# Small untuned loop for receiving – Trask noise and gain analysis

The article Small untuned loop for receiving mentioned Trask’s active loop amplifier.

(Trask 2010) published a two stage design using passive augmentation, arguing certain benefits of the approach.

• Zin=2.25Ω
• NF 2.42dB
• Voltage gain 36dB
• OIP2 80dBm
• OIP3 40dBm

This article presents a noise gain analysis for the 8m perimeter loop used in the article Small untuned loop for receiving to achieve a S/N degradation of no worse than 1dB at 7MHz.

The analysis assumes linear components, that there is no significant intermodulation distortion in the preamplifier. That is a significant challenge on which success of the system depends.

## External noise

From the above chart (ITU-R P.372-12 (7/2015)), we can take the external or ambient noise figure Fa to be about 45dB at 7MHz, Ta=290*10^(45/10)=9.17e6K.

## A trial loop

Lets run the calculations on a trial loop.

If we choose an untuned square loop of say 2m sides made from 6mm conductor loaded with a Trask’s 2.25Ω preamplifier, we have a loop with antenna factor (AF) of 49.7dB.

The spreadsheet above takes care of the tedium of the calculations.

The stated voltage gain of 36dB must be adjusted for input and output resistance to get power gain of 22.5dB

The ambient noise Fa is taken from ITU P.372-12 as 45dB (but it varies with precinct type and frequency of course).

The loop antenna factor is calculated using Calculate small loop Antenna Factor. Antenna Factor is sensitive to the loop geometry, including wire diameter. Larger conductor diameter will reduce the loop inductance and decrease Antenna Factor, giving higher loop Gain.

The spreadsheet calculates the equivalent noise temperature of each element of the system, and their contribution to total noise temperature. (Keep in mind that noise power  received is proportional to noise temperature.)

In this case, the receiver, loop amplifier and loop all contribute to the total noise temperature, such that the external noise is only 18.1% of the total noise and the S/N at the receiver output will be 7.5dB worse than the ratio of ExternalSignal to ExternalNoise.