## Finding transceiver Teq

We have explained how to calculate Teq from Noise Figure, but most transceiver specifications do not give Teq or Noise Figure directly, in fact they don’t really contain sufficient information to reliably calculate Teq or Noise Figure.

Credible equipment reviews might provide an estimate of Noise Figure or Teq.

The best approach is to directly measure Noise Figure using a known noise generator and the Y Factor Method.

Transceiver specifications usually state receiver sensitivity in the form of some input signal voltage for a given S/N ratio, and that is at some stated receiver bandwidth setting. This might seem at first to provide enough information to calculate Noise Figure, but the problem is that the selectivity specification typically specifies a bandwidth at -6dB response, but they typically do not give the bandwidth of an equivalent rectangular filter that admits the same noise power, the Effective Noise Bandwidth (ENB) which is the quantity needed to relate sensitivity specification and Noise Figure.

(Duffy 2009), (Duffy 2009b), (Duffy 2009c) describe a method of measuring and calculating ENB but it is beyond the scope of this discussion. Suffice to say the method is indirect, it uses a sensitivity measurement and for very low noise receivers, calculated NF is very sensitive to small errors in measured sensitivity.

A rough estimate of Noise Figure can be had by assuming ENB=2kHz for a SSB telephony receiver, with an uncertainty of about 1.5dB.

If for example SSB sensitivity was specified as 0.11µV for 10dB S/N, that is equivalent to -126.2dBm for 10dB S/N, and that implies that the total noise power (from source and receiver) is -126.2-10=-136.2dBm. Now if we assume that the ENB=2kHz, the noise power from the generator can be calculated as -174+10*log(2000)=-141dBm. The Noise Figure is given by the increase in total noise over that of the source alone, so NF=-136.2–141.0=4.8dB. Teq can then be calculated as 586K.

(Wilson 2012) gives Noise Figure for the popular IC-9100 transceiver with optional 3kHz roofing filter as 4, 3 and 2dB on 144, 432 and 1296MHz. Unfortunately, the ARRL method is indirect, calculated from a sensitivity measurement and for very low noise receivers, calculated NF is unduly sensitive to small errors in measured sensitivity (Duffy 2014), they report sensitivity (MDS) to precision of 1dB, and in any event the measured configuration is not the basic configuration.

For the purposes of the studies in this series, sensitivity of the IC-9100 will be taken as 0.11µV for 10dB S/N, and ENB=2kHz, giving NF=4.8dB, Teq=586K.

## References

- Allison, B; Tracy, , M; Gruber, M. 2011. Test Procedures Manual Rev L. ARRL Newington.
- Duffy, O. 2006. Receiver sensitivity metric converter. VK1OD.net (offline).
- ———. 2009. Measuring receiver bandwidth. VK1OD.net (offline).
- ———. 2009b. Noise Figure Y factor method calculator. VK1OD.net (offline).
- ———. 2009c. Noise Figure Meter. VK1OD.net (offline).
- ———. 2014. ARRL Test Procedures Manual (Rev L) – Noise Figure calculation. https://owenduffy.net/blog/?p=945 (accessed 23/02/14).
- Wilson, M. 2012 ICOM IC-9100

MF/HF/VHF/UHF Transceiver In QST Apr 2012.

Designing high performance VHF/UHF receive systems – Part 5