0
\documentclass[11pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{listings}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
Similarly, the state-space averaging is used to described the AC small signal dynamics:
\begin{multline}
\begin{bmatrix}
L_1 & 0 & 0 & 0\\
0 & L_2 & 0 & 0\\
0 & 0 & C_1 & 0\\
0 & 0 & 0 & C_2
\end{bmatrix} \frac{d}{dt} \begin{bmatrix}
i_{L1}(t)\\
i_{L2}(t)\\
v_{C1}(t)\\
v_{C2}(t)
\end{bmatrix} =\\ \begin{bmatrix}
0 & 0 & D & -D'\\
0 & 0 & -D' & D\\
-D & D' & -\frac{D'}{R_l} & -\frac{D'}{R_l}\\
D' & -D & -\frac{D'}{R_l} & -\frac{D'}{R_l}
\end{bmatrix} \cdot \begin{bmatrix}
i_{L1}(t)\\
i_{L2}(t)\\
v_{C1}(t)\\
v_{C2}(t)
\end{bmatrix} + \begin{bmatrix}
D'\\
D'\\
\frac{D'}{R_l}\\
\frac{D'}{R_l}
\end{bmatrix} \cdot \hat{v}_g(t) + \\ \begin{bmatrix}
V_{C1} + V_{C2} -(V_g - V_D)\\
V_{C1} + V_{C2} -(V_g - V_D)\\
-I_{L1} -I_{L2} + \frac{V_{C1}}{R_l} + \frac{V_{C2}}{R_l} - \frac{V_g - V_D}{R_l}\\
-I_{L1} -I_{L2} + \frac{V_{C1}}{R_l} + \frac{V_{C2}}{R_l} - \frac{V_g - V_D}{R_l}
\end{bmatrix} \cdot \hat{d}(t)
\end{multline}
Also, $\hat{v}_{C1}(t) = \hat{v}_{C2}(t) = \hat{v}_C(t) \ and \ \hat{i}_{L1}(t) = \hat{i}_{L2}(t) = \hat{i}_L(t)$. While DC state equations are:
\begin{equation}
\begin{bmatrix}
0\\
0\\
0\\
0
\end{bmatrix} = \begin{bmatrix}
0 & 0 & D & -D'\\
0 & 0 & -D' & D\\
-D & D' & -\displaystyle\frac{D'}{R_l} & -\displaystyle\frac{D'}{R_l}\\
D' & -D' & -\displaystyle\frac{D'}{R_lZ_l} & -\displaystyle\frac{D'}{R_l}
\end{bmatrix}\cdot \begin{bmatrix}
I_{L1}\\
I_{L2}\\
V_{C1}\\
V_{C2}
\end{bmatrix} + \begin{bmatrix}
D'\\
D'\\
\displaystyle\frac{D'}{R_l}\\
\displaystyle\frac{D'}{R_l}
\end{bmatrix} \cdot (V_g - V_D)
\end{equation}
The state space equations hence become,
\begin{multline}
sL\cdot \hat{i}_L(s) = (D - D')\cdot \hat{v}_C(s) + D'\cdot \hat{v}_g(s) + (2V_C-V_g+V_D)\cdot \hat{d}(s) \\
sC\cdot \hat{v}_C(s) = (D'-D)\cdot \hat{i}_L(s) - \displaystyle\frac{2D'}{R_l} \hat{v}_C(s) + \displaystyle\frac{D'}{R_l} \hat{v}+g(s) + (-2I_L + 2\displaystyle\frac{2V_C}{r_l} - \displaystyle\frac{V_g-V_D}{R_l})\cdot \hat{d}(s)
\end{multline}
Steady state values are:
\begin{equation}
V_C = \displaystyle\frac{1-D}{1-2D} \cdot (V_g-V_D)
\end{equation}
and \\
\begin{equation}
I_L=\displaystyle\frac{1-D}{(1-2D)^2} \cdot \displaystyle\frac{V_g}{R_l}
\end{equation}
\end{document}

Warning: Overfull and Underfull.

  • A tip: If you indent lines by 4 spaces or enclose words in backticks `, they'll be marked as code, as can be seen in my edit. You can also highlight the code and click the "code" button (with "{}" on it). – user31729 Jun 3 '15 at 9:34
  • And some not so nice comment from me: You have posted some questions, with answers to it. Please consider to accept the answers – user31729 Jun 3 '15 at 9:37
  • The underfull message says it is on line 73 and that ends with \\ in your last question I told you how to fix that: remove the \\ – David Carlisle Jun 3 '15 at 9:56
  • @David Thank you. I shall keep that in mind. The thing is I have code running for over 2000 lines and it is difficult to keep track. I am just posting sections of it here, as soon as I repair 1 another seems to flag up. Thanks anyway. – Reddy Jun 3 '15 at 10:07
  • This question is an exact duplicate of your previous question (both the underfull and overfull parts of the question) I added an answer this time but am voting to close the question. Please don't ask duplicate questions. – David Carlisle Jun 3 '15 at 10:10
0

If I compile your code, I get the following warnings:

Overfull \hbox (33.51332pt too wide) detected at line 69

Underfull \hbox (badness 10000) in paragraph at lines 73--75

I assume you get the same error messages. Now with this it is really easy to get rid of the errors, you just have to go and look around those lines.

Line 68:

sC\cdot \hat{v}_C(s) = (D'-D)\cdot \hat{i}_L(s) - \displaystyle\frac{2D'}{R_l} \hat{v}_C(s) + \displaystyle\frac{D'}{R_l} \hat{v}+g(s) + (-2I_L + 2\displaystyle\frac{2V_C}{r_l} - \displaystyle\frac{V_g-V_D}{R_l})\cdot \hat{d}(s)

This is a very long formula, if you split it up on two lines or shorten it, the overfull warning will disappear.

Line 74:

and \\

As @David Carlisle mentioned in his comment, take away those \ and the warning will disappear.

When you encounter such warnings, the easiest way to solve them is to go see at the corresponding lines (as the warning will give you a line number) and see if deleting the line will make the warning go away. If it does, then you know where the error lies and can play around with that line until you find an acceptable solution.

  • 1
    I have been trying that. The problem is solved for now. I am new to latex and have a lot to do, so please bear with me. Thanks a lot! :) – Reddy Jun 3 '15 at 10:07
0

One solution on splitting the long equation is as follows (used align in place of multiline):

\documentclass[11pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{listings}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
Similarly, the state-space averaging is used to described the AC small signal dynamics:
\begin{multline}
\begin{bmatrix}
L_1 & 0 & 0 & 0\\
0 & L_2 & 0 & 0\\
0 & 0 & C_1 & 0\\
0 & 0 & 0 & C_2
\end{bmatrix} \frac{d}{dt} \begin{bmatrix}
i_{L1}(t)\\
i_{L2}(t)\\
v_{C1}(t)\\
v_{C2}(t)
\end{bmatrix} =\\ \begin{bmatrix}
0 & 0 & D & -D'\\
0 & 0 & -D' & D\\
-D & D' & -\frac{D'}{R_l} & -\frac{D'}{R_l}\\
D' & -D & -\frac{D'}{R_l} & -\frac{D'}{R_l}
\end{bmatrix} \cdot \begin{bmatrix}
i_{L1}(t)\\
i_{L2}(t)\\
v_{C1}(t)\\
v_{C2}(t)
\end{bmatrix} + \begin{bmatrix}
D'\\
D'\\
\frac{D'}{R_l}\\
\frac{D'}{R_l}
\end{bmatrix} \cdot \hat{v}_g(t) + \\ \begin{bmatrix}
V_{C1} + V_{C2} -(V_g - V_D)\\
V_{C1} + V_{C2} -(V_g - V_D)\\
-I_{L1} -I_{L2} + \frac{V_{C1}}{R_l} + \frac{V_{C2}}{R_l} - \frac{V_g - V_D}{R_l}\\
-I_{L1} -I_{L2} + \frac{V_{C1}}{R_l} + \frac{V_{C2}}{R_l} - \frac{V_g - V_D}{R_l}
\end{bmatrix} \cdot \hat{d}(t)
\end{multline}
Also, $\hat{v}_{C1}(t) = \hat{v}_{C2}(t) = \hat{v}_C(t) \ and \ \hat{i}_{L1}(t) = \hat{i}_{L2}(t) = \hat{i}_L(t)$. While DC state equations are:
\begin{equation}
\begin{bmatrix}
0\\
0\\
0\\
0
\end{bmatrix} = \begin{bmatrix}
0 & 0 & D & -D'\\
0 & 0 & -D' & D\\
-D & D' & -\displaystyle\frac{D'}{R_l} & -\displaystyle\frac{D'}{R_l}\\
D' & -D' & -\displaystyle\frac{D'}{R_lZ_l} & -\displaystyle\frac{D'}{R_l}
\end{bmatrix}\cdot \begin{bmatrix}
I_{L1}\\
I_{L2}\\
V_{C1}\\
V_{C2}
\end{bmatrix} + \begin{bmatrix}
D'\\
D'\\
\displaystyle\frac{D'}{R_l}\\
\displaystyle\frac{D'}{R_l}
\end{bmatrix} \cdot (V_g - V_D)
\end{equation}
The state space equations hence become,
\begin{align}
sL\cdot \hat{i}_L(s) &= (D - D')\cdot \hat{v}_C(s) + D'\cdot \hat{v}_g(s) + (2V_C-V_g+V_D)\cdot \hat{d}(s)\nonumber \\
sC\cdot \hat{v}_C(s) &= (D'-D)\cdot \hat{i}_L(s) - \displaystyle\frac{2D'}{R_l} \hat{v}_C(s)\nonumber\\
&\phantom{=} + \displaystyle\frac{D'}{R_l} \hat{v}+g(s) + (-2I_L + 2\displaystyle\frac{2V_C}{r_l} - \displaystyle\frac{V_g-V_D}{R_l})\cdot \hat{d}(s)
\end{align}
Steady state values are:
\begin{equation}
V_C = \displaystyle\frac{1-D}{1-2D} \cdot (V_g-V_D)
\end{equation}
and 
\begin{equation}
I_L=\displaystyle\frac{1-D}{(1-2D)^2} \cdot \displaystyle\frac{V_g}{R_l}
\end{equation}
\end{document}
  • I tried it, but didn't work for some reason. But aren't you using `\` which has been advised to not be used. – Reddy Jun 3 '15 at 10:10
0

This is a duplicate but since I hav ethis:

\documentclass[11pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{listings}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
Similarly, the state-space averaging is used to described the AC small signal dynamics:
\begin{multline}
\begin{bmatrix}
L_1 & 0 & 0 & 0\\
0 & L_2 & 0 & 0\\
0 & 0 & C_1 & 0\\
0 & 0 & 0 & C_2
\end{bmatrix} \frac{d}{dt} \begin{bmatrix}
i_{L1}(t)\\
i_{L2}(t)\\
v_{C1}(t)\\
v_{C2}(t)
\end{bmatrix} =\\ \begin{bmatrix}
0 & 0 & D & -D'\\
0 & 0 & -D' & D\\
-D & D' & -\frac{D'}{R_l} & -\frac{D'}{R_l}\\
D' & -D & -\frac{D'}{R_l} & -\frac{D'}{R_l}
\end{bmatrix} \cdot \begin{bmatrix}
i_{L1}(t)\\
i_{L2}(t)\\
v_{C1}(t)\\
v_{C2}(t)
\end{bmatrix} + \begin{bmatrix}
D'\\
D'\\
\frac{D'}{R_l}\\
\frac{D'}{R_l}
\end{bmatrix} \cdot \hat{v}_g(t) + \\ \begin{bmatrix}
V_{C1} + V_{C2} -(V_g - V_D)\\
V_{C1} + V_{C2} -(V_g - V_D)\\
-I_{L1} -I_{L2} + \frac{V_{C1}}{R_l} + \frac{V_{C2}}{R_l} - \frac{V_g - V_D}{R_l}\\
-I_{L1} -I_{L2} + \frac{V_{C1}}{R_l} + \frac{V_{C2}}{R_l} - \frac{V_g - V_D}{R_l}
\end{bmatrix} \cdot \hat{d}(t)
\end{multline}
Also, $\hat{v}_{C1}(t) = \hat{v}_{C2}(t) = \hat{v}_C(t) \ and \ \hat{i}_{L1}(t) = \hat{i}_{L2}(t) = \hat{i}_L(t)$. While DC state equations are:
\begin{equation}
\begin{bmatrix}
0\\
0\\
0\\
0
\end{bmatrix} = \begin{bmatrix}
0 & 0 & D & -D'\\
0 & 0 & -D' & D\\
-D & D' & -\frac{D'}{R_l} & -\frac{D'}{R_l}\\
D' & -D' & -\frac{D'}{R_lZ_l} & -\frac{D'}{R_l}
\end{bmatrix}\cdot \begin{bmatrix}
I_{L1}\\
I_{L2}\\
V_{C1}\\
V_{C2}
\end{bmatrix} + \begin{bmatrix}
D'\\
D'\\
\frac{D'}{R_l}\\
\frac{D'}{R_l}
\end{bmatrix} \cdot (V_g - V_D)
\end{equation}
The state space equations hence become,
\begin{align}
sL\cdot \hat{i}_L(s) &= (D - D')\cdot \hat{v}_C(s) + D'\cdot \hat{v}_g(s) + (2V_C-V_g+V_D)\cdot \hat{d}(s) \\
sC\cdot \hat{v}_C(s) &=
\!\begin{aligned}[t]&(D'-D)\cdot \hat{i}_L(s) - \frac{2D'}{R_l} \hat{v}_C(s)\\
& + \frac{D'}{R_l} \hat{v}+g(s) + (-2I_L + 2\frac{2V_C}{r_l} -
 \frac{V_g-V_D}{R_l})\cdot \hat{d}(s)
\end{aligned}
\end{align}
Steady state values are:
\begin{equation}
V_C = \frac{1-D}{1-2D} \cdot (V_g-V_D)
\end{equation}
and% never do this \\
\begin{equation}
I_L=\frac{1-D}{(1-2D)^2} \cdot \frac{V_g}{R_l}
\end{equation}
\end{document}

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