The Anderson Loop is the simplest detector. Most hams don`t refer to it as an Anderson Loop, and I`ve only seen the loop described as such by the folks who patented it. A good example of an analyzer that uses this detector is the VK5JST Aerial Analyzer. Below is a basic schematic of the detector. Another popular detector is the Wheatstone bridge.
The RigExpert AA-520 uses a wheatstone bridge as do several other popular analyzers. I`ve included a schematic of the bridge below even though you can find it in countless places on the web. The directional coupler is also popular. The two popular ones that I see are the transmatch and the Bruene bridge. There are also stripline directional couplers for VHF and UHF. I`ve not tried the stripline couplers on HF, but they may work fine. Most folks seem to wind some turns on toroids or binocular ferrites. Below is a schematic of a transmatch coupler. I am settling on a transmatch directional coupler and an AD8302 combination. I have several AD8302 chips (less than $2 from china), and I want to use this as a launch-pad to build a more capable Vector network analyzer later on. I`ve worked out the math I need to use with the AD8302. I hope to have something put together over the next few weeks.