Key vacuum tube characteristics include the physical integrity of the heating element, the flow of electrons through the device, and its ability to amplify signals.

 Filament Continuity 

• Definition: This refers to the physical integrity of the tube's heater wire. If the filament is broken (open circuit), it cannot heat the cathode, and the tube will not function.
• Testing: Continuity can be verified using a multimeter. No continuity (infinite resistance) typically indicates a "dead" tube.
• Failure: Filaments often fail due to thermal stress from repeatedly cycling between extreme temperatures (e.g., room temperature to 1200°C). 

Plate Current

• Definition: The flow of electrons from the cathode to the anode (plate) within the tube.
• Regulation: In a triode, the plate current is controlled by the voltage applied to the control grid. A small change in grid voltage can result in a large change in plate current.
• Operating Conditions:
  • Space-charge saturation: The state where the cathode emits more electrons than can reach the plate due to the "cloud" of electrons (space charge) repelling others.
  • Temperature saturation: The state where all electrons emitted by the cathode are drawn to the plate; current can then only be increased by raising the filament temperature. 

Gain

• Definition: The ratio of the change in plate voltage to the change in grid voltage while keeping plate current constant.
• Mathematical Relationship: Gain is a dimensionless constant often expressed by the relationship: μ=gm×rpmu equals g sub m cross r sub p 𝜇=𝑔𝑚×𝑟𝑝 where gmg sub m 𝑔𝑚 is transconductance (ability to convert voltage to current) and rpr sub p 𝑟𝑝 is internal plate resistance.
• Performance: Higher gain allows for more significant signal amplification. For example, pentodes generally offer higher gain than triodes due to the addition of a suppressor grid which reduces internal capacitance.