Electromyography (EMG) Explained: Signal Acquisition & Processing

Electrical circuits is a course teaching how to utilize materials and energy sources effectively, covering communications, computers, industry, hardware, and software. Circuit theory is a mathematical approach for solving circuit equations, easier than electromagnetism which involves more complex equations. Three conditions must be met to use circuit theory: (1) Electrical effects must occur simultaneously in all system parts (lumped parameter system), meaning signal wavelength must be much larger than system dimensions; (2) Net charge of all components must equal zero; (3) No magnetic coupling between components. For a 50 Hz signal with wavelength 6 × 10^6 meters, system dimensions must be ≤ 6 × 10^5 meters to qualify as lumped parameter. Electric charge (Q) is discrete, with elementary charge of an electron being approximately 1.6 × 10^-19 coulombs. Voltage (V) is defined as work done per unit charge (V = W/Q). Current (I) is the rate of charge flow (I = dQ/dt), measured in amperes. Charge is discrete but current appears continuous because it involves collective movement of many discrete charges. When analyzing circuits, reference directions must be established using arrows for current and plus/minus signs for voltage. For current: if calculated value is positive, actual current flows in assumed direction; if negative, it flows opposite. For voltage: plus sign indicates higher potential point, minus indicates lower potential point. Ideal components in circuit theory have three characteristics: (1) Exactly two terminals; (2) Can be described mathematically using voltage and current relationships; (3) Can be simplified to basic mathematical expressions. Examples include ideal resistors, capacitors, and inductors. Voltage drop occurs when moving from higher to lower potential (plus to minus reference), while voltage rise occurs when moving from lower to higher potential (minus to plus reference). Conventional current direction is defined as positive charge flow direction, opposite to actual electron movement. This convention was established historically and remains standard in circuit analysis.

Circuit theory is the foundational subject of electrical engineering that all students must master first. Without understanding circuit theory, studying other electrical subjects becomes impossible. The instructor uses a water tank analogy to explain voltage (height of water), current (flow of water), and resistance (obstacles impeding flow). Electric current is defined as the amount of electric charge passing through a cross-section in one second, measured in amperes (A). The elementary charge of an electron is approximately 1.6 × 10^-19 coulombs. In electrical circuit analysis, direct current (DC) is represented by uppercase letters (I, V, R), while alternating current (AC) is represented by lowercase letters (i, v, r). Voltage is measured in volts (V) and represents the electric potential difference between two points. Resistance is the property of a material that opposes the flow of electric current, named from the Latin word 'resistere' meaning to resist or oppose. The unit of resistance is the ohm (Ω), named after Georg Ohm. Conductance is the reciprocal of resistance, measured in siemens (S), and is useful for calculating parallel circuits. The work done (energy transferred) in an electric circuit is given by the formula W = V × Q.

Current is electron flow measured in amperes, voltage is electrical potential difference measured in volts, and impedance is resistance in AC circuits. Power equals voltage multiplied by current (watts). Ohm's Law states current is directly proportional to voltage and inversely proportional to impedance. Using a water tower metaphor: voltage represents height, current represents flow rate, and impedance represents spigot width. Higher impedance (fat, scarred, or coagulated tissue) reduces current flow even at constant voltage, potentially causing unintended current paths through nearby tissue.

An electrical circuit is a complete path for current flow consisting of conductors and components. The three fundamental properties are voltage (V, measured in volts), current (I, measured in amperes), and resistance (R, measured in ohms). Current represents the flow of electric charge, with one ampere equal to 6.25 × 10^18 electrons passing per second. Two theories explain current flow: conventional current (from positive to negative terminal) and electron flow (from negative to positive terminal). Engineering disciplines typically use conventional current, while science uses electron flow theory. Both are valid as long as consistency is maintained in analysis.

Electric circuit theory introduces fundamental concepts including electric circuits as interconnections of circuit elements (resistors, capacitors, ammeters), electric charge as an electrical property of atoms, electric current as the rate of change of charge with respect to time (i = dq/dt), where one ampere equals one coulomb of charge flowing in one second, direct current (DC) as constant current, alternating current (AC) as sinusoidally varying current, voltage as the energy required to move a unit charge away from an electric field (V = dw/dq), and power as the rate of energy transfer (P = VI), with power flowing from sources to sinks.

The complete signal processing chain involves: (1) Analog-to-Digital conversion (sampling) that maps continuous-time spectra to discrete-time spectra; (2) Processing in the discrete domain using frequency response H(e^(jω̂)); (3) Digital-to-Analog conversion (reconstruction) that maps back to continuous-time. An anti-aliasing filter precedes A/D conversion to remove frequencies above the Nyquist frequency (half the sample rate). The conversion process involves dividing by the sampling rate when putting on the hat (going to discrete domain) and multiplying by the sample rate when taking it off (returning to continuous domain). Frequencies can only be accurately reconstructed up to half the original sample rate.

The conversion of analog signals to digital signals is called sampling, performed by an Analog-to-Digital Converter (ADC). The ADC contains a sampler that takes discrete samples from continuous analog signals. Analog signals have infinite values because they are continuous over time, which digital systems cannot process directly. The sampling interval (T_s) is the time between consecutive samples. A smaller sampling interval results in more samples and better signal quality. Frequency is the number of signal cycles per second, measured in Hertz. When samples are taken with large intervals, the reconstructed signal appears distorted. After sampling, the signal becomes discrete-time (defined only at specific points) while values remain continuous. If sampling is performed incorrectly, signal distortion occurs. The sampler performs a 'sample and hold' operation, capturing the signal value and holding it constant for a duration equal to the sampling interval.

ADC converts continuous analog signals to discrete digital quantities through four stages: filtering (removing unwanted frequencies), sampling (capturing instantaneous values), holding (maintaining stable input), and quantization (assigning digital values). The Nyquist Sampling Theorem requires sampling at least twice the highest signal frequency. Quantization divides the signal range into discrete levels—more bits provide finer resolution and closer digital approximations. Higher bit counts and faster sampling rates together improve signal fidelity, transforming smooth analog waveforms into stepped digital representations.

Computers cannot process analog signals directly, so an analog-to-digital converter (ADC) is used. The ADC divides the continuous signal into equal time intervals called samples. The frequency of these samples is called the sampling rate, measured in samples per second (Hz). For example, 44.1 kHz means the amplitude is measured 44,100 times per second.

Signal processing involves sampling, reconstruction, and aliasing. The workflow converts analog signals (like microphone input) to digital through ADC, processes them with microprocessors (smartphones, computers), then reconstructs them to analog via DAC. Band-limited signals contain frequencies up to a maximum bandwidth. Anti-aliasing filters remove high frequencies before sampling. Ideal sampling converts continuous signals to discrete digital signals by taking samples at regular intervals determined by sampling frequency fs = 1/ts. The digital signal x[n] consists of floating-point values representing signal values at discrete time points. CD audio uses 44,100 samples/second. The Fourier transform converts signals from time to frequency domain, showing how sampling creates periodic spectral replicas at multiples of fs.