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70% TO 80% OF PROBLEMS COULD'VE BEEN FOUND JUST USING ONE'S EYES. 
"Oh LOOK, the Plug is out of the Wall..."
Say Ahhh...
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TroubleShooting
-&-Repair------
--LOOK..., SNIFF..., ASK..., & LISTEN...
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Remember:  L S A L   Look, Sniff, Ask & Listen
Troubleshooting electronic or mechanical equipment is pretty much like a doctor diagnosing an ailment. When examining a patient, the doctor Looks, Asks, and Listens, they may even Sniff.
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MAKE NO ASSUMPTIONS!   --when ever possible--
Watch out for assumptions: making an Assumption is bad enough; but two assumptions--end to end, can be murder.
Once upon a time there was a patient who told his doctor that he was in great pain: "...no matter where I touch, it hurts." 

The doctor--taking him at his word--wonders, what could be wrong with this poor fellow? He must really be in serious trouble if he hurts all over! 

The patient, it turns out, had a broken finger. --Bad assumption.
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Time and Effort searching for documentation is Time well spent!
Not having a schematic, or data sheets, etc., is the bane of the troubleshooter.
However, when "flying blind," one is forced to make some, "assumptions."  --Bummer.
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-are not compatible!-----

Never allow yourself to get upset or angry; if that starts to happen, turn off the bench & WALK AWAY; take a break, go get a coke, go home... 

--Don't Push your Luck!--
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KEEP a RECORD
Keep track of your troubleshooting; preferably in a bound notebook. Record everything!---
Also, it's not a bad idea to draw a troubleshooting flow chart of the system you are working on. I know this seems like wasted effort and wasted time, but in the long run, it will often prove the quickest way. 
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When it comes to Troubleshooting and Repair, the Military teaches two categories of proficiencies, referred to as "Learning Sets" and "Learning Theory."
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 Learning Sets:
Troubleshooting using the probabilities approach.
This approach relies on the troubleshooter's experience more than understanding circuit theory. Ironically, the most productive troubleshooters are often those people who know the least about circuit theory, and more about what devices cause which symptoms.

In the old days it was a matter of pulling and testing/replacing vacuum tubes. Now days, if the device isn't socketed, it is unsoldered and tested/replaced.
 

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 Learning Theory:
Troubleshooting using the logical progression approach.
This approach relies on the troubleshooter's understanding of circuit theory; of course, adding experience yields the best of both worlds.
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The age old question: Do I start at the beginning, and work forward; or do I start at the end--the output, and work backwards? 

The answer: If it isn't the power supply, it is most likley the output stages where the higher power components live.  __Or NOT!
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A General Troubleshooting Sequence
One for  All Most Occasions

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REMOVE ALL POWER
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First UnPlug!  
LOOK, SNIFF, ASK, & LISTEN!
Often the trouble can be found by just looking.

Also Listen to the owner of the device under scrutiny! 

 
KEEP a RECORD
Keep track of your troubleshooting; preferably in a bound notebook. Record everything!

Keep a log or better still, keep a notebook, of what you have tried and the results. This will keep you from going over previous ground. 
 

 
MEASURE Resistances
Measure Resistance of A.C. Plug looking for OPEN: Open Fuse, Open Transformer; or Faulty Switch; or SHORTED Transformer winding (pri & sec), etc.
 
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 RESTORE POWER
 
Isolation Transformer  
Substitute Fuse  
APPLY POWER  
MEASURE VOLTAGES  
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Intermittent Problems
Intermittent troubles are the worst kind of troubles! 
 

Cold solder joint.
 Solder that looks "good" can actually be open or intermittently open.

ICís pin(s) folded up under device--sometimes making contact, sometimes not.

Finding Intermittents
Circuit Cooler for temperature cycling. 

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Failure Modes
Cold solder joint.
 Solder that looks "good" can actually be open or intermittently open.
 

Shorted Capacitor
Electrolytic is more likely than other types of capacitors to fail.

Open or Shorted rectifier.

Defective Resistor:
Discolored Burned / Charred 
Open 
Value Changed
Shorted

IC Socket:
    IC not pushed in far enough.
     ICís pin(s) folded up under device--sometimes making contact, sometimes not.

  Socket Open
    IC sockets, possible manufacturing defect--very very rare (I've seen it 3 times in > 30 years. 
     Be careful, Murphy makes his money on things like that! 
 

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Troubleshooting Breadboards or New layouts

ALWAYS double check against the original drawings: 

Using DATA SHEETS, verify Schematic & Layout. 

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