Yes, countless antenna professionals have, and TI has a great application note on the basics of PCB antenna design. You probably won't find a design for 433 MHz.
Not an Arduino problem, and the antenna professionals rarely, if ever, look at or post on the Arduino forum.
May I add that the antenna is easy, the network to match the antenna to the transmitter IC is where the trial and error and engineering comes into play.
I'm using Arduino as a base for my project. There are many examples of projects, here and elsewhere, that use the inexpensive 433MHz xmit/rcv option with Arduino. Many people here on these forums are probably doing, more or less, exactly what I'm doing.
I'm not asking how to replace the gasket on my oil pan or how to make a dovetail joint.
I have a Coilcraft kit with appropriate inductors, and I have a set of capacitor wands. I know how to create PI and T resistor impedance pads, but I do not have access to a spectrum analyzer. Does anyone have a tried layout they would like to share?
Don't need a spectrum analyzer. Make a simple RF indicator with a wire antenna, a two diode voltage doubler and a filter cap and and measure the output voltage with your DVM. Tune for peak voltage.
My recollection is that the antenna was apparently designed to be matched to a module with a 50R output, which is what the module I was using should have been.
The end of the balanced line should be impedance matched. The antenna is unbalanced. Care should be taken at the transition to avoid reflection. Reflection could greatly reduce antenna output.
I have calculated an antenna for you, the mmana program for non-commercial use on the network is available, a device for analysis can be bought inexpensively called NanoVNA, there is a small gain relative to the isotropic emitter, go ahead