Week 8: Alternating current

Question 1

Define direct current

Answer 1

Direct: refers to when electricity flows constantly in one direction, voltage remains steady over time & current does not change direction e.g., in batteries

Question 2

Define alternating current

Answer 2

AC: refers to when electricity repeatedly reverses in flow direction, current flows one way & then the other, Voltage changes periodically, e.g., ECG

Question 3

Define the terms period and frequency

Answer 3

Period (T): Time taken for one cycle to complete

Frequency (f): Number of cycles per second (Hz)
f=1/T

Question 4

Define a Capacitors

Answer 4

Stores electrical charge in two plates separated by a gap or dielectric .

Capacitance depends on:
1. Plate area
2. Distance between plates
3. Material between them

Question 5

Define Capacitance reactance

Answer 5

Capacitive reactance is the opposition that a capacitor presents to the flow of alternating current (AC). It depends on the frequency of the signal and the capacitance value.
measured in ohms (Ω).
Reactance of a capacitor is infinite when DC is 0
As frequency increases, capacitive reactance decreases → the capacitor allows AC to pass more easily.

As frequency decreases, capacitive reactance increases → the capacitor blocks low-frequency signals.

At 𝑓=0 (DC), capacitive reactance is infinite → a capacitor blocks DC.

Question 6

Define Capacitance

Answer 6

Definition: Capacitance is the property of a component (typically a capacitor) that allows it to store electrical energy in an electric field.

Unit: Farads (F)

Behavior: Capacitors oppose changes in voltage by storing and releasing charge.

In AC circuits: Capacitors cause current to lead the voltage
C=Q/V
C= Capacitance
Q= charge
V=voltage

Question 7

Define impedance

Answer 7

Impedance is the total opposition that a circuit or component presents to the flow of alternating current (AC). It combines both resistance (real opposition to current) and reactance (opposition due to capacitors and inductors) into a single quantity.

Impedance is denoted by
𝑍
Z and measured in ohms (Ω).

Question 8

Define inductance

Answer 8

Definition: Inductance is the property of a component (typically an inductor) that resists changes in current by storing energy in a magnetic field.

Unit: Henrys (H)

Behavior: Inductors oppose changes in current and generate a voltage that counters the change.

In AC circuits: Inductors cause current to lag behind the voltage

L=Φ/I
L= inductance
Φ= magnetic flux
I= current producing the flux

Question 9

Define reactance

Answer 9

Definition: Reactance is the opposition to alternating current (AC) caused by either inductance or capacitance.

Unit: Ohms (Ω)

Types:
1. Inductive Reactance, Increases with frequency.
2. Capacitive Reactance , Decreases with frequency.

Behavior: Reactance affects the phase relationship between voltage and current but does not dissipate energy as heat like resistance does.

Question 10

Describe frequency domain

Answer 10

The frequency domain is a way of representing a signal, system, or dataset in terms of the frequencies it contains, rather than how it changes over time (time domain) or space. Represents how much of the signal lies within each frequency band.

Example: An ECG signal transformed to show dominant frequencies (like heart rate).

Frequency domain = signal vs frequency.

Question 11

Describe the time domain

Answer 11

The time domain is a way of representing a signal or system by showing how it changes over time
Time-domain representation shows the shape, duration, timing, and transients of a signal.

Most raw measurements (sound waves, ECG signals, temperature records) are first observed in the time domain.

Signals can be transformed from the time domain to the frequency domain using Fourier analysis.

Example: An ECG waveform showing heartbeats over seconds.
Useful for observing when events happen.
Time domain = signal vs time.

Question 12

Define fourier analysis

Answer 12

Fourier analysis is a mathematical method used to break down any complex signal or function into a sum of simpler sinusoidal components—sine and cosine waves—at different frequencies.

Fourier analysis transforms a signal from the time domain into the frequency domain.

It Helps identify the frequency components of any signal. e.g., amplitude, phases and what frequencies are present

Crucial for understanding the spectral content of ECG signals

Question 13

Define a fourier series and it’s key features

Answer 13

It breaks down periodic signals into a sum of sine and cosine waves. Each wave has a specific frequency, amplitude, and phase.
e.g., A square wave can be represented as a sum of sine waves.

Key features:
- Only sine terms: The sawtooth wave is odd-symmetric, so its Fourier series contains only sine components.
- Amplitude decay: The amplitude of each harmonic is inversely proportional to its harmonic number (n), i.e., (1/n).
- Alternating signs: Each term alternates in sign, contributing to the sharp drop characteristic of the waveform.
- Convergence: The series converges pointwise except at discontinuities, where it exhibits Gibbs phenomenon (overshoot near the jump).

Question 14

Describe the fourier analysis of a sawtooth wave

Answer 14

A sawtooth wave is a periodic function that increases linearly over time and then sharply drops.
Fourier analysis of a sawtooth wave reveals that it can be decomposed into an infinite sum of sine functions with linearly decreasing amplitudes and alternating signs. This series converges to the original waveform over its period.

Question 15

Define harmonic composition

Answer 15

Refers to the structure of a complex signal
A Harmonic wave is an integer multiple of the fundamental frequency that makes up a signal.

Harmonic composition = the set of harmonic frequencies + their relative strengths that combine to form a complex periodic signal.
Determines the shape & sound quality of a signal

HC is determined using fourier analysis

Question 16

Describe frequency response & what is considered an inadequate response

Answer 16

FR: Refers to how a system behaves at different input frequencies, e.g., level of amplification or attenuation across spectrum.
A good FR should pass all relevant frequencies without distortion.
A measurement system must have a FR that matches the signal it’s measuring

Inadequate: If a system filters out or distorts key frequencies, the signal gets corrupted.
Example: If an ECG monitor can’t handle low frequencies, it might miss slow heart rhythms.

Question 17

Describe the frequency composition of an ECG

Answer 17

Most ECG content is below 40 Hz
Full range ~0.67 to 150 Hz (adults) based on AHA/SCST guidelines.

If your measurement system does not capture the full frequency range, the ECG becomes distorted.

Ambulatory provides an approximation, only records frequency up to 40 Hz, any sine waves above 40 Hz are rejected

12-lead has a higher frequency to provide greater diagnostic information.

ECG signals contain multiple frequency components:
- P wave: low frequency (~0.5–5 Hz)
- QRS complex: higher frequency (~10–40 Hz)
- T wave: intermediate (~1–7 Hz)

Question 18

Define noise & signal

Answer 18

Noise: any unwanted artefact or interference that interrupts the signal we want to measure, e.g., in audio a hiss or in imaging pixel distortion.
Noise masks/ distorts the signal

Signal: Refers to the desired information you want to detect/measure or analyse

Question 19

Describe the signal to noise ratio

Answer 19

A measure that compares the desired strength of a signal to the amount of unwanted interference (noise) present in a system

SNR=signal/noise

A higher SNR provides a cleaner ECG, as the signal is greater than the noise

Question 20

Name common sources of noise in a hospital

Answer 20

1. Mains: 50 Hz
2. Muscle activity: 25 Hz-KHz
3. Bleep (50 MHz-500 MHz)
4. Mobile phones / radios 900 MHz- 2 GHZ
5. Fluorescent lights: ~100 Hz

Question 21

Describe noise reduction techniques

Answer 21

1. Removal of a noise source e.g., lights or computer
2. Relax the patient, e.g., stop tremors
3. Use of screening rooms
4. Use of differential amplifiers & Twisted wires to remove common mode noise by ensuring wires receive equal noise
5. Filtering, selectively removes signals of a particular frequency or range of frequencies
6. Signal averaging, signal is acquired many times and averaged, requires a regular signal and irregular noise