When designing a directional coupler like the Stockton bridge, it is very useful to know the signal levels that are developed internally. The power ratings of the termination resistors, in particular, require knowledge of the voltages developed across them. The current through the transformer windings also must be known in order to ensure that the toroid cores don't reach saturation.
This page links to a .PDF page showing the signal and power levels expected in a conventional two-transformer Stockton SWR bridge circuit at various levels of power input. The numbers shown here apply to a circuit using transformers with a 10:1 turns ratio, but can easily be extended to other cases since voltages and currents in this circuit scale linearly with the turns ratio.
Most amateur radio applications use diode detectors to convert the bridge outputs to dc levels for monitoring and display. This approach results in some non-linearity in the readings, especially at low power; even so, it's adequate for all but the most demanding requirements. If operation at very low power levels - down to a few milliwatts -- is required, a good alternative to the diode detector is a log amplifier, similar to Analog Devices' AD8370.
The .PDF file includes calculations for both types of detectors. I have not yet implemented a design using the AD8370.Click here to open the .PDF file