One of the most common problems an amplifier builder has to deal with is hum. There are different possible sources of hum. Trouble shooting a humming bird can be quite frustrating. So I thought I write some guidelines how to approach this. These are meant mainly for power amps. Some of the guidelines can be applied to preamps as well, but generally preamps are more difficult since they need to handle much smaller signals.
If you have sume hum, don't just blindly try any suggestions. Rather use a systematic approach to find the source of the hum and remove it. When someone asks for help on internet forums to fix some hum often a plethora of different suggestions follows without attempting to understand the cause of the hum.
In 90% of the cases hum is caused by a ground loop or improper grounding of the chassis. So check this first. Disconnect the amp from any source and short the inputs. If the hum goes away it is a ground loop in the system. If it still hums check if safety earth and chassis are properly connected. Safety earth should always have a tight connection to the chassis which in turn should have a connection to signal ground. Either directly or through some low Ohm resistor or antiparallel diodes. I prefer the straight connection.
System ground loops are caused by multiple ground connections. For example if preamp and power amp have their signal ground connected to safety earth, the interconnect between them creates a loop, which picks up hum. Have the signal ground connected to safety earth only at one place in the system, preferably preamp.
If the above did not fix the problem, there can be different other causes. A systematic approach should be applied to first identify the area where the hum is picked up. I usually start at the input side of the amp and work my way downstream, following the signal path. Connect the input tube grid to ground. If the hum goes away, the problem lies between input jack and grid (shielding, volume pot, etc). If the hum persists, move up to the next stage until you reach the output tube. This way you locate the area where the hum is picked up. Then check the stage which is affected further.
Common causes: too much ripple on B+, heater without reference to ground. Inadequate filtering of B+ can be easily verified by temporarily adding more filter capacitance. Doubling the last cap at the stage concerned should cut the hum in half. If that is the case, apply more filtering to that stage. In power amps DC heaters are normally not needed for indirectly heated tubes, yet this is the most common suggestion when someone reports a hum problem. More often it is forgotten to reference the heatesr to ground. In power amps this can be done by putting two resistors across the heater line and connect the mid point between them to ground. Even better to slightly bias the heaters positive. This can be done by connecting the midpoint of those resistors to a postive voltage of 20-30V. The volltage can be obtained by a resistor divider from B+ to ground, which at the same time can act as a bleeder. Important to bypass the resistor at the ground side with a capacitor, so that the heaters have a AC referecne to ground. The divider resistor should not be of too high resistance. The maximum allowed resistance between heater and cathode is 20k Ohm for most tubes. Elevating the heaters above ground biases the parasitic diode between heater wire and cathode positively so it won't conduct. This reduces heater-cathode leakage. I apply this technique in preamps. In power amps the direct reference to ground is usually sufficient.
With the above techniques, most of the hum issues can be solved. Of course there can be many more reasons for hum. Poor ground wire layout, coupling from power transformers, etc. Also in these cases the above approach can help to identify the area of the circuit in which the hum is coupled into the signal and narrow down the search. Also be aware that there can be several hum sources, fixing one can reveal another problem which was hidden by the sronger hum source.
Be aware that in some amps just grounding a grid might not be possible. For example in DC coupled stages or if fixed bias is used. In those cases some other means need to be found to remove the signal from the grid. Only try the approach described here if you fully understand how to do it.
This is by no means a comprehensive guidline for hum issues. A hum free amp requires careful planning and layout to start with. Some hum issues can be very tricky to hunt down. But 90% of the hum can be quickly fixed by following the hints mentioned above.