# EFHW transformer measurement – how accurate does the load need to be?

Several articles on this site use the following technique for measurement of transformer performance, and the question arises, how accurate does the load need to be?

Let’s set some limits on the range of ReturnLoss of interest. Measured ReturnLoss is limited by the instrument, and in the case of a VNA, its noise floor and the accuracy of the calibration parts used are the most common practical limits. That said, in practical DUT like an EFHW transformer, would would typically be interested in measuring ReturnLoss between say 10 and 32dB (equivalent to VSWR=1.05) with error less than say 3dB.

There are many contributions to error, and one of the largest is often the choice of transformer load resistor. This article explores that contribution alone.

Let’s say the load resistor used is 2% high, 2450+2%=2499Ω. To measure ReturnLoss with such a resistor is to imply that the transformer is nominally  $$\frac{Z_{pri}}{Z_{sec}}=\frac{51}{2499}$$ and ReturnLoss should be measured wrt reference impedance 51Ω.

To measure ReturnLoss wrt 50Ω gives rise to error.

Above is a chart of calculated ReturnLoss wrt Zref=51 (the actual ReturnLoss) and Zref=50 (the indicated ReturnLoss) for a range of load resistances, and the error in assuming RL50 when RL51 is the relevant measure.

For example, if Rload=48.5Ω, RL51=32.00dB whereas RL50 (which would be indicated on a VNA calibrated for Zref=50) is 36.35dB, and error of +4.35dB which falls outside our 3dB limit stated earlier… so this load resistance is incompatible with the stated measurement criteria.

Let’s say the load resistor used is 1% high, 2450+1%=2475Ω. To measure ReturnLoss with such a resistor is to imply that the transformer is nominally  $$\frac{Z_{pri}}{Z_{sec}}=\frac{50.5}{2475}$$ and ReturnLoss should be measured wrt reference impedance 50.5Ω.

To measure ReturnLoss wrt 50Ω gives rise to error.

Above is a chart of calculated ReturnLoss wrt Zref=50.5 (the actual ReturnLoss) and Zref=50 (the indicated ReturnLoss) for a range of load resistances, and the error in assuming RL50 when RL50.5 is the relevant measure.

To take the same example, if Rload=48.5Ω, RL50.5=33.89dB whereas RL50 (which would be indicated on a VNA calibrated for Zref=50) is 36.35dB, and error of +2.45dB which falls within our 3dB limit stated earlier… so this load resistance is compatible with the stated measurement criteria.

## Is there a simpler way?

Let’s review the meaning of directional coupler Directivity.

Above is a diagram from Mini-circuits.

An important property of a directional coupler is its Directivity, $$Directivity=10 \log \frac{P3}{P4}$$.

If we  take a directional coupler that is perfectly calibrated for Zref=50+j0Ω and use it to measure a perfect load of $$\frac{2450+0.1\%}{49}=50.05 \text{ Ω}$$ we will measure ReturnLoss that equates to the Directivity of that coupler.

Above is a calculation of the ReturnLoss wrt 50+j0Ω of a load of 50.05+j0Ω. ReturnLoss is 66.03dB, so Directivity of the coupler used in this way is 66.03dB.

Above is a calculation of the uncertainty and confidence limits of a measurement of ReturnLoss indicating 55dB using this directional coupler with Zref=50+j0Ω when the measurement context is actually Zref=50.05+j00Ω.  When the indicated ReturnLoss is 55dB, the actual ReturnLoss wrt Zref=50.05+j0 is between 52.8 and 57.9dB, of 55 +2.86/-2.15.

So, a more accurate load resistor allows measurement to greater ReturnLoss within the discussed confidence limits.

## Conclusions

The accuracy of the secondary side load when measuring ReturnLoss (and related parameters like InsertionVSWR) is important.

The transformer should usually be loaded with a resistance of turns^2 * 50Ω.

A resistance accuracy of 1% in that resistance is sufficient to sustain most bench measurements of a practical EFHW transformer and field measurement with an antenna attached.