General/Chapter 4 Study Guide

Chapter 4: Components and Circuits

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Section 4.3: Basic Components

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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:

$ \frac{E_s}{E_p} = \frac{N_s}{N_p} $

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 $ X_c $ and changes with frequency

$ X_c = \dfrac{1}{2 \pi f C} $

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 $ X_L $

$ X_L = 2 \pi f L $

In summary:

Capacitors oppose changes in voltage.

Inductors oppose changes in current.