The beamwidth of Voyager 1's antenna is about 0.5 degrees. In practical terms, that's very narrow, about an 8 metre wide beam at a kilometre distance.

At its current distance, by the time the beam reaches Earth it is 224 million kilometres wide, 1.5x the distance from the Earth to the sun.

Now imagine the light from a car's taillights lighting up the back wall of a garage as it reverses in. Then spread that same amount of light out over that 224 million km wide beamwidth. That's what Voyager is putting out and what the Deep Space Network dishes have to listen for.