The main difficulties with the antenna setup were:

1. quite considerable distance (150 m) with some light obstacles (trees and rooftops);
2. the mailbox is uphill; because of hill curb there is no direct line of sight for the receiver antenna if placed on a ground floor;
3. I wanted a dissimulated and cheap transmitter antenna (in the case it gets vandalized or stolen), which puts some limits on its size and appearance.

I spent a few months tinkering with antennas trying to get decent reception downhill close to the ground (1–2 m). The best I have got was about 50% transmission loss. Elevating the antenna to the house roof level (5–6 m) solved the issue. So, while some obstacles might not be as problematic, having an earth hump in the middle is a communication killer.

HC-12 allows for quite wide range of frequencies, circa 433–484 MHz, with a step of 0.4 MHz. I wanted to step a bit away from the default (channel #1, 433.4 MHz), so I opted for the channel #7, 435.8 MHz.

More information on HC-12 configuration can be found on a dedicated page.

I have tested several antenna types. The simplest one is a helical ("spring") antenna, which is sold with HC-12 (you need to solder it to the ANT2 hole).

This antenna is ideal for prototyping, but you will not get long range with it.

More advanced is "whip" antenna, which is just a piece of straight wire soldered to HC-12 (same ANT2 hole).

If you get the wire length right (approx. ¼ of the wavelength, see below), this antenna works very well. It can also be bent to some extent, and costs almost nothing. The problem in my case was that I was mounting the module in the false floor of the mailbox, which forced the module, and hence, the antenna, in horizontal position. The distance to the mailbox wall did not allow for any useful vertical tip, and the antenna in horizontal position is not effective.

One can buy a ready 433 MHz antenna, and there are many varieties available, usually fit with RP-SMA male connector. To connect them, you will need to equip the module with a short internal coaxial cable RP-SMA-female-to-IPX-female (as on the photo below). IPX small round connector is then connected to the ANT1 socket of HC-12.

I made tests with a foldable whip antenna (on this photo attached to the receiver):

I believe, this antenna internally combines a whip section and a helical section (hence the thick diameter). This antenna works a bit better than the wire whip antenna, but, unfortunately, is not at all discrete nor cheap, and it was difficult to find a good place for it in mailbox either. But it could be a good option for the receiver.

Note that industrial antennas are designed for 433 MHz. They will work for 435.8 MHz too, but a bit less effectively.

This is a custom-built whip antenna providing a short flexible coax feeder:

It solves the problem of the original simple whip antenna by allowing vertical antenna positioning along the mailbox wall while connecting to the horizontally-placed module. This was the final variant adopted for transmitter. The parts are:

1. 155 mm isolated copper install wire 2.5 mm² (this is the antenna itself)
2. 411 mm RG316 coaxial cable (feeder)
3. shrink tube to join antenna to the feeder
4. RP-SMA male connector

A thick install wire is used to make a rigid antenna. This wire is soldered to the coax cable center wire (you would need a strong soldering iron to heat up the install wire tip); the shield wire of the coax cable is trimmed and left unconnected on the antenna side. A shrink tube protects the connection (put two layers if the connection is not rigid enough). RP-SMA connector is mounted as usual (there are many guides on the Internet) and is protected with another shrink tube. Be sure to check the result for shorts and disconnections — even though it looks like an easy assembly, I got it right from a third try only.

All the antennas described so far were monopole antennas. On the receiver side space is not a problem, so we can opt for a dipole antenna, which is known ([4]) to give better results than monopole. This was the final variant adopted for the receiver. The cable in this case can be made arbitrarily long. I needed about 6–7 m to reach the roof; I used a longer 9 m cable piece that I had.

Dipole antenna uses same parts as for monopole, but you have two aligned 155 mm antenna wires (dipole legs) instead of one. The coax cable center is soldered to the dipole half pointing up; the cable shield is soldered to the dipole half pointing down. The gap between the two legs should be made as small as possible, but without sacrificing convenience of soldering.

Antenna casing is made from PVC cable trunking. Cable exit provides some cable strain reliefs made from a plastic bottle cap.

As per [1], monopole antenna length is ¼λ, where wave length λ is:

λ ＝ speed of light 299792458 m/s ÷ 435.8 MHz ≈ 687.9 mm

Consequently,

monopole length ＝ λ ÷ 4 quarter wave length
    × copper velocity factor 0.95 × insulation velocity factor 0.95 ≈ 155 mm

See [2] for explanation of velocity factor. The same source suggests that, in order to avoid losses in the feeder, its length should be multiple of ½λ. In our case feeder consists of two parts — an internal SMA-to-IPX coaxial cable (I have got a pre-assembled 215 mm cable) and external coaxial cable. ½λ total cable length would fall a bit short, but λ looks about right. The length of the external cable would be then:

external cable length ＝ (λ − 215 mm) × 0.95 × 0.95 ≈ 427 mm

I also shove off a few millimeters for SMA connectors, which gives the final cable length of 411 mm. It is not necessary to be very precise here; centimeter-like tolerances are just fine.

Even though antennas physics is well established science, building good antennas still looks more like an art. Some sources among many I have read that were particularly useful in making this device:

[1] SparkFun Tutorial — if you know nothing about antennas, this will get you going in 10 mins. The tutorial is for a different radio module, but the antenna descriptions are fully applicable;

[2] LowPowerLab Article on Velocity Factor — I did quite a few calculations using speed of light in vacuum until I realized that in antenna case the speed is lower. This is something often omitted or poorly explained in tutorials, and this article just gets it right. There are also some useful suggestions on feedline length;

[3] ULRS Antennas — the site for drone builders, but it has got a simple dipole calculator and many crazy ideas for high-performance antennas. If you miss inspiration, check it out;

[4] Antenna Theory — if you want to find a way in myriad of parameters and understand how the things work, this is the right place.