Measurement of Sine Waves

At any point in time on a sine wave, the voltage has an instantaneous value. As a cycle represents a continuous set of instantaneous values, other dimensions have been defined to enable comparing one wave to another. The peak value U_p is the maximum value. It applies to either the positive or negative peak. The peak-to-peak value,U_pp, is the voltage (or current) from the positive peak to the negative peak. Average value is an arithmetic average of all the values in a sine wave for one half-cycle, where U_avr = 0.637 U_p

RMS Value

To compare AC and DC voltage, the effective value of the AC voltage should be calculated using the root-mean-square (rms) value of the sinusoidal voltage. The (rms) value of a sinusoidal voltage or current is equal to the dc voltage and current that produces the same heating effect. The formula is U_rms = 0.707 U_p. The factor 0.707 for rms value is derived as the square root of the average (mean) of all the squares of the sine wave. To convert from rms to peak value, the formula U_p = 1.414 U_rms is used. Unless indicated otherwise, all sine wave ac measurements are in rms values.

Phase Angle

The angular measurement of a sine wave can be related to the angular rotation of an AC generator, as shown in the diagram above. It is based on 360^o of rotation for the complete cycle of a sine wave. The diagram shows angles in degrees over the full cycle of a sine wave. Since 360^o = 2π rad, angles can be also expressed in radians using the formula in the illustration above.
The phase angle of a sine wave specifies the position of that sine wave relative to a reference. The illustration shows the phase shifts of a sine wave. There is a phase angle of 30^o between sine wave A and sine wave B.

Laws of Resistive AC Circuits

Ohm's Law and Kirchoff's Law apply to AC circuits in the same way they apply to DC circuits. If a sinusoidal voltage is applied across a resistor, there is a sinusoidal current. It is zero when the voltage is zero, and is max. when the voltage is max. The voltage and the current are in phase with each other.
In a resistive circuit that has an AC voltage source, the source voltage is the sum of all the voltage drops, just as in a DC circuit. Remember, both the voltage and the current must be expressed in the same way, i.e., both in rms, both in peak, etc.

Superimposed DC and AC Voltages

Many practical circuits use both DC and AC voltages combined. For example, an amplifier needs DC voltages in order to conduct any current. When a small AC signal is applied to the input, the resulting output of an amplifier consists of DC with a superimposed AC signal.
The figure shows DC and AC sources in series. These two voltages add up algebraically. If U_dc is greater than the peak value of the sinusoidal voltage, the combined AC and DC voltage is a sine wave that never reverses polarity. That is, the sine wave is riding on a DC level. If U_dc is less than the U_p, the sine wave will be negative during a portion of its lower half-cycle.

Non-Sinusoidal AC Waveforms

The pulse and the triangular waveform are the other two major types of signals widely used in electronics. Any waveform that repeats itself at fixed intervals is periodic. The periodis denoted with a T. Triangular waveforms are formed by voltage or current ramps. A ramp is a linear increase or decrease in the voltage.
An ideal pulse consists of two equal but opposite steps separated by an interval of time called the pulse width. The duty cycle of the pulse is the ratio of the pulse width to the period and is usually expressed in a percentage.