# Loss tangent ($$\tan{\delta}$$)

The loss tangent (generally shown as "$$\tan{\delta}$$") is defined as —

\begin{align} \label{eq:13501a} \tan{\delta} = \frac{\textsf{Resistive impedance}}{\textsf{Reactive impedance}} \end{align}

For a capacitor —

\begin{align} \label{eq:13502a} \tan{\delta} &= \frac{R_C}{(1/2\pi \, f \, C)} \\[0.7em]%eqn_interline_spacing &= R \, (2\pi \, f \, C) \nonumber \end{align}

For an inductor —

\begin{align} \label{eq:13503a} \tan{\delta} &= \frac{R_L}{(2\pi \, f \, L)} \end{align}

where —

 $$R_C$$ = equivalent resistance of capacitor $$R_L$$ = equivalent resistance of inductor $$C$$ = capacitance $$L$$ = inductance $$f$$ = frequency

A smaller loss tangent is generally preferred. For a "perfect" system (i.e., no energy dissipation), the loss tangent is 0.

The loss tangent is the inverse of the Q (quality factor):

\begin{align} \label{eq:13504a} Q = \frac{1}{\tan{\delta}} \end{align}

The loss tangent is often included in the properties of piezoelectric ceramics. Unlike for most acoustic materials, the loss tangent for piezoelectric ceramics is not fixed but depends on factors such as the static prestress, the electric field strength, etc.