To: RFI Group From: Alan E.E. Rogers Subject: Correction antenna temperature for cable attenuation and antenna mismatch

Transcription

1 RFI MEMO #030 MSSCHUSETTS INSTITUTE OF TECHNOLOGY HYSTCK OBSERVTORY WESTFORD, MSSCHUSETTS 0886 July 25, 2006 Telephone: Fax: To: RFI Group From: lan E.E. Rogers Subject: Correction antenna temperature for cable attenuation and antenna mismatch difficult problem in radiometry is the correction for the effects of the antenna VSWR and cable between the Dicke switch and the antenna. In a 3 position switched radiometer P = g T + T - - power on antenna R P = g T + T - - Power on load L L R P + g T + T + T - power on load + calibration c L c R From which where T = T P P P P + T g = gain c L c L L P = power on antenna P L = power on load P c = power on load + cal T R = receiver system noise T c = excess calibration noise T L = ambient load temperature If the antenna is connected via cable then the relation between the antenna temperature and the measured temperature can be modeled using the sum of the multiple reflections between the antenna and the LN. The 2-way cable delay is where τ = 2 ( vc) = cable length v = velocity factor c = free space velocity The cable attenuation, cab, is approximately given by 2 cab = 3.0 f db

2 for LMR-240 whose one way loss is about 3 db per 00 feet at 50 MHz. This loss results in a temperature T reaching the LN where ( 2 ) ( ) T = T Γ cab + T cab L where Γ = antenna reflection coefficient this ignores multiple reflections between the antenna and the LN. If the LN is mismatched 2 ( ) ( 2 2 ) 2 ρ ( )( 2 2 ) T = T + a+ a + b + T c + d + T T c + T cab c + d cab obs out R out L j where a α cos( 2π fτ j) = j= j= ( π τ ) j b= α sin 2 f j ( π τ) ( a ) ( π τ) ( a ) c= a+ cos 2 f cab Γ Γ d = b+ sin 2 f cab Γ Γ α = cab Γ Γ a Γ a = LN reflection coefficient T out = noise transmitted out of LN input ρ = correlation coefficient between output noise and noise transmitted out of the LN input. T R and T out are both approximately 20 K and the LN input reflection coefficient is 0.0( f 00) approximated by while ρ ~0.5. The parameters of this model which are difficult to separately measure with test equipment ( Tout, ρ and Γ a ) can be checked by comparing the observed temperature over a wide frequency range with a long open ended cable is connected to the radiometer. nother check can be made by terminating the cable with a load of known reflection coefficient (for example at 0 db pad given Γ = 0.). With known parameters the amplitude of the observed periodic ripple can be used to measure the antenna reflection coefficient and correction of the observed temperature, 2 averaged over one cycle of ripple, for the ( Γ ) loss factor. This modeling makes it possible to obtain the true corrected antenna temperature over a wide range of frequency without the complication of using a matching circuit which is an intrinsically narrow band device and has to be tuned for each observed frequency. The 2-fold objectives of EDGES: ] To measure the cosmic background magnitude and spectral index from 00 to 200 MHz with < 5% absolute accuracy. 2

3 2] To set limits on the smoothness of the variation of spectral index from MHz and to apply this limits to model of the global EOR signature. The first objective may be best accomplished using a 25 foot (or longer) section of calibrated cable between the Dicke switched LN and the antenna while the second objective will be best served with the shortest possible connection between the LN and the antenna cor npoly 0 dtyp 99 smooth 0 mdl 0.0 t50mhz 42 tr 9 tc 494 file: 2006_203_8.acq cqiris attn 0 fpgatm 46.0 degc 5e+02 6e+02 3e+02 e+02 5e+0 Mon Jul 24 7:43: Fig. Modeled effect of Γ = 0. on 25 cable 3

4 cor npoly 0 dtyp 99 smooth 0 mdl.00 t50mhz 42 tr 9 tc 494 file: 2006_203_8.acq cqiris attn 0 fpgatm 46.0 degc 8e+02 6e+02 Mon Jul 24 6:54: Fig 2. Modeled effect of open 25 cable cor npoly 0 dtyp 99 smooth 0 mdl 0.00 t50mhz 266 tr tc 506 file: 2006_203_7.acq cqiris attn 0 fpgatm 45.9 degc start 2006:203:7:4:3 stop 2006:203:7:4:32 resolution 22.0 khz 5e+02 6e+02 3e+02 e+02 5e+0 Tue Jul 25 08:58: Fig 3. Measured spectrum with Γ = 0. on end of 25 LMR-240 4

5 cor npoly 0 dtyp 99 smooth 0 mdl 0.00 t50mhz 42 tr 9 tc 494 file: 2006_203_8.acq cqiris attn 0 fpgatm 46.0 degc 8e+02 6e+02 Tue Jul 25 08:59: Fig 4. Measured spectrum with 25 LMR-240 open at the end. 5