This calculator estimates the efficiency of a T match tuner using a simple loss model.
The simple loss model is to consider the capacitors to be lossless, and the only loss therefore to be in the inductor. This is not a bad approximation as the loss in practical ATUs with air spaced capacitors is almost entirely in the inductor. The model assumes Q of the inductor is constant for all values of inductance. In practical variable inductors, Q does vary with inductance, but over the narrow range of inductance used on one band, the assumption is reasonable.
L and C can be measured and tabulated for future reference.
If a good estimate can be made of the value of C1, L can be estimated from the settings to tune a known load (eg a dummy load) and Qli can be estimated from efficiency measured on a known load.
The following is an example of use with my MFJ-949E ATU.
Table 1 gives measured values of the switched inductor in an MFJ-949E ATU. Measurement of the input variable capacitor at 10 points reveals that it is reasonably approximated by 228-20*setting(pF).
The measured efficiency of the tuner on a 50Ω dummy load on 80m tuned using 8.3µH and 148pF is at 94%. By trial in the calculator, Qli=170. Qli can now be used for other loads on the 80m band.
If I then tune an antenna at 3.6MHz and use using 14µH and 55pF, taking Qli as 170, I can calculate T match efficiency at 76%. (Balun losses are not included.)
A similar efficiency test on a known load at 1.8MHz indicates ATU Qli=140.
If I take a certain inverted-L that is too short to tune with the ATU, but wind a 40µH loading coil to approximately resonate the feed point impedance, I find that I can tune it using 26µH and 124pF, taking Qli as 140, I can calculate T match efficiency at 75%. I estimate the Inverted-L is about 40% efficient at the loaded feedpoint, so combined with the ATU, efficiency is about 30%.
This might seem poor, but possibly acceptable. Since I wanted to use it after a 150W AM transmitter (for 112W out), it is unacceptable as the inductor would be likely to be damaged by the 38W of heat dissipation implied.
Knowing the input capacitor, inductor inductance and Q, a fairly good estimate of T match efficiency can be calculated. Accuracy depends on the accuracy of estimates of the parameters, and will be of greatest value on the lower HF bands were parameter estimates are better and T match efficiency is typically poorest.
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