I know what impedance is in terms of ac circuits, but when I look at my 6 inches of copper wire, all I see is 0 ohms resistance. How do I get to 50 from there? See why I need the basics. I don't even know enough to ask what I don't know?
It all depends upon your viewpoint---- replace your transmitter with a DMM on resistance range,& your piece of wire will read as "infinity".
Am I to understand you're saying only attach one lead of the DMM? Otherwise, I don't see how you get infinity.
To RF,your length of wire when used as a part of an antenna possesses both inductance & capacitance,as well as
resistance.
At resonance ,the inductive & capacitive reactances cancel,leaving you with real resistance,& "Radiation Resistance"
This is not a real physical resistance,but looks like one to the external circuit.
Many people get "all bent out of shape" trying to get their heads around radiation resistance,but things which are not real resistors,but act like one are common in Electrical Theory.
One such is internal resistance in a Dry or a Wet Cell,where the internal chemical reaction decreases in activity as the cell becomes flat,looking to the external circuit like an increase in resistance.
Another is in an Electric motor .
Running unloaded,it looks like a high Inductive Reactance,& draws a small current,lagging the input voltage.
Apply a mechanical load,& the current increases,with the lag decreasing towards the resistive case.
It looks like a resistance in parallel with the motor inductance,but is really caused by the mechanical load.
In the same manner,the act of radiating electromagnetic waves from an antenna looks like a resistive loss,in phase with that caused by the real resistance,but is,of course,the whole object of the device.
A resonant 1/2 wavelength dipole is (in free space) about 70 Ohms,that of a1/4 wavelength vertical,half of that.
There is nothing magical about 50 Ohms,it is a standard coaxial cable impedance,& luckily,many practical antennas are closer to that value than the theoretical one.
50 Ohms has become the standard for RF interconnections,as it makes it a lot easier to measure signal levels,etc.
I am guilty of being unable to get my head around it. Unlike the examples you site, motor reactance, battery resistance etc, difficult as they are for a newbie to wrap their head around, those things don't exist outside of a circuit! Antennae require a whole new concept where one end of a wire is simply dangling free. The "resistance" or impedance of that antenna isn't quite so obvious. In fact, I'd venture that antennas would probably be an easier concept in which to get ones head around, if they were taught that before possessing conceptual knowledge of circuits.
In the real big,bad world where antennas live,there is no such thing as "dangling free".
We need to look at a dipole first,as it is the easiest to explain.
A half wavelength dipole consists of two quarter wavelength wires fed from either side of the RF source.
There are reasons why feeding one with coaxial cable is not optimum,but lets ignore them & say one leg is connected to the coax braid & the other to its centre conductor.
There is capacitance between the two legs of the antenna,& inductance along the legs.
(There is capacitance between all objects,& all conductors possess inductance--the familiar coil shape is so we can get increased inductance).
Also,of course,there is real resistance in the circuit.
An antenna is,thus,an LCR circuit,& has a resonant frequency.
Radiation Resistance:-So-called "radiation loss" occurs in all AC circuits,& efforts are made to minimise it.
Antenna designs wish to
maximise radiation so they can do the job they are intended for.
At resonance,
XL & Xc,cancel,leaving the antenna impedance (between the two feedpoints) as
Z=
Rr+
Rloss.
Where
Rr refers to Radiation Resistance &
Rloss to "real" resistance,(which will dissipate RF power as heat,hence it is "lost").
In a well designed antenna
Rloss is very low,compared to
Rr.
So far,we are talking about a dipole,but what you want is a single 1/4 wavelength element vertical antenna.
But what happens to the missing leg?
Many books show a quarter wave vertical as "working against ground" with one side of the feeder going to an earth stake,so the ground takes the place of the missing dipole leg.
Real "dirt" is a fairly poor conductor,so real resistance
Rloss increases,making the antenna less efficient.
This sort of design works reasonably well when the "ground" is replaced by a car body,or a tin roof.but that is not always possible.
What is usually done,is to create a "groundplane" of conductive material to connect to the "earthy"(braid) side of the feeder.
At VHF/UHF this is usually a set of four or more 1/4 wavelength "radials" mounted at the base of the antenna.
Without such a "groundplane" a 1/4 wavelength conductor,only connected to one side of the RF feeder will be
very inefficient.
http://www.rfcec.com/RFCEC/Section-3%20-%20Fundamentals%20of%20RF%20Communication-Electronics/07%20-%20ANTENNA/Antenna%20-%20Ground%20Plane%20Antenna%20(By%20Larry%20E.%20Gugle%20K4RFE).jpgWith the groundplane elements at right angle to the vertical element,the feed impedance at resonance will be
approx. 35 Ohms,but there is a sneaky trick--bending the grounplane elents down to about 45 degrees,the feed impedance is close to 50 Ohms.
http://vk6ysf.com/146mhz_ground_plane_antenna.htmHe uses more radials & a different frequency,but he gives design figures for one on 435MHz,which is close to what you want.
The frequency range over which antennas are useable varies in proportion to their centre frequency.
Hams quite often use antennas which cover most of their "70cm " Band,which is around 5MHz or so wide.
(Your 433Mhz device is actually operating in this Amateur Radio Band,but such low power devices are allowed by the Licencing Authorities)