Call a member function prepare () on null in

I picked up this class that connects to MySql via PDO, in that link . It works correctly. But I decided to turn it into a static class. And here is the modified code.

class db {
    private static $dsn;
    private static $username;
    private static $password;
    private static $db; 
    private static $conn;

    private static $arrConnAttr;//Array of connection attributes. Ex: ["PDO::ATTR_ERRMODE", "PDO::ERRMODE_EXCEPTION"]
    private static $pathErroLog;//Path to save the erro log files. Ex:$_SERVER['DOCUMENT_ROOT'] . "/myDirRootProject/LogError"
    private static $arrCatchConnResult;//Path to save the erro log files. Ex:$_SERVER['DOCUMENT_ROOT'] . "/myDirRootProject/LogError"
    private static $die;//If we set $setValues["die"]=NULL, during the object initialization, errors will not stop the process. 

    public static $sql;

    public function __construct(array $setValues=NULL) {          

         xdebug_break();
         $arrInitDefault["dsn"]="localhost";
         $arrInitDefault["username"]= "root";
         $arrInitDefault["password"]="";
         $arrInitDefault["db"]="drset2014";



         $arrInitDefault["arrConnAttr"]= ["PDO::ATTR_ERRMODE"," PDO::ERRMODE_EXCEPTION"];

         $arrInitDefault["pathErroLog"]= dirname(__FILE__)."/Log/Error";//Default path to dir. Note: error pathLog can be "/Log/Error/UserName" or "/Log/Error/UserId", etc
         $arrInitDefault["die"]=  TRUE;         

         $arrInitDefault["sql"]=  FALSE;


         if(!is_null($setValues)){
              $arrInitDefault=  array_merge($arrInitDefault,$setValues);
          }

          //After merge, initialaze private variables with result merged $arrValues

          self::$dsn = $arrInitDefault["dsn"];
          self::$username= $arrInitDefault["username"];
          self::$password= $arrInitDefault["password"];
          self::$db= $arrInitDefault["db"];

          self::$arrConnAttr= implode(",", $arrInitDefault["arrConnAttr"]);
          self::$pathErroLog=$arrInitDefault["pathErroLog"];
          self::$die=$arrInitDefault["die"];
         //This try and catch  is only to estabilish the connection during the initialization
         try {

                $dns=self::$dsn;
                $username=self::$username;
                $password=self::$password;
                $db=self::$username;

                self::$conn= new PDO("mysql:host=$dns; dbname=$db", "$username", "$password");//Now private $conn is a PDO object
                self::$conn->setAttribute(PDO::ATTR_ERRMODE, PDO::ERRMODE_EXCEPTION);        

         }// End of try
         catch(PDOException $e){//If had some error. The PDO object ($this->conn) could not be created. Throw an error.      
          self::$arrCatchConnResult = self::saveLogError($e->getMessage());//Save a message in the log file and throw a message
          $msg=self::$arrCatchConnResult["strToHTML"];
          self::$conn=null;                 
                 if(self::$die){                   
                       die($msg);
                 }
           }
    }

    public static function saveLogError($msg=NULL,$sql=NULL) {
     #xdebug_break();

     xdebug_break();
       $year = date("Y");
       $month = date("M"); 
       $day = date("d");
       $dt = date("d.M.Y_H.i.s");

       $pathErroLog=  self::$pathErroLog."/".$year."/".$month."/".$day."/";
       if (!is_dir($pathErroLog)) {
          mkdir($pathErroLog,0777,true);
       }//If is not a dir, create it.

       $sqlErrorStringTXT="";
       $sqlErrorString="";
       if(!is_null($sql)){
        $sqlErrorStringTXT = "Sql: $sql";
        $sqlErrorStringHTML = "<kbd>Sql</kbd>: $sql";
       }

///////////////  Maybe should be good save errors in database too.   

$strToTxt=<<<EOF
>>>>>  Mensagem de erro:  <<<<< \n 
Date:     $dt \n
Msg:     $msg \n  
$sqlErrorStringTXT \n
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
EOF;

//Save error message to the file
$f=$pathErroLog."$dt.txt";
$myfile = fopen($f, "w") or die("Unable to open file!");
fwrite($myfile, $strToTxt);
fclose($myfile);

//Create a string to be displayed in the broser
$strToHTML=<<<EOF
<div class="alert alert-danger" role="alert">
Date:     $dt <br/>
Msg:     <span class="label label-danger">$msg</span><br/>  
$sqlErrorStringHTML<br/>
</div>
EOF;

$arrCatchConnResult["status"]=0;
$arrCatchConnResult["strToTxt"]=$strToTxt;
$arrCatchConnResult["strToHTML"]=$strToHTML;

return $arrCatchConnResult;

}//End of saveLogError()

    public static function get_values() {
              try {           
                     $stmt = self::$conn->prepare(self::$sql); 
                     $stmt->execute();
                     while ($field = $stmt->fetch(PDO::FETCH_ASSOC)) {
                      $arrResult[]=$field;
                    }
                    return $arrResult; 
              } 
              catch (PDOException $e) {
                    self::$arrCatchConnResult =  self::saveLogError($e->getMessage(),  self::$sql);//Save a message in the log file and set a message   
                    $msg= self::$arrCatchConnResult["strToHTML"];
                    self::$conn = null;
                    if(self::$die){                           
                          die($msg);
                    }
              }
         }


}//End of class db

On my index.php page, I'm calling it this way:

include './class/db.php';
db::$sql ="select * from city";         
echo "<pre>";
   print_r(db::get_values());
echo "</pre>";

When I run the page I get an error of type:

Fatal error: Call to a member function prepare() on null in C:\xampp\htdocs\drReference\private\class\db.php on line 126

It seems that when I transform in static class the constructor is not called, since in these types of classes the creation of objects is not necessary. I could try to solve this by passing the code from the con- troller to a connect function for example, and call this function every time it was to start a query.

My question is, is there any way to continue with the static class and force boot through the constructor?