4.3 AC/DC Circuit Fundamentals and Passive Components

4.3 AC/DC Circuit Fundamentals and Passive Components

Modern biomedical devices operate using a combination of alternating current (AC) and direct current (DC). Power distribution networks and building outlets supply AC, whereas the internal microelectronics, displays, and sensors of medical equipment require regulated DC. To bridge this gap and manipulate these electrical signals, circuits utilize passive components. The three fundamental passive components are resistors, capacitors, and inductors, which behave differently depending on whether they are exposed to AC or DC signals.

AC vs. DC Fundamentals

Understanding the distinctions between Alternating Current (AC) and Direct Current (DC) is critical for troubleshooting power supplies and ensuring electrical safety in patient-care areas.

Direct Current (DC)

In a DC circuit, charge carriers (electrons) flow continuously in a single direction. The voltage and current remain relatively constant over time. Common sources of DC power include batteries (used in portable patient monitors, infusion pumps, and telemetry transmitters) and DC power supplies that convert building AC power to low-voltage DC (typically $3.3\text{ V}$, $5\text{ V}$, or $12\text{ V}$) to run digital circuits.

Alternating Current (AC)

In an AC circuit, the flow of charge carriers periodically reverses direction. The voltage and current vary sinusoidally over time, alternating between positive and negative peaks. The rate of this alternation is the frequency, measured in Hertz ($Hz$, cycles per second). In North America, standard wall outlet power is supplied at $120\text{ V}$ AC at a frequency of $60\text{ Hz}$. In Europe and many other regions, the standard is $230\text{ V}$ AC at $50\text{ Hz}$.

Because AC voltage fluctuates, we use the Root Mean Square (RMS) value to describe its effective voltage. The RMS voltage represents the equivalent DC voltage that would produce the same heating effect in a resistor. The relationship between RMS voltage and peak voltage ($V_{peak}$) for a sinusoidal wave is:

$V_{RMS} = 0.707 \times V_{peak} \quad \text{or} \quad V_{peak} = 1.414 \times V_{RMS}$

For example, a $120\text{ V}$ AC mains supply actually has a peak voltage of approximately $170\text{ V}$ ($120 \times 1.414$).

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Passive Components: Resistors

Resistors are components designed to introduce a specific amount of electrical resistance into a circuit. They are used to limit current, divide voltages, and establish bias levels.

Resistor Color Coding

Axial lead resistors are marked with colored bands to indicate their resistance value, multiplier, and tolerance. The standard 4-band system is read from left to right (with the tolerance band, usually gold or silver, positioned on the far right):

• 1st Band: First digit of resistance value
• 2nd Band: Second digit of resistance value
• 3rd Band: Multiplier (power of 10)
• 4th Band: Tolerance (accuracy of the nominal value)

Color Code Worked Example

A resistor has bands of Red, Red, Orange, and Gold.

1. Red = 2 (1st digit)
2. Red = 2 (2nd digit)
3. Orange = $\times 1,000$ or $10^3$ (Multiplier)
4. Gold = $\pm 5\%$ (Tolerance)

• Calculation: $22 \times 1,000 = 22,000\ \Omega = 22\text{ k}\Omega$ with a tolerance of $\pm 5\%$. The actual resistance will measure between $20.9\text{ k}\Omega$ and $23.1\text{ k}\Omega$.

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Passive Components: Capacitors

A capacitor consists of two conductive plates separated by an insulating material called a dielectric. It stores electrical energy in an electrostatic field created between the plates.

Key Concepts

• Capacitance ($C$): The ability to store electrical charge. Measured in Farads ($F$). Because the Farad is a very large unit, capacitors in medical devices are typically rated in microfarads ($\mu F$), nanofarads ($\text{nF}$), or picofarads ($\text{pF}$).
• Energy Storage Formula: The energy ($E_C$, in Joules) stored in a capacitor is: $E_C = \frac{1}{2} C V^2$ This formula is critical for defibrillators, which charge a large internal capacitor to high voltages ($V$) to store energy that is then discharged into the patient's heart.
• AC vs. DC Behavior:
  • DC: A capacitor blocks DC. When connected to a DC source, current flows only until the capacitor is fully charged, at which point it acts as an open circuit.
  • AC: A capacitor allows AC to pass. As AC voltage alternates, the capacitor continuously charges and discharges, resulting in an AC current flow. The opposition to this flow is called capacitive reactance ($X_C = \frac{1}{2\pi f C}$), which decreases as frequency increases.
• Combinations:
  • Parallel: $C_{total} = C_1 + C_2 + C_3 + \dots$
  • Series: $\frac{1}{C_{total}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} + \dots$

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Passive Components: Inductors and Transformers

An inductor is a passive component, typically consisting of a coil of wire wrapped around a core (air, iron, or ferrite). It stores energy in a magnetic field generated by current flowing through the coil.

Inductors

• Inductance ($L$): The property that opposes any change in electrical current. Measured in Henries ($H$).
• Energy Storage Formula: The energy ($E_L$, in Joules) stored in an inductor is: $E_L = \frac{1}{2} L I^2$
• AC vs. DC Behavior:
  • DC: An inductor passes DC. Once the magnetic field stabilizes, an inductor acts as a simple short circuit (neglecting the small resistance of the wire).
  • AC: An inductor opposes AC. Because AC current is constantly changing, the inductor continuously generates a back-electromotive force (back-EMF) that opposes the current change. This opposition is inductive reactance ($X_L = 2\pi f L$), which increases with frequency.

Transformers

A transformer uses the principle of electromagnetic induction (mutual inductance) to transfer electrical energy from one AC circuit to another without direct electrical connection. It consists of two or more coils (primary and secondary windings) wrapped around a shared magnetic core.

• Step-Up Transformer: Has more turns on the secondary coil ($N_s > N_p$), which increases the output voltage ($V_s > V_p$) while decreasing output current.
• Step-Down Transformer: Has fewer turns on the secondary coil ($N_s < N_p$), which decreases the output voltage ($V_s < V_p$) while increasing output current. This is standard in linear DC power supplies to drop mains $120\text{ V}$ AC down to safe levels like $12\text{ V}$ AC before rectification.
• Isolation Transformer: Has a 1:1 turns ratio ($N_s = N_p$). Its primary purpose is not to change voltage, but to electrically isolate patient-connected equipment from the building ground, drastically reducing the risk of electric shock (microshock and macroshock).

The relationship between voltages, currents, and turns is governed by:

$\frac{V_p}{V_s} = \frac{N_p}{N_s} = \frac{I_s}{I_p}$