Want to divide an AC signal precisely?  Use a ratio transformer, a box consisting of one or more specially-wound multi-tap transformers.  Apply an AC signal to the box's input terminals, set the "taps" to the fractional amount of AC you'd like to see at the output, and away you go!

Ratio Transformers, AC Ratio Standards and Inductive Voltage Dividers are all essentially the same kind of device.  They consist of one or more high-quality magnetic cores around which multiple, multi-tap windings are wrapped.  Typically, a single continuous length of wire is wrapped around the core and tapped in ten or more places, providing for selection of decimal fractions of the input, e.g. 0.1, 0.2...0.7, 0.8, 0.9, 1.0.  The taps are routed to a rotary switch that connects the desired tap to the output.  Apply one volt to the input, dial up "4" on the rotary switch and 0.4 volts appears at the output.

Almost all ratio transformers consist of multiple switch decades similar in fashion to resistance decade boxes. Some of the better boxes have seven or eight decades.  The most common ratio transformer, the Gertsch RT5, consists of five decades of taps plus an interpolating potentiometer, allowing for selection of output as low as 0.000001 (on-millionth) of the input voltage.  For example, a dial setting of say 0043501 produces an output of 4.3501 millivolts per volt of applied AC input.  

Most multi-decade boxes consist of two or more cores around which multiple, independent, continuous wire segments are wound.  Each wire segment is associated with its own switch decade and consists of multiple taps.  For example, a first decade might consist of a total of 2000 turns tapped every 200 turns.  A second winding, wound on the same core would have a total of 200 turns tapped every 20 turns.  A third winding, again wound on the same core, would have a total of 20 turns tapped every 2 turns.  Each decade's output is routed to the next lower decade in a sort of cascade-Kelvin-Varley arrangement, which incidentally is the subject of the Gertsch's primary patent (Riordan, 1958). Decade output A is subdivided by decade winding B producing decade output B, which is turn subdivided by decade winding C, and so on.  Examples: The 7-decade Gertsch model 1011 implements seven decades distributed over two cores, while the ESI DT72A implements 7 decades over four cores, providing a very slight improvement in accuracy over the Gertsch unit. 

Ratio transformer accuracy stems from the fundamentals of transformer design.  A winding with N turns on the primary and M turns on the secondary will produce precisely M/N volts at its output given both primary and secondary windings are wound on the same core, special low-loss high-mu tape-wound cores are utilized (which improves coupling) and good winding practices are observed.   Linearity of a good ratio transformer exceeds that of the best commercially available semiconductor multiplying D/A converters.  Some of the better ratio standards exhibit less than 0.5ppM linearity error. 

You can't apply DC to a ratio transformer, and there's always a maximum AC voltage which can be applied to the input.   Transformers are "volt-second absorbers" and obey the transformer equation, which among other things, states that the maximum voltage a core can support is a linear function of the frequency of the AC signal.  This gives rise to a frequency-dependent maximum voltage rating, something typically stamped on the patent plate of the unit.  Common values are 0.35F and 2.5F.  Examples:  A 0.35F -rated box allows for 0.35 volts of AC input per hertz signal frequency.  For example, you can impose a maximum of 21 volts at 60 Hz (21 x 0.35).  Boxes rated at 0.35F employ smaller cores and have a higher maximum frequency, typically 3,000 - 20,000 Hz.  Boxes rated 2.5F employ much larger cores and operate best between 30 Hz and 1,000 Hz.  The patent plate on most boxes typically indicates a second maximum AC voltage figure, which derives not from the frequency /voltage characteristics but from maximum ratings of winding insulation and rotary switch components. This is the maximum voltage you can apply regardless of input signal frequency.

Who made ratio transformers?  Primarily, Gertsch et. al., and Electro-Scientific, aka ESI.  Gertsch started producing units in Los Angeles, about 1955, and continued production until about 1992, during which time the Gertsch factory changed hands - first Gertsch, then Singer Gertsch, then Ailtech Gertsch, then Eaton (which redesigned several of the more popular boxes and dropped the Gertsch name on them).  Gertsch cut a lot of new ground in RT design and unquestionably produced the widest variety - at least 35 models, in every imaginable configuration.    ESI produced a much smaller range of ratio transformers, though some models were sold in large quantities and rank amongst the best ratio transformers produced.  North Atlantic made three or four units, and a there were a few others, including one or two designed in Brazil and a couple from Italy and France.  A small, less accurate but truly handy 3-decade unit was produced by Coast Coil company.  Tegam Corporation, in Geneva, Ohio, has continued the manfacture of a few Gertsch/Eaton units and two of the higher-end ESI models.  Tegam essentially took over the RT business in the US, after acquiring exsting Gertsch/Eaton and ESI inventory, jigs, fixtures, etc.

Most RTs were purchased by the US Military and used in testing of avionics and other bridge circuits.  Specially wound and tapped RTs with ratios according to Sine and Cosine came into existence for synchro/resolver testing in aircraft servomechanism control.  Though RTs exceed the performance potential of semiconductor DACs and ADCs, the move towards semiconductor based control and changes in avionics design served to obsolete most ratio transformers.

What are the best RTs out there?  The two industry-standard cal-lab quality boxes were the Gertsch et. al model 1011, and the ESI model DT72A.  These were premium 7-decade wideband units rated 0.35 volts per Hz, with sub-ppM nonlinearity.   Typical Ebay prices range from $100 for a banged up unit to over $1000 for a well cared for box. 

Beyond this, the ESI / Tegam PRT73, a modern, electronically controlled "digital" ratio standard ranks as the most sophisticated box with the greatest number of features.  The PRT73 is optionally equipped with a 2.5 V/Hz section to compliment its standard 0.35V/Hz section, and which brings the unit to a total of eight decades. Linearity error is sub-PPM, approaching that of the Gertsch 1011 and ESI DT72A. Ratio is displayed as eight 7-segment displays, and there's an IEEE-488 interface for automatic control.  PRT73s were produced in limited numbers for the US military, and were used to supercede dozens of ratio transformers and serve as a cal-lab standard for AC voltage division.  Most of them were equipped with the additional 2.5V/Hz switch deck.  A small number of PRT73s have appeared on Ebay, apparently from recently released military surplus sales. Owing to their relatively young age and typically light use, most are in good condition.  They fetch between $2,000 and $3000, and are truly a bargain. Once they're gone, they're gone, and a new, fully equipped PRT73 is over $12,000 new.

In Gertsch: Gertsch made several massive dual-deck units incorporating separate, isolated,  low and high frequency sections, including the behemoth 7-decade model 1009.  This was essentially two RTs in one box, rated 0.35V/Hz and 2.5V/Hz. The 1009 might represent the ultimate in Gertsch's RT box building, but of the dual deck units the six-decade Gertsch/Singer/Ailtech/Eaton model 1000 is the best choice, owing to the use of ultra-premium switch decks that last a lifetime (the 1009 was so internally crowded that they could only fit standard-duty switch decks).   A simple general purpose RT such as the RT-5 is a good general purpose 5+1 decade box to have on hand and can be found for $50 or less.  The RT-60 is a compact 5-decade 0.35V/Hz unit that takes up little space.  The RT-9 is a 5+1 decade box rated 2.5 V/Hz.  (Use 2.5V rated boxes for power-frequency stuff at 120 volts).  Eaton produced the M1012, a modern 7-decade 2.5 V/Hz unit, very rare, and probably the best power-frequency rotary-switch RT produced, though again, the Gertsch 1000 is a great 6-decade choice.