactance of L cancels with capacitive reactance of C, creating a short circuit and leaving the remaining resistance (load) as the only circuit impedance

Impedance transformation:

- Transformers change voltages and current
- Ratio of voltage to current is impedance
- Impedance of transformer also changed (car transmission)

Impedance matching:

- Interval impedance of components allows limits on power delivery
- Example: hearing aid battery (high impedance) and D-cell (low impedance) have same E = 1.5 V
- Maximum Power Transfer Theorem - maximum power transfer occurs when source and load output impedances are equal and purely resistive (no reactance)
- Hence, adding inductors and capacitors to lengthen and shorten antennas, and make it resonant.

- Maximum power happens at resonant frequency of the circuit
- Amateur equipment: source impedance at output should be 50 ohms (for coax)
- Antennas often designed with feed point impedance of 50 ohms (changes with frequency)
- If impedance difference between transmitter output impedance and load impedance are too great, it can reflect power back and damange transmitter
- To match impedance at transmitter output wtih impedance of antenna, use impedance-matching circuit
- LC circuits (capacitors and inductors)
- Pi network: two capacitors on either side of an inductor; the capacitors are connected to ground
- T network: two capacitors on either side of an inductor; the inductor is connected to ground

- Another way to match impedances is using transformers
- Impedance transformers equalize impedances of source and load to maximize transfer of power
- Stress caused by lots of power and high transformation ratios
- High power can lead to core saturation and harmonic distortion

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General Class Ham LicenseChapter 2: Procedures and Practices: General/Chapter 2 Study Guide Chapter 3: Rules and Regulations: General/Chapter 3 Study Guide Chapter 4: Components and Circuits: Chapter 5: Radio Signals and Equipment: General/Chapter 5 Study Guide Chapter 6: Digital Modes: General/Chapter 6 Study Guide Chapter 7: Antennas: General/Chapter 7 Study Guide Chapter 8: Propagation: General/Chapter 8 Study Guide Chapter 9: Electrical and RF Safety: General/Chapter 9 Study Guide Flags· Template:GeneralFlag · e |