AC waveform
Alternating current changes direction repeatedly. A sine wave is a common AC waveform. One complete cycle has a positive half and a negative half. Frequency is the number of cycles each second.
Frequency and time period
Frequency is measured in hertz (Hz). Time period is the time for one cycle. They are reciprocals.
f = 1/T | T = 1/f
Peak, peak-to-peak and instantaneous values
Peak value is the maximum value from zero. Peak-to-peak value is the difference between the positive and negative peaks. Instantaneous value is the value at one particular moment.
RMS value
RMS means root mean square. For a sine wave, RMS is the DC value that would produce the same heating effect in a resistor. Do not apply the sine-wave conversion to every waveform.
Vrms = Vpeak / √2 | Irms = Ipeak / √2
Average value
The average of a complete symmetrical sine wave is zero. The average over one half-cycle is 0.637 times the peak value. This half-cycle value is useful when studying rectifier output.
Phase
Phase describes the position of a waveform within its cycle. Two signals can have the same frequency but different phase. A phase difference is measured in degrees or radians.
Inductive reactance
An inductor opposes AC through inductive reactance. This reactance increases as frequency or inductance increases.
XL = 2πfL
Capacitive reactance
A capacitor opposes AC through capacitive reactance. This reactance falls as frequency or capacitance increases.
XC = 1/(2πfC)
Impedance
Impedance is the combined opposition of resistance and reactance in an AC circuit. It is measured in ohms. In a series RLC circuit, impedance depends on the difference between inductive and capacitive reactance.
Z = √[R² + (XL − XC)²]
Series and parallel RLC circuits
A series RLC circuit carries the same current through R, L and C. A parallel RLC circuit has the same voltage across its branches. Their impedance and current behaviour change with frequency.
Power factor
In a sinusoidal AC circuit, power factor is the cosine of the phase angle between voltage and current. A purely resistive load has a power factor of one. Inductive and capacitive loads can have a lower value.
Power factor = cos φ
Audio- and radio-frequency transformers
Audio transformers operate over an audio frequency range. RF transformers operate at radio frequencies and need suitable core materials, winding layout and low parasitic capacitance. Transformers can provide isolation, voltage change and impedance matching.