Add the actionBackupDatabase() to the app\controllers\SiteController.php file:

class SiteController extends Controller
{
    ...
 
    /** 
     * Get host name or database name from database connection string in 
     * Yii::$app->db->dsn:
     *   [dsn] => 'mysql:host=localhost;dbname=acme_mydatabase'
     * Usage:
     *   $db = Yii::$app->getDb();
     *   $dbName = $this->getDsnAttribute('dbname', $db->dsn);
     */ 
    private function getDsnAttribute($name, $dsn)
    {
        if (preg_match('/' . $name . '=([^;]*)/', $dsn, $match)) {
            return $match[1];
        } else {
            return null;
        }
    }
 
    /**
     * Dumps the MySQL database that this controller's model is attached to.
     * Serve the sql file as a download so that the user can save the backup to their local computer.
     *
     * @param string $tables Comma separated list of tables to download, or '*' to download them all.
     */
    function actionBackupDatabase($tables = '*') 
    {
        $return = '';
 
        $db = Yii::$app->getDb();
        $databaseName = $this->getDsnAttribute('dbname', $db->dsn);
 
        // Do a short header
        $return .= '-- Database: `' . $databaseName . '`' . "\n";
        $return .= '-- Generation time: ' . date('D jS M Y H:i:s') . "\n\n\n";
 
        if ($tables == '*') {
            $tables = array();
            $result = $db->createCommand('SHOW TABLES')->queryAll();
            foreach($result as $resultKey => $resultValue) {
                $tables[] = $resultValue['Tables_in_'.$databaseName];
            }
        } else {
            $tables = is_array($tables) ? $tables : explode(',', $tables);
        }
 
        // Run through all the tables
        foreach ($tables as $table) {
            $tableData = $db->createCommand('SELECT * FROM `' . $table . '`')->queryAll();
 
            $return .= 'DROP TABLE IF EXISTS `' . $table . '`;';
            $createTableResult = $db->createCommand('SHOW CREATE TABLE `' . $table . '`')->queryAll();
            $createTableEntry = current($createTableResult);
            $return .= "\n\n" . $createTableEntry['Create Table'] . ";\n\n";
 
            // Output the table data
            foreach($tableData as $tableDataIndex => $tableDataDetails) {
                $return .= 'INSERT INTO `' . $table . '` VALUES(';
 
                foreach($tableDataDetails as $dataKey => $dataValue) {
                    if(is_null($dataValue)) {
                        $escapedDataValue = 'NULL';
                    } else {
                        // Convert the encoding
                        //$escapedDataValue = mb_convert_encoding( $dataValue, "UTF-8", "ISO-8859-1" );
                        $escapedDataValue = $dataValue;  // no char conversion (keep it as UTF-8)
 
                        // Escape any apostrophes using the datasource of the model.
                        $escapedDataValue = str_replace("'", "\'", $escapedDataValue);  // escape apostrophes
                        //if (stripos($escapedDataValue, ' ') !== false) {
                        //    $escapedDataValue = "'" . $escapedDataValue . "'";  // quote string if spaces found
                        //}
                        //if (!is_numeric($escapedDataValue)) {
                        //    $escapedDataValue = "'" . $escapedDataValue . "'";  // quote string if non-numeric
                        //}
                        $escapedDataValue = "'" . $escapedDataValue . "'"; // quote string for all fields w/o NULL
                    }
 
                    $tableDataDetails[$dataKey] = $escapedDataValue;
                }
                $return .= implode(',', $tableDataDetails);
 
                $return .= ");\n";
            }
 
            $return .= "\n\n\n";
        }
 
        // Set the default file name
        $fileName = $databaseName . '-backup-' . date('Y-m-d_H-i-s') . '.sql';
 
        // Serve the file as a download
        header("Content-Type: text/x-sql");
        header('Content-Disposition: attachment; filename="'. $fileName . '"');  // File will be called $fileName
        echo $return;
    }
 
    /**
     * Dumps the MySQL database that this controller's model is attached to.
     * This action will serve the sql file as a download so that the user can save the backup to their local computer.
     *
     * @param string $tables Comma separated list of tables you want to download, or '*' if you want to download them all.
     */
    function actionBackupDatabaseLarge($tables = '*') 
    {
        Yii::$app->response->format = Response::FORMAT_RAW;  // Raw for Text output
 
        $db = Yii::$app->getDb();
        $databaseName = $this->getDsnAttribute('dbname', $db->dsn);
 
        // Set the default file name
        $fileName = $databaseName . '-backup-' . date('Y-m-d_H-i-s') . '.sql';
 
        // Serve the file as a download
        header("Content-Type: text/x-sql");
        header('Content-Disposition: attachment; filename="'. $fileName . '"');  // File will be called $fileName
 
        // Do a short header
        echo '-- Database: `' . $databaseName . '`' . "\n";
        echo '-- Generation time: ' . date('D jS M Y H:i:s') . "\n\n\n";
 
        if ($tables == '*') {
            $tables = array();
            $result = $db->createCommand('SHOW TABLES')->queryAll();
            foreach($result as $resultKey => $resultValue) {
                $tables[] = $resultValue['Tables_in_'.$databaseName];
            }
            //echo "Tables: " . print_r($tables, true);  //debug
        } else {
            $tables = is_array($tables) ? $tables : explode(',', $tables);
        }
 
        // Run through all the tables
        foreach ($tables as $table) {
            $tableCountData = $db->createCommand('SELECT COUNT(*) AS total FROM `' . $table . "`")->queryAll();
            $totalRecs = $tableCountData[0]['total'];
            //echo "Total: " . print_r($tableCountData, true);  //debug
 
            // SQL CREATE code
            echo 'DROP TABLE IF EXISTS `' . $table . '`;';
            $createTableResult = $db->createCommand('SHOW CREATE TABLE `' . $table . '`')->queryAll();
            $createTableEntry = current($createTableResult);
            echo "\n\n" . $createTableEntry['Create Table'] . ";\n\n";
 
            // Process table data in chunks to avoid running out of memory
            for($startIdx = 0, $chunkSize = 10000; $startIdx < $totalRecs; $startIdx += $chunkSize) {
                $tableData = $db->createCommand('SELECT * FROM `' . $table . "` LIMIT {$startIdx},{$chunkSize}")->queryAll();
 
                // Output the table data
                foreach($tableData as $tableDataIndex => $tableDataDetails) {
                    echo 'INSERT INTO `' . $table . '` VALUES(';
 
                    foreach($tableDataDetails as $dataKey => $dataValue) {
                        if(is_null($dataValue)) {
                            $escapedDataValue = 'NULL';
                        } else {
                            // Convert the encoding
                            //$escapedDataValue = mb_convert_encoding( $dataValue, "UTF-8", "ISO-8859-1" );
                            $escapedDataValue = $dataValue;  // no char conversion (keep it as UTF-8)
 
                            // Escape any apostrophes using the datasource of the model.
                            $escapedDataValue = str_replace("'", "\'", $escapedDataValue);  // escape apostrophes
                            //if (stripos($escapedDataValue, ' ') !== false) {
                            //    $escapedDataValue = "'" . $escapedDataValue . "'";  // quote string if spaces found
                            //}
                            //if (!is_numeric($escapedDataValue)) {
                            //    $escapedDataValue = "'" . $escapedDataValue . "'";  // quote string if non-numeric
                            //}
                            $escapedDataValue = "'" . $escapedDataValue . "'";        // quote string for all fields without NULL
                        }
 
                        $tableDataDetails[$dataKey] = $escapedDataValue;
                    }
                    echo implode(',', $tableDataDetails);
 
                    echo ");\n";
                }
            }
 
            echo "\n\n\n";
        }
    }
}    

Add a call to action BackupDatabase in app\views\layouts\main.php file:

<?php
echo Nav::widget([
    'options' => ['class' => 'navbar-nav navbar-right'],
    'items' => [
        ['label' => 'Home', 'url' => ['/site/index']],
 
        // Admin menu only
        !Yii::$app->user->isGuest && Yii::$app->user->identity->username === 'admin' ?
            ['label' => 'Admin', 'url' => ['/site/admin'], 
                'items' => [
                    ['label' => 'Backup Database', 'url' => ['/site/backup-database']]
                    ['label' => 'Backup Database (Large)', 'url' => ['/site/backup-database-large']]
            ]] : 
            '',
    ],
    ...
]);
NavBar::end();
?>