The diac is a common component used to trigger triacs. The construction of a diac is similar to that with a transistor, but with both junctions doped to similar levels so that the two junctions' revers break down characteristics are similar. This is a fun project to demonstrate the use of a pair of bipolar transistors operating in their negative resistance region to simulate a diac triggering a triac in an incandescent lamp dimmer. The circuit is not optimized for performance -it is only intended to demonstrate the principle.
The waveforms above should look like the last 90 degrees of the positive and negative half cycles of the AC line, but this is what the hot AC line actually looks like in my neighborhood. No wonder some jurisdictions require appliances to meet power factor requirements. By the way, be careful to consider your scope probe's voltage rating when probing the AC mains, even through an isolation transformer, since the peak voltage may be higher than the probe or scope's rated voltage. I used a X100 probe rated at 1kV.
I'm not going to spend much space on this because this is not a beginners' project and the operation of this kind of lamp dimmer is covered elsewhere on the web.
The photograph above shows the voltage across an incandescent light bulb that is being driven by the triac dimmer circuit. Notice that the lamp is only being driven 1/2 the time of each half of the power line cycle. That means that the lamp only gets half the average power. The fraction of each power line half cycle applied to the lamp is determined by the time within the half cycle that the triac, which switches the voltage across the lamp, turns on. When the voltage goes to zero, the triac turns off and waits for the next trigger pulse. That's how this kind of dimmer works. But varying the phase within each half cycle at which the triac turns on.
Within each half cycle, the power line voltage charges the .068 uf capacitor through the 250K pot....