# Directional Coupling at kHz Frequencies

I want to precisely measure the forward and reverse power on a high-voltage power supply that operates from 10-100kHz, at power levels on the order of 20W. To do this, I need to make or buy a directional coupler with a fairly weak coupling constant of 20-40dB.

For systems operating from 100's of MHz to GHz, I have built simple 1/4λ coupled transmission line directional couplers with a bit of stripline. A coupled transmission line design does not seem practical for 10's of kHz, so my intuition is that I'll need a discrete element directional coupler. Ham radio sites have lots of tutorials on high-frequency coupling, but I'm having trouble finding resources for coupling at low frequencies.

What topology should I consider for a directional coupler at this frequency, power level, and coupling constant?

• Why would you expect a return power - is the load at some distance away? Is it not possible to measure the load's impedance and calculate mismatches? – Andy aka May 6 '15 at 17:40
• In this case the load is an atmospheric plasma, so the load's impedance can vary widely and measuring it is not trivial. – brandoncurtis May 6 '15 at 17:47
• @Andyaka has a valid point. At these frequencies, it's hardly necessary to think of Forward and Reverse power, just measure the voltage, current and the phase relationship. Even at 100 kHz, unless the load is hundreds of metres away, you are effectively measuring the load impedance. If you like, you can then assume that it's a 50 ohm system, and convert to Forward and Reverse power. Voltage you would measure directly with an ADC, current with a transformer, resistor and ADC. – tomnexus May 6 '15 at 19:17
• Thank you, that makes sense. I need to sit down with the oscilloscope and a Rogowski coil and work through this! – brandoncurtis May 7 '15 at 4:27

Look up "Power dividers and directional couplers" in Wikipedia and go down to the section on "Cross-connected transformers". These form a directional coupler that can be tailored to any degree of coupling. Select transformers whose bandwidth spans 10 kHz to 100 kHz at your impedance level of interest, and are sufficient to handle the voltage and current, and you should be in business.

On the web, you can find a number of other references to the same thing, usually used at rf frequencies, but the info is adaptable to your case by appropriate selection of transformer bandwidth.

Remember that the terms "forward and reverse power" only have meaning when referring to a transmission line of a given impedance, assuming you are talking about the average power flow over many cycles.