Hi, allow me to add to this discussion.
I was in the USAF during the early Vietnam years. My specialty was Aircraft Radio Repairman. I spent 2 years working on Phantoms. F4C and F4D models, but mostly on the F4D. I never worked on an F4E.
The F4C was basically an F4B (Navy/ Marines version) with minimal required Air Force modifications such as flight controls in the rear cockpit, low pressure tires and a few other things.
The radio used in the F4B and F4C was the RT 546.
The F4D was the complete Air Force version with all the gadgets they required at the time.
The Radio was changed to an RT793 and, as far as I can find out, remained the radio installed during the rest of the Air Force F4 Phantom production run which is what divinee said. And, as divinee said, the RT793 is related to the ARC 51.
One time I got called out to check the radio on a plane I had never worked on before and the radio was an ARC 51 which I had never seen before. I took the radio back to the shop, opened it up and to my surprise, there was basically an RT793 hiding inside. Just a few small differences. From the outside they do not look at all alike.
This photo link in Northstar98 above post shows the control box sitting on top of the grey RT793 radio unit. These would have been used in F4D and later air Force Phantoms.
Navy and Marine Phantoms probably used different radios.
PS- Squinting at the picture above it says it is actually an RT793A. There is probably some slight difference between the RT793 and RT793A. They may or may not be interchangeable. They look identical.