A1's and Focus :-
As you know by now the LINE OUTPUT TRANSFORMER (loptx) generates the 25 kilovolts of power to the CRT(tube),
it also provides the First anode(A1's) and the Focus Voltages.

Thats why the loptx usually has three wires from its top, the very thick one clips onto the top middle of the tube .
(beware this is a VERY very dodgey voltage (It Kills) so never go near it without full safety precausions , It may hold a charge for months even if the set is unplugged,
You can feel if the 25kv is there on a tv by touching the front face of the tube , with the back of you hand , it pulls the little hairs.
A1's
Next the A1's this is usually the thinest wire and usually comes from the bottom part of the loptx
******Warning do not touch anything with the power on ***********
****** Switch off between each test ***************************
A1's or its is sometimes called the second grid(G2) or even SCREEN, this voltage is about 200v to 700v adjustable by the bottom adjusting knob on the loptx, It is applied to a small metal tube_like anode inside the crt neck, providing acceleration to the electron beam ,
It works like a brightness control , if turned up too far thin lines will appear sloping across the screen (flyback lines) some TV's are very fussy about this voltage setting, so if you turn it make a note of its position before you move it, and out it back the same place afterwards(unless of course you get an improvement).
A1's are usually easy to test, the socket pin being naked,
"Warning the picture will darken during the measurement because the meter will draw some current, which will lower the voltage a bit"
There is usually a resistor between where the wire joins the crt base pcb and the actual crt socket, if there is a volts drop across it , then there may be a leakage fault after it (socket or crt or capacitor).
If there is a capacitor at the terminal, to test , disconnect one end of it and retest the voltage .
Focus
The other wire of medium thickness and usually comes from about the middle of the loptx, carries the 2kv to 4kv voltage to the CRT, it is usually adjusted by the top knob on the loptx, and goes up to the crt base pcb socket.
It is heavily insulated and goes into a pin in the tube base socket , usually with a spark gap and capacitor,
If the focus is poor, then the usual reasons are:-
(1) the tune(crt) is faulty
(2) The loptx is faulty
(3) The crt base socket is faulty
(4) The Capacitor on the crt base pcb is leaky.
******Warning do not touch anything with the power on ***********
****** Switch off between each test ***************************
To test the voltage at the crt base socket is difficult on most sets , as the wire is very protected (insulated), however it can be done,
If the voltage is low then disconnect the wire at the crt socket , leave loose and touching nothing but your eht meter probe (I sometimes sellotape it to the other wires and bend the bare end away to keep it still) and switch on the set
If the voltage is now ok (twist the top knob on the loptx,to max/min to see if the voltage moves up/down, ) then its NOT the loptx , of course if the voltage is low or missing then it is the LOPTX
That leaves you with the crt and its socket
(the spark gap is inside the socket moulding usually) and capacitor .
If the loptx IS giving out 2-4kv then you will need to test its with the wire reconnected back in the socket,
if its now still ok then its probable the crt,
if it falls low then unplug the crt base panel from the tube and test again,(with the crt unplugged from the pcb)
if its now ok, then crt fauly,
If its still no/low then change the socket and capacitor and any external sparkgap (if any) one fault that occurs is that green verdigris growns in the sparkgap area causing a leakage, usually caused by damp, How does the damp get in there ? its all closed off.
It is difficult to measure the voltage, as most meters do not go above 1000v (I have a separate 30kv eht meter)
It is possible to make a focus probe, from a lot of 1meg 1 watt resistors in a plastic tube say 11 resistors , in a series chain, the last one connected to earth and the second to last one connected to the meter + terminal and the meter -ve terminal to earth also, this should make a 10 to 1 divider so 5 kv will measure 500v and so on,
the top end of the chain should have an old voltmeter probe fitted into the plastic tube, to act as the test prod
although this method may not be very accurate, after testing a few sets , good /bad focus voltage will soon be easy to recognise.
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