I don't have the EC Author badge on my site yet, but I do have the EC Blog Network widget and I had a problem with the php version. I couldn't get it to work on my WP site, so I installed the Iframe code instead.
If you want to try it with your EC Author badge, log into your EC Author account, and click on the link that says "Click here for more options" (below the section where you copy the PHP code). That will take you to a page that gives you the option of either PHP or Iframe.
I realize that PHP is preferred, but until I learn more about PHP, I will have to stick with the Iframe. To install the PHP, I wonder if we have to go into a different editing section in our WP admin? Perhaps into: Appearance >> Editor >> then one of the "Templates" down the right side?
When I installed the EC Blog Network widget, I went to WP admin >> Appearance >> Widgets >> and put the code inside my Recommended Resources widget.