Define the wave form.

A waveform is the shape or profile of a signal (like voltage or current) as a function of time, often displayed on an oscilloscope.

The time period ($T$) is the time taken for one complete cycle of a periodic waveform to occur. It is the reciprocal of frequency ($T = \frac{1}{f}$).

Radio frequency (RF) refers to any frequency within the electromagnetic spectrum associated with radio wave propagation, typically ranging from about $3 \text{ kHz}$ to $300 \text{ GHz}$.

The Root Mean Square (RMS) value of a sine wave is the effective value of an AC voltage or current, equivalent to the DC voltage or current that would produce the same amount of heat in a resistive load. For a sine wave, $V_{rms} = \frac{V_{peak}}{\sqrt{2}}$.

The crest factor is the ratio of the peak value to the RMS value of a waveform. For a sine wave, the crest factor is $\sqrt{2}$ or approximately 1.414.

The instantaneous value of a sine wave is its magnitude at any specific point in time. It is typically represented by $v(t) = V_m \sin(\omega t + \phi)$ for voltage or $i(t) = I_m \sin(\omega t + \phi)$ for current.

Two alternating quantities (like voltage and current) are said to be inphase when they reach their maximum, minimum, and zero values at the same instant in time.

Phase lead occurs when one alternating quantity (e.g., voltage) reaches its maximum or zero value earlier in time than another alternating quantity (e.g., current).

• Voltage and current are always in phase.
• It dissipates electrical energy entirely as heat.

Capacitive reactance ($X_C$) is the opposition offered by a capacitor to the flow of alternating current. It is measured in ohms ($\Omega$) and is inversely proportional to both frequency and capacitance ($X_C = \frac{1}{2\pi f C}$).

In a pure capacitive circuit, the current leads the voltage by $90^\circ$ (or $\frac{\pi}{2}$ radians).

Impedance ($Z$) is the total opposition to the flow of alternating current in an AC circuit, combining both resistance and reactance. Its unit is the ohm ($\Omega$).

• The voltage across the inductor leads the current by $90^\circ$, while the voltage across the resistor is in phase with the current.
• The total impedance is $Z = \sqrt{R^2 + X_L^2}$.

The Q-factor (Quality factor) of a coil (inductor) is a measure of its energy storage capability relative to its energy dissipation per cycle. It is the ratio of its inductive reactance to its resistance ($Q = \frac{X_L}{R}$).

The skin effect is the tendency of alternating current (AC) to flow predominantly near the surface of a conductor, rather than uniformly throughout its cross-section, especially at higher frequencies.

Susceptance ($B$) is the imaginary part of admittance, representing the ease with which alternating current flows through a reactive component (capacitor or inductor). Its unit is the siemens (S).

True power (or real power, $P$) in an AC circuit is the actual power consumed by the resistive components and converted into useful work or heat. It is measured in watts (W) and is calculated as $P = V_{rms} I_{rms} \cos\theta$, where $\cos\theta$ is the power factor.

A transformer works on the principle of mutual induction. When an alternating current flows through the primary coil, it produces a continuously changing magnetic flux, which links with the secondary coil and induces an electromotive force (EMF) in it.

The turn ratio of a transformer is the ratio of the number of turns in the secondary winding ($N_s$) to the number of turns in the primary winding ($N_p$), i.e., $\frac{N_s}{N_p}$. It determines the voltage and current transformation.

• Air-core transformer
• Iron-core transformer (including laminated iron core)
• Ferrite-core transformer

An autotransformer is a type of transformer that has only one winding, which acts as both the primary and secondary winding. It has a common portion of the winding shared by both circuits, allowing for voltage transformation by tapping different points on the single coil.

The resonant frequency ($f_r$) of an LC circuit is the specific frequency at which the inductive reactance ($X_L$) equals the capacitive reactance ($X_C$), causing the circuit to behave purely resistively and allowing maximum current flow (in series) or maximum impedance (in parallel).

• Series resonant circuit
• Parallel resonant circuit

The purpose of a filter circuit is to selectively pass certain frequencies of a signal while attenuating or blocking others. They are used to remove unwanted noise, separate signals, or smooth out rectified AC voltage.