This how you can make the very simple AM radio transmitter shown below. It uses only a few parts.
Make your transmitter powerful enough to transmit only a few feet or a metre or less. You don't want to interfere with your neighbor's radio and certainly not with emergency services and so on. I'll point out how to limit it below.
On the left below is the circuit diagram and on the right is how I laid it out on a breadboard, in case you want to make one too.
The chip is an oscillator and is what provides the radio carrier frequency, 1.8MHz (megahertz or cycles per second.)
1.8MHz is not in the AM radio band that a normal AM radio can receive, which is around 540KHz (kiloherz) to 1.6MHz. But it was the only one I could find locally. You can get a 1MHz oscillator chip online from the Scitoys website. 1MHz is in the normal AM radio band.
The transformer I used is a doorbell transformer which I got from a local electronics store, but hardware stores may have it too since it's literally usually used for doorbells.
It would be better, however, to use an audio transformer but I couldn't find any locally. You can get one online from the Scitoys website.
The antenna is simply a length of wire in a straight line. The shorter it is, the shorter the distance you'll broadcast. Since you don't want to interfere with other's broadcasting on the same frequency, keep the antenna short. To broadcast to my crystal radio sitting nearby or to my battery powered radio I need only about 1 foot of antenna wire.
While this is a simple AM radio transmitter, it is also a bad one in the sense that it not only transmits at the frequency of the oscillator but also at a range of frequencies above and below it. It also broadcasts on harmonic and subharmonic frequencies which are multiples and submultiples. For example a harmonic of 1.8MHz is 2x1.8, or 3.2MHz. A subharmonic of 1.8MHz is 1.8/2, or 0.9MHz (900kHz). Use it only for fun, demonstrations or science fair projects.
To limit it's range, don't use a powerful sound source or keep the volume of the sound source low. Also, keep the output antenna wire short.
Video - How to Make AM Radio Transmitter
Here's a video I made showing step-by-step how to make this simple AM radio transmitter on the breadboard as shown in photos above, along with demonstrations of me using it.
Video - Amplitude Modulation with Simple AM Radio Transmitter
This video uses this simple AM radio transmitter to explain how Amplitude Modulation (AM) works.