Use of thermistors in old tube equipment

Is there a general rule for thermistor placement and values required for tube equipment designed to run off of 110 AC, but is now used on 120 AC ( which is the average for NA outlets)?  How many are required and is one used before the power switch and the other line to the power transformer?  This is to be used to soften the inrush current when powering the equipment 

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There should be no change to the thermistor. You need an extra ballast resistor for the extra 10V.
R = 10 / (current at 110V).
Power rating = 100 / R

However 110 to 120 is only an increase of 9% and the original 110V rating was likely +/- 10%, or even 117V +/- 10%.

See also 117Zxx family rectifier tubes for heater direct to mains. They are rated at a nominal 117V  and from 1939, maybe for battery  & mains transportable radios. They typically had a two stage ballast resistor, the first being HT and filament supply and then an additional dropper to filament series voltage (1.35 V times number of tubes plus one as the output tube would be 2.6V) the 1.5V tubes are really 1.4V and recommended to be 1.35V neasured on the detector and first audio amp.

The mains only sets have more robust indirect heaters of 150mA, 200 mA or 300mA. Europe later used 100 mA for radios and 300 mA for TVs due to the higher 220V to 240V mains supply, though parts of Europe did have 110V nominal systems in the earlier days.

In general there should be no resistors or thermistors between the main switch and the mains. Also generally only one thermistor to limit inrush. Older sets may also have had a barretter, which is iron wire in hydrogen. Like a tungsten filament it is opposite to a thermistor to limit inrush (disc thermisotrs are still used on SMPSUs). They increase in resistance when hot so protect the radio against a rise in supply voltage.

A tungsten lamp filament can be 1/10th resistance when cold, so I've added SMPSU thermistors to light switches in the past. 

Some actual measurements of plain tungsten filaments for an 220V to 240V oven lamp:

Cold (about 19 °C)
25W (small ES, old) 195 Ω
26W (small ES, new) 169 Ω

Hot @ 121.5V AC (based on measuring AC current)
25W (small ES, old) 1841 Ω
26W (small ES, new) 1599 Ω

Hot @ 235V AC based on wattage
25W (small ES, old) 2209 Ω
26W (small ES, new) 2124 Ω

So the Thermistor is to protect the filaments or heaters (mostly tungsten, but some 1.4V tubes used nickel) till they heat up. Being carbon based (originally) they reduced in resistance from the series current. Thus ino extra one, nor a change is needed even for a 15% change in supply voltage. A suitable extra resistance (after the on/off switch is fine). A small transformer can also used, but the phase is important to ensure subtracting 10 to 20V instead of adding. That's more normal for a 220V transformer based radio used in the UK, where the mains can be 245V.

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In a swedish article about electrical utilities in the USA from as early as 1928, which mainly concerns the distribution mains in New York and other big cities, it is said that the mains voltage usually is 115 or 120 V.  So in practice, equipment for the american market had to accept mains voltages around 120 V already in the late 1920's.  The article can be found here, its title is in swedish "Några data om växelströmsdistribution vid amerikanska elektricitetsverk" , which in english would become "A few facts about AC distribution at american electrical utilities".

Regarding distribution voltages in Sweden in old days, 110 V was mostly used for DC mains in cities that were electrified very early (1890's). This voltage was seldom used for AC mains where 127 V was more common (127 V phase-neutral will give 220 V phase-phase in a 3-phase system). From the 1920's to 1960's, the 127 V mains were gradually changed to 220 V.  An unique case was the city of Helsingborg which for many years had 150 V mains, both DC and AC. It was changed to 220 V probably in the mid-1950's.  The nominal voltage of 220 V was changed to 230 V in 1989, but it was more a formality than a real voltage change, as the tolerance range was changed at the same time so the upper voltage limit did not change, it was just the lower limit that was raised.

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So, summary:

Most "110V" tube gear probably is fine at 120V and may have been on 115V +/- 10%.

The thermistor is for the low cold resistance of the series tube heaters. An additional thermistor shouldn't be added.

If 120V really is too much, which is unlikely, calculate resistor value and wattage for an added resistor after the power switch on the live feeding the existing ballast and thermistor.

Likely the chassis can be live if the line cord is reversed.

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The concern by many radio and audio equipment restorers is the loss of resistance when replacing a selenium bridge rectifier with a silicon one, and the inrush when turning tube equipment with the silicon diode bridge rectifier, in addition to higher voltage from the wall. Restorers are placing a CL80 before the power switch because of the inrush current when turning on the unit that was modified as a safety precaution and to return some resistance that was lost upon replacement of the selenium bridge rectifier 

I might add, that the original circuit designs of these radios are that of perfection with what the engineers had available!

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Replacing a selenium rectifier or bridge requires one suitable resistor at the output of the silicon, not a thermistor, whiich would be too low a value when it heats up.

Nothing should be added between the main switch and the AC line.

A SMPSU uses a themistor after the main power switch because there is no mains transformer or resistor ballast to limit in-rush current and the capacitor(s) on the silicon rectifiers are about x10 to x20 the value of that in old tube radio. That thermistor is to ensure the supply doesn't trip, not to protect the equipment.

See article on Selenium.

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