I'm watching this show called [Jericho](https://en.wikipedia.org/wiki/Jericho_(2006_TV_series). It takes place after a nuclear attack that destroys 23 American cities. When the bomb first exploded in Denver they said that it was most likely an H-Bomb. However, later it was later revealed that each bomb was only 20 kilotons. These are supposed to be ex-soviet nukes. When the bomb was revealed it looked like something that would be dropped by a plane. They keep calling them high-yield nuclear devices. Is it possible that they were H-Bombs?
H bombs can definitely be dropped by planes. The largest bomb ever was the Tsar Bomb, dropped from a Tu-95.
There is not as big a divide between atomic bombs and hydrogen bombs as you might think. At the low end, a small amount of deuterium and tritium (isotopes of hydrogen) are added in the hollow centre of the fission package. This release neutrons when compressed by the explosion. These neutrons interact with the plutonium or uranium to increase the fission yield. This allows a smaller amount of Pu or U to be used, reducing the size, weight and cost of the bomb. An example is the WE177A, which weighed 600lb and would typically be carried by a fighter (although in practice RAF planes never carried live weapons other than on bomb tests). The WE.177C weighed 1000lb, delivered 190kt, and was also delivered by strike fighters.
Staged nuclear weapons add more hydrogen in a secondary stage outside the core. It is possible to get most of the yield from fusion, but in practice they usually use the neutrons to increase fission yield. These are larger, and as far as I know only delivered by bombers or missiles in the strategic role.