by Richard Flagg, AH6NM (rf@hawaii.rr.com)
Editor's Note: Ed Cole, The SETI League's volunteer Regional Coordinator for Alaska, has contributed a companion spreadsheet to perform the calculations discussed in this article.
G/T - A Receiving System Figure of Merit
The sensitivity of a radio telescope is a function of many factorsincluding antenna gain (G) and system noise temperature (T). We allunderstand the need for high gain antennas and low noise preamplifiers.But how do we measure just how well the system is performing? A convenientfigure of merit is the ratio (G/T) - the higher this ratio the better thesensitivity of the system to weak signals. To obtain G/T one coulddetermine G and T separately, but these are difficult measurements.Fortunately it is relatively easy to obtain the ratio (G/T) by a singlemeasurement (and a little arithmetic).
T - The Total System Noise Temperature
Before proceeding with the measurement of G/T let's discuss T in a littlemore detail. T is the total system noise temperature (in degrees Kelvin)and is equal to the sum of the noise generated in the receiving system (Tr)and the noise delivered from the antenna (Ta) when the antenna is lookingat a region of the sky free of strong sources. Ta includes the galacticbackground temperature as well as additional noise picked up by the antennasidelobes viewing the earth at ambient temperature.
The receiving system temperature (Tr) is related to the system noise factor(Fn) by:
Where the noise factor (Fn) is simply the noise figure (NF) in dB expressedas a ratio:
Determining G/T
The principle behind determination of G/T is to measure the increase innoise power which occurs when the antenna is pointed first at a region ofcold sky and then moved to a strong source of known flux density - usuallythe sun.
This ratio of received power is known as the Y-factor.
The following equation shows the relationship between G/T, the measuredY-factor, and the value of solar flux (F) at the observing frequency.
where:
- Y = sun noise rise expressed as a ratio (not dB)
- k = Boltzmann's constant 1.38 *10^-23 joules/deg K
- L = beamsize correction factor
- Lam = wavelength in meters (at the operating frequency fo)
- F = solar flux at fo in watts / meter^2 / Hz
Beamsize Correction (L)
The beamsize correction factor (L) is dependent upon antenna beamwidth. andapproaches unity for small dishes with beamwidths larger than a fewdegrees. If your dish has a beamwidth larger than 2 or 3 degrees just setL=1 and forget about equation (5).
where:
- Ws = diameter of the radio sun in degrees at fo
- Wa = antenna 3 dB beamwidth at fo
The diameter of the radio sun (Ws) is frequency dependent. Assume a valueof 0.5 degrees for frequencies above 3000 MHz, 0.6 degrees for 1420 MHz,and 0.7 degrees for 400 MHz.
Solar Flux Density (F)
The next term which we need to discuss is (F) - the solar flux density atthe test frequency. The USAF Space Command runs a worldwide solar radiomonitoring network with stations in Massachusetts, Hawaii, Australia, andItaly. These stations measure solar flux density at 245, 410, 610, 1415,2695, 4995, 8800, and 15400 MHz. If you are lucky enough to be operatingnear one of these eight "standard" frequencies then all you have to do isuse the reported flux density. However if you are operating - say midway- between two given frequencies then you will need to interpolate betweenflux densities at the lower and higher frequencies. The best interpolationscheme is to graph the flux density at several frequencies and use a curvefitting routine to determine the flux density at your operating frequency.
The solar flux density obtained from the USAF must be multiplied by10^-22 in order to get the units correct for use in equation (4). In otherwords, if the 1415 MHz solar flux density is 98 *10^-22 watts/meter^2/Hz,the operator may simply state "the solar flux at 1415 Mhz is 98".
The solar flux at 2800 MHz (10.7 cm) is measured at the Dominion RadioAstronomy Observatory in Canada. This flux should only be used for G/Tcalculations if you are operating at or near 2,800 MHz.
G/T Sample Calculation
Assume that you have measured a sun noise rise of 9 dB using your 1420 MHzradio telescope. The solar flux density at the test frequency of 1415 MHzis reported to be 98.
First convert the sun noise rise in dB to a power ratio:
Determine the other factors:
Lam = (300/1420) = 0.211m
and Lam^2 = 0.045 m^2
F = 98 *10^-22 w/m^2/Hz
L= 1 (since you know that your 3 meter dish has a beamwidth of about 5 degrees)
and finally solving for G/T:
= ((7.94-1)*8**3.14*1.38*10^-23) / (98*10^-22*0.045)
G/T = 5.5
or expressed in dB:
Great - the G/T is 7.4 dB - so what? Should you be walking around with asilly grin - or slinking around looking for a rock to hide under? Well,for one thing this number is a reference point by which to judge the valueof any future modifications to the system. To put it in perspective letsdo the calculation in reverse and estimate what values of G/T and Y areexpected given an antenna size (gain) and preamp noise temperature.
Assume that your 3 meter dish with an efficiency of 50% has a calculatedgain of 30 dBi (power ratio of 1000) and that your preamp is advertised tohave a noise temperature of 45 degrees K. Further assumptions include 10deg K due to the galactic background, 25 deg K due to spillover, 30 deg Kdue to 0.5 dB of attenuation between the feed and the preamp and 5 deg Kdue to the receiver and cable following the preamp. Therefore the totalreceiving system temperature is estimated to be:
The expected value of G/T is therefore ( 1000/115 ) = 8.7 = 9.4 dB
By the way, we can do this calculation by converting temperature into dBreferenced to 1 deg K. and leaving the dish gain in dBi. Our temperatureexpressed in this way is
And G/T in dB is simply ( 30dB - 20.6dB) = 9.4 dB
So the expected value of G/T was 9.4 dB but we measured 7.4 dB. Why? Anumber of factors could be responsible, but the effect has been to eitherlower the dish gain or raise the system temperature from what was assumed.Its time to make sure the feed is focused and free of bird nests, and thatno unexpected losses exist in the receiving system.
One final calculation shows what value of Y is expected given assumptionsabout antenna gain and system temperature.
Rewriting equation (4) and solving for Y yields:
Remember to enter G/T as the ratio - not in dB.
If our system was working exactly as expected a sun noise rise of 10.8 dBwould have been measured - corresponding to a calculated G/T of 9.4 dB.
Measuring Y
The determination of G/T is completely dependent on an accurate measurementof Y. Perhaps the easiest measurement technique is to use a power meter(or a true RMS voltmeter) connected to the receiver IF . For thismeasurement to work the receiver must be operating in a linear region. Ifthe receiver saturates when the antenna is pointed to the sun you are goingto measure a dissapointing Y factor and spend lots of time trying to fixsomething that isn't broken. Of course the receiver AGC should be turnedoff. The Y factor is simply the change in meter reading on and off thesun. The accuracy of this method is dependent on the linearity of both thepower meter and the receiver.
A better technique is to use a precision adjustable RF attenuator locatedbetween the preamp and the receiver. An RF power meter is connected to thereceiver IF. Set the attenuator to 0 dB when the antenna is looking at thecold sky and adjust the receiver gain to get a convenient reference levelon the power meter. Point the dish at the sun and crank in attenuationuntil the power meter once again reads the cold sky reference level. The Yfactor is equal to the amount of attenuation needed to return the meterreading to the reference. This technique could also be used by measuringthe DC output voltage from the receiver detector if a power meter is notavailable. Accuracy of the attenuator method depends on calibration of theattenuator - not receiver and power meter linearity.
Whatever technique you use - measure Y several times and take an average.The average of five measurements is probably adequate. Try and use solarflux measurements obtained about the same time your measurements were madefor the calculation of G/T.
Where to get the Solar Flux
As mentioned earlier - the USAF operates a worldwide solar flux monitoringnetwork. These data are disseminated thru NOAA's Space Environment Center- Space Weather Operations group in Boulder, Colorado (303 497-3171). TheSpace Environment Center also distributes the solar flux data for all eightfrequencies via the world wide web. Set your brouser to:
The 2,800 MHz flux from Canada is available at:
The Learmonth, Australia eight frequency data may be found at:
And finally - for the most recent 45 days of solar flux measurements, see:
Well, that's what I know about G/T - hope this information is helpful.Please let me know if you find any errors or know of improvements to thesemeasurement techniques. I hope the formulas aren't too hard to interpret.Again - let me know if you have trouble with them.
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