powershell json format variable in tmsl script

I use powershell and i want to put variable in json format into TMSL create role script. I want to put this variable into TablePermission parameter

json variable:

$filter=
[

    {
          "name": "DimGeography",
          "filterExpression": "DimGeography[CountryRegionCode] = \"US\" "
        }
]

TMSL script:

$Query='
    {  
    "create": {  
        "parentObject": {  
        "database": "AW Internet Sales"  
        },  
        "role": {
      "name": "test_filter",
      "modelPermission": "read",
      "tablePermissions": "'+$filter+'"
    }
        }
          
    }'

This is script which I want to parametrize

{
  "createOrReplace": {
    "object": {
      "database": "AW Internet Sales",
      "role": "SalesManagerUS"
    },
    "role": {
      "name": "SalesManagerUS",
      "modelPermission": "read",
      "tablePermissions": [
        {
          "name": "DimGeography",
          "filterExpression": "DimGeography[CountryRegionCode] = \"US\" "
        }
      ]
    }
  }
}

How can I put $filter to $Query to receive working script like above ?

You could try the below snippet :

    $filter=
'[

    {
          "name": "DimGeography",
          "filterExpression": "DimGeography[CountryRegionCode] = \"US\" "
        }
]'


function populate-tsml ($filter)
{


$Query='
    {  
    "create": {  
        "parentObject": {  
        "database": "AW Internet Sales"  
        },  
        "role": {
      "name": "test_filter",
      "modelPermission": "read",
      "tablePermissions": '+$filter+'
    }
        }
          
    }'

    return $Query

    }

  $Query =   populate-tsml -filter $filter

OUTPUT :