Field based limit using simple query string query

Hi,
Consider a elastic document has a filed named site. We can use query string query to limit the search results to the related site just like this:

GET my_index/_search
{
 "query": {
   "query_string": {
     "default_field": "*",
     "query": "search_text AND site:my_site"
   }
 }
}

I was trying this functionality for simple query string and seems not working. this:

GET my_index/_search 
{
 "query": {
   "simple_query_string": {
     "query": "search_text +site:my_site",
     "default_operator": "and",
     "fields": ["*"]
   }
 }
}

Is this query correct? how can I have such functionality to simply filter my results based on a field?

Thanks in advance

Use a bool query and put the simple query in the must part and add a term query on the site field in the filter part.