A ratio transformer is an adjustable precision AC voltage divider.
An obvious parallel would be a 10-turn precision potentiometer, which "divides" the voltage present at the outside terminals. These typically have a linearity of 0.25 percent, although some are rated as tightly as 0.05 percent. But a Gertsch AC Ratio Standard has a rated terminal linearity of 0.0001 percent.
A modern approach for an op amp feedback network would be to use precision matched resistor network, but even those have a typical division accuracy of about 0.1 percent. In contrast, a Gertsch ratio transformer instrument covers a full range of ratios and typically is 100 times as accurate.
Various construction selections are possible:
Ratio transformers are signal devices, not power devices. While they are protected by fuses, they are transformers and the creative technician can burn them up. In some models, fuses may not protect an output potentiometer, which also can burn up. Then the faulty equipment might be put in a rack, never used again, and end up looking pretty good when it is sold. So caveat emptor!
One cost for ratio accuracy is a limitation to audio frequencies. DC cannot be ratioed in any transformer (though one could imagine various chopper arrangements to convert DC to precision AC for measurement). In the ideal case, a Gertsch ratio transformer would work on 400Hz or 60Hz power frequencies, depending on transformer size.
The frequency limitation is both a hassle and an advantage: We have a pretty good generator for 60Hz signals from the AC power lines, needing only a little power transformer to provide isolation for use. And 60Hz is a frequency that op amps and switching devices should have no problem handling in further processing, such as precision rectification, multiplication or synchronous rectification.
Ratio transformers were produced in a variety of configurations, and the rack mount versions can last a long, long time. The equipment uses no tubes, transistors or power supplies, so there is just not much there to wear out or die. Models with the cheaper switches could be a problem, since switch replacement was suggested as a factory activity. But the heavy duty switches on other models probably should not wear out and can be readjusted. In any case, no calibration is ever needed, so if the equipment "transforms" it ought to be working right, even if it is 50 years old. Unless, of course, somebody got into it.
I did buy a coaxial RatioTran (one not described in the 1958 catalog) that turned out to be faulty. The "coaxial" description means that two 10-position switches are controlled by two disks rotating on one shaft, which is also the control for the output potentiometer. The device had a noisy or intermittent output pot. Upon opening it up a burnt smell indicated that something had been overloaded. Presumably somebody had tried to multiply a voltage up without knowing that the last stage is typically a precision pot and without setting that pot to the end of travel. That could be a common problem, because the simple diagram on the panel generally does not show a pot. And a suitable precision replacement (10 turn 25 ohms, or 1 turn 5 ohms) could be very expensive even if one could be found.
Ratio transformer equipment is available at a wide range of prices, from $20 to $2000. The price seems to be set mainly by to a general lack of desire for the equipment, which comes from a lack of information on what the equipment is and what it can do. The rack-mount ratio transformer equipment is especially heavy (an RT-4R weighs about 40lbs), so shipping costs can be high.
There probably are a wide range of modern applications for precision ratio generation and measurement, but a few come to mind immediately: