I need to reduce the fontsize of only one equation/formula because it's too long

Question

\begin{equation}
\left| Y(j \omega) \right| = \sqrt{\frac{\omega^2 \left( C\ped{DC} + C\ped{eq} \right)^2 + \omega^4 \left[ \left( R\ped{eq} C\ped{eq} C\ped{DC} \right)^2 - 2 \left(  C\ped{DC} + C\ped{eq} \right) \left( L\ped{eq} C\ped{eq} C\ped{DC} \right) \right] + \omega^6 \left( L\ped{eq} C\ped{eq} C\ped{DC} \right)^2}{1 + \omega^2 \left[ \left( R\ped{eq} C\ped{eq} \right)^2 - 2 L\ped{eq} C\ped{eq} \right] + \omega^4 \left( L\ped{eq} C\ped{eq} \right)^2}}.
\label{eq:cmut:abs_y_w_eq}
\end{equation}

Hi. This is an equation I have to write. It's too long. (I cannot show you the results because I don't have enough reputation points to post images). How can I reduce the fontsize of the equation (without reducing the fontsize of the number of the reference)? Any suggestion to solve this problem? Thank you.

Answer 1

Reducing the size won't help; assuming the standard settings for 10pt article on A4 paper, even at \scriptsize the formula is too wide. With \tiny it is not overfull, but it becomes unreadable.

A possibility is to avoid the radical, squaring the left hand side, and using multlined from the mathtools package for the numerator:

\documentclass[a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc} % or other encoding
\usepackage[italian]{babel}

\usepackage{amsmath,mathtools}

\begin{document}
\begin{equation}
\lvert Y(j \omega) \rvert^2 =
  \frac{
    \begin{multlined}[b]
    \omega^2 ( C\ped{DC} + C\ped{eq} )^2 \\
    \qquad{} +\omega^4 [ ( R\ped{eq} C\ped{eq} C\ped{DC} )^2 -
      2 (C\ped{DC} + C\ped{eq} ) ( L\ped{eq} C\ped{eq} C\ped{DC} ) ] \qquad\\
    {} + \omega^6 ( L\ped{eq} C\ped{eq} C\ped{DC} )^2
    \end{multlined}
   }
   {
    1 + \omega^2 [ ( R\ped{eq} C\ped{eq} )^2 - 2 L\ped{eq} C\ped{eq} ] +
    \omega^4 ( L\ped{eq} C\ped{eq} )^2  
   }.
\label{eq:cmut:abs_y_w_eq}
\end{equation}
\end{document}

The two \qquad commands are just to widen the middle row which shouldn't be broken, but becomes the longest, spoiling the alignment.

Don't overuse \left and \right; in this formula none of them is needed.

A different strategy might be to use symbolic names for the coefficients: with the same preamble as before (but mathtools is not necessary), you can write

\begin{align}
\lvert Y(j \omega) \rvert &=
\sqrt{
  \frac{X_2 \omega^2 + X_4 \omega^4 + X_6 \omega^6}
   {1 + Y_2 \omega^2 + Y_4 \omega^4}
},\\[2ex]
%%%
X_2 &= ( C\ped{DC} + C\ped{eq} )^2
\notag\\
X_4 &= ( R\ped{eq} C\ped{eq} C\ped{DC} )^2 -
      2 (C\ped{DC} + C\ped{eq} ) ( L\ped{eq} C\ped{eq} C\ped{DC} )
\notag\\
X_6 &= ( L\ped{eq} C\ped{eq} C\ped{DC} )^2
\notag\\
Y_2 &= ( R\ped{eq} C\ped{eq} )^2 - 2 L\ped{eq} C\ped{eq}
\notag\\
Y_4 &= ( L\ped{eq} C\ped{eq} )^2
\notag
\end{align}

and get the following result