Effect of receiver mismatch on line loss and system noise performance

The input circuit of LNAs optimised for best Noise Figure are often not matched for maximum power transfer. This gives rise to standing waves on the feedline used to connect the antenna to the LNA, which may increase feed line loss, and on the face of it, may significantly degrade system performance.

Take for example an array of 4 long Yagis on 1296MHz with 2.5m of LDF4-50A to a combiner, relay and FET LNA. Lets assume that the equivalent noise temperature at the LNA input terminals is 75K (NF=1dB). (This would require an LNA with LNA NF<0.7dB in a practical system.)

The loss in the LDF4-50A under matched conditions is 0.2dB (Teq=14K), but the input impedance of a noise optimised FET amplifier is not usually 50+j0Ω, rather something quite different. Taking an example design, the input impedance of a NF optimised MGF1302 LNA is probably worse than 2.3+j28Ω (depending on the actual input circuit).

The loss in the coax with a load of 2.3+j28Ω can be calculated using TLLC, giving 2.3dB of loss (PowerIn/PowerOut) which is alarming in a low noise receive system. The impedance looking into the coax is 62+j215Ω.

To understand the full impact, it is necessary to compare the power delivered to the load from the 50Ω source with and without the coax in situ, and an interesting thing occurs. More power is delivered by the source to the coax input than if directly connected to the LNA, so much so that it approximately offsets the high loss in the coax under standing waves.


Ansoft designer model of LNA input circuit

The effect was explored in Ansoft designer using the circuit above. The coax was modelled with k, C1 and C2 parameters from TLLC for LDF4-50A at 1296MHz, and the length of the line varied. The power absorbed by the LNA input varied, but very little as the length of the line was changed.

LNA front end loss

LNA front end loss

Above is a plot for front end loss relative to zero length of coax vs coax length, and a plot of matched line loss for comparison. It will be noted that although the coax operates under very high VSWR (load end VSWR is 29:1), the system loss taking into account the effects of the load on the source is comparable with the matched line loss.

The solution to the above scenario can be found from the TLLC results for the given load and line parameters. With a load of 2.3+j28Ω, load end mismatch loss is 8.85dB, meaning that such a load would absorb 8.85dB less power from a 50+j0Ω source than a matched load (a consequence of noise figure optimisation). The source end mismatch is 6.77dB, so 8.85-6.67=2.08dB more power is delivered by the source into the line than it would directly into the LNA. From the TLLC results, line loss under the mismatch conditions is 2.28dB, so the total front end loss relative to zero coax length is 2.28-2.08=0.2dB.

The effect has not been explored in the general case, but for a range of loads, source impedances and line lengths, a similar effect was observed. A subject for further analysis!

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