MismatchLoss of severely mismatched EFHW transformer – system response

It is easy to become focused on the behavior of a component, but don't lose sight of the fact that it is but a component of a system where components interact, and the system response is the bigger / more complete picture.

In the article MismatchLoss of severely mismatched EFHW transformer , a caveat stated and restated was:

Transmitters are not necessarily well represented as a Thevenin source, so measurements using such sources (VNA, SA with TG) and application of linear circuit theory are not necessarily applicable.

So, can we estimate a likely system response to a 30+j0Ω load, good 1:49 transformer and modern HF 100W (20dBW) SSB transceiver designed for a nominal 50Ω load?

The following analysis gives a likely solution and it deals with a common implementation where the source is anything but a Thevenin source.

PA VSWR protection

Most transceivers of this type incorporate several PA protection measures, and one of them is commonly to reduce IF gain so that reflected power measured in a directional coupler near the antenna jack is not more than say 4W. This accommodates VSWR up to 1.5 without power reduction due to VSWR protection.

So, with an extreme mismatch, Pref=4W due to the PA protection system.

30+j0Ω load via an ideal 1:49 transformer

The scenario of 30+j0Ω load if that of the quoted measurement in the previous article, used without comment on its merit.

Lets use the calculation from the previous article, the equivalent case of a 50Ω Thevenin source with load of (30+j0)/49=0.6122+j0Ω.

The quantity 1/(1-|s|^2) is the MismatchLoss, \(MismatchLoss=\frac{P_{fwd}}{P_{fwd}-P_{ref}}=\frac1{1-\frac{P_{ref}}{P_{fwd}}}\) and it is 20.92, so we can calculate that if Pref=4w (by virtue of PA protection), that \(P_{fwd}=\frac{P_{ref}}{0.952}=\frac4{0.952}=4.202 \text{ W}=6.235 \text{ dBW} \).

So, the PA protection has reduced Pfwd from available by 20-6.235=13.77dB.

Additionally, MismatchLoss of 13.2dB further reduces the power into the 30+j0Ω load, so the power into the load is 27.0dB lower than the transmitter's capability of 100W or 20dBW. Note that this 20-27=-7dBW or 0.2W reconciles with the earlier calculation of Pfwd-Pref=4.2=4=0.2W.

Loss in a good real transformer core and conductors might add another 1dB of loss, for a total of 28dB lower than the transmitter's capability of 100W or 20dBW.

Perhaps 160mW into the 30+j0Ω load.

So what gets hot here?

  1. The transmitter protection has reduced power output, so it is safe and probably runs much cooler that at full power;
  2. The transformer core and copper losses are probably around 20% (1dB) of 200mW into the transformer, so 40mW… it is not going to get very hot.

This discussion has been about steady state operation. VSWR protection is usually implemented using the ALC control circuits; and during transients, excessive dissipation and excessive distortion are likely. It would be naive to depend on VSWR protection for operation of such a transmitter into such a mismatched load.

The performance degradation of the SYSTEM is mostly a result of MismatchLoss at the transformer input and the resulting PA protection system reducing output power.

So, someone connecting up a 1:49 EFHW transformer to an end fed quarter wave is pretty naive and will endure significant system degradation, but most modern ham proof transceivers contain protection schemes that will prevent damage.