Any idea to export this circuitikz to PDF?

Question

Any idea to export this circuitikz to PDF?
I used tikzpicture but it cut part of image on the right. That is probably due to the incompability between tikz and circuitikz.
Note that the PDF size should be the same as the image size, so please don't suggest compile and export the whole PDF page.

\documentclass[]{article}
\usepackage{circuitikz}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{backgrounds}
\usetikzlibrary{external}
\tikzexternalize 


\begin{document}


\begin{tikzpicture}
\centering
  \begin{circuitikz}
    \draw (0,0) node (N5){}
    to [short,o-](2,0) 
    to[short,*-](4,0)
    to[D](4,2)
    to[D](4,4)
    to[short,-*](2,4) node (N1){}
    to[short,-o](0,4) node (O){}; 
    \draw (4,0) 
    to[short,*-](8,0) 
    to[D](8,2)
    to[D](8,4)
    to[short,-*](4,4);
    \draw (2,0)
    to[Tnpn,n=q2](2,2) node(N2){}
    to[Tnpn,n=q1](2,4);
    \draw (8,0)
    to[short,*-](10,0) node(N4){}
    to[Tnpn,n=q4,mirror](10,2)
    to[Tnpn,n=q3,mirror](10,4)
    to[short,-*](8,4);
    \draw
    (q1.B) to[short,-o](1,3) node[left]{$Q_1$}
    (q2.B) to[short,-o](1,1) node[left]{$Q_2$}
    (q3.B) to[short,-o](11,3) node[right]{$Q_3$}
    (q4.B) to[short,-o](11,1) node[right]{$Q_4$};
    \draw (2,2) to[short,*-*](4,2) to[Telmech=M](8,2) to[short,*-*](10,2) node(N3){};
    % adding current
    \begin{scope}[on background layer, very thick,decoration = {
        markings,
        mark = at position 0.05 with {\arrow{>}}}
    ] 
    \draw[line width = 3pt, red!40, postaction = {decorate}] (O.north)
    -- node[above, red]{$i$} (N1.north east) |- (N3.north west) |-
    (N5.north); 
    \end{scope}
    % adding voltage
    \draw[line width = 3pt, red!40, ->] (N5) to[out = 150, in = 210]
    (O) node[left, red]{$V$};
  \end{circuitikz}
\end{tikzpicture}

\end{document}

Answer 1

IMHO the problem is the resulting bounding box of the tikzpicture not an incompatibility. You could fix this using \useasboundingbox:

\documentclass{article}
\usepackage{circuitikz}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{backgrounds}
\usetikzlibrary{external}
\tikzexternalize 

\begin{document}

\begin{tikzpicture}% circuitikz is also a tikzpicture
%  \begin{circuitikz}% but only tikzpicture is externalized.
    \draw (0,0) node (N5){}
    to [short,o-](2,0) 
    to[short,*-](4,0)
    to[D](4,2)
    to[D](4,4)
    to[short,-*](2,4) node (N1){}
    to[short,-o](0,4) node (O){}; 
    \draw (4,0) 
    to[short,*-](8,0) 
    to[D](8,2)
    to[D](8,4)
    to[short,-*](4,4);
    \draw (2,0)
    to[Tnpn,n=q2](2,2) node(N2){}
    to[Tnpn,n=q1](2,4);
    \draw (8,0)
    to[short,*-](10,0) node(N4){}
    to[Tnpn,n=q4,mirror](10,2)
    to[Tnpn,n=q3,mirror](10,4)
    to[short,-*](8,4);
    \draw
    (q1.B) to[short,-o](1,3) node[left]{$Q_1$}
    (q2.B) to[short,-o](1,1) node[left]{$Q_2$}
    (q3.B) to[short,-o](11,3) node[right]{$Q_3$}
    (q4.B) to[short,-o](11,1) node[right]{$Q_4$};
    \draw (2,2) to[short,*-*](4,2) to[Telmech=M](8,2) to[short,*-*](10,2) node(N3){};
    % adding current
    \begin{scope}[on background layer, very thick,decoration = {
        markings,
        mark = at position 0.05 with {\arrow{>}}}
    ] 
    \draw[line width = 3pt, red!40, postaction = {decorate}] (O.north)
    -- node[above, red]{$i$} (N1.north east) |- (N3.north west) |-
    (N5.north); 
    \end{scope}
    % adding voltage
    \draw[line width = 3pt, red!40, ->] (N5) to[out = 150, in = 210]
    (O) node[left, red]{$V$};
  \useasboundingbox(0,0) rectangle (12,4);% not needed any longer after commenting circuitikz but sometimes useful
%  \end{circuitikz}
\end{tikzpicture}

\end{document}

However, if you need a PDF with the picture only, a very simple solution would be to use class standalone and correct it using option border:

\documentclass[border={-15mm 3mm 16mm 3mm}]{standalone}
\usepackage{circuitikz}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{backgrounds}
%\usetikzlibrary{external}
%\tikzexternalize 

\begin{document}

\begin{tikzpicture}
  \begin{circuitikz}
    \draw (0,0) node (N5){}
    to [short,o-](2,0) 
    to[short,*-](4,0)
    to[D](4,2)
    to[D](4,4)
    to[short,-*](2,4) node (N1){}
    to[short,-o](0,4) node (O){}; 
    \draw (4,0) 
    to[short,*-](8,0) 
    to[D](8,2)
    to[D](8,4)
    to[short,-*](4,4);
    \draw (2,0)
    to[Tnpn,n=q2](2,2) node(N2){}
    to[Tnpn,n=q1](2,4);
    \draw (8,0)
    to[short,*-](10,0) node(N4){}
    to[Tnpn,n=q4,mirror](10,2)
    to[Tnpn,n=q3,mirror](10,4)
    to[short,-*](8,4);
    \draw
    (q1.B) to[short,-o](1,3) node[left]{$Q_1$}
    (q2.B) to[short,-o](1,1) node[left]{$Q_2$}
    (q3.B) to[short,-o](11,3) node[right]{$Q_3$}
    (q4.B) to[short,-o](11,1) node[right]{$Q_4$};
    \draw (2,2) to[short,*-*](4,2) to[Telmech=M](8,2) to[short,*-*](10,2) node(N3){};
    % adding current
    \begin{scope}[on background layer, very thick,decoration = {
        markings,
        mark = at position 0.05 with {\arrow{>}}}
    ] 
    \draw[line width = 3pt, red!40, postaction = {decorate}] (O.north)
    -- node[above, red]{$i$} (N1.north east) |- (N3.north west) |-
    (N5.north); 
    \end{scope}
    % adding voltage
    \draw[line width = 3pt, red!40, ->] (N5) to[out = 150, in = 210]
    (O) node[left, red]{$V$};
  \end{circuitikz}
\end{tikzpicture}

\end{document}

Note: With option tikz class standalone does also provide to generate several PDF pages in the same PDF, one for each tikzpicture. To change the options from page to page, you can use \standaloneconfig, e.g.,

\standaloneconfig{border={3mm 3mm 3mm 3mm}}

before the corresponding tikzpicture.

An even simpler suggestion would be to use \documentclass[landscape]{article} and \pagestyle{empty} and afterwards use pdfcrop to cut of the large white margins from the generated PDF. With

pdfcrop --margins 10pt original.pdf

the resulting original-crop.pdf would be almost the same as shown above.

Answer 2

Although the proposed way to have an independent PDF proposed by @cabohah is arguably the correct/best way, the main error here is that you are nesting tikzpictures. Instead of

\begin{tikzpicture}
    \begin{circuitikz}
...
    \end{circuitikz}
\end{tikzpicture}

use just

\begin{tikzpicture}
...
\end{tikzpicture}

circuitikz is just an alias for tikzpicture; it works most of the time but not when externalize is involved. This is mentioned in the manual:

(FAQ section). Although I admit it is a bit hidden; I am pondering to change all the \begin{circuitikz}...\end{circuitikz} in the manual...

Also, notice that \centering inside a tikzpicture is doing nothing but harm. Probably you are mixing the concept of figure and tikzpicture?