Many people who get analog electronics still struggle a bit to design oscillators. Even common simulators often need a trick to simulate some oscillating circuits. The Barkhausen criteria state that for stable oscillation, the loop gain must be one, and the phase shift around the feedback loop must be a multiple of 360 degrees. [All Electronics Channel] provides a thorough exploration of oscillators and, specifically, negative resistance, which is punctuated by practical measurements using a VNA. Check it out in the video below.
The video does have a little math and even mentions differential equations, but don’t worry. He points out that the universe solves the equation for you.
In an LC circuit, you can consider the losses in the circuit as a resistor. That makes sense. No component is perfect. But if you could provide a negative resistance, it would cancel out the parasitic resistance. With no loss, the inductor and capacitor will go back and forth, electrically, much like a pendulum.
So, how do you get a negative resistance? You’ll need an active device. He presents some example oscillator architectures and explains how they generate negative resistances.
Crystals are a great thing to look at with a VNA. That used to be a high-dollar piece of test gear, but not anymore.
