Broadband VHF Radiometry with a Notch-Filtered Antenna Exhibiting a Large Impedance Mismatch Richard H. Tillman and Steven W. Ellingson, Bradley Department of Electrical and Computer Engineering Virginia Tech Blacksburg, VA

Abstract—VHF radiometry is employed in radio astronomy, ionospheric riometry, and in the measurement of signals and noise in communications applications. Accurate techniques for broadband VHF radiometry are well-known, however these techniques assume well-matched broadband antennas and/or receivers having real-valued input impedance over the bandwidth of interest. In this paper we demonstrate through theory and measurement the efficacy of accurate VHF radiometry over a large fractional bandwidth using a thin (thus, narrowband) dipole connected to a receiver whose first stage consists of notch filters that contribute significant and variable reactance throughout the passband. This technique facilitates the use of small antennas combined with aggressive notch filtering, resulting in compact systems that may be used in high-interference environments.

I. I NTRODUCTION In this paper we describe methodology for radiometry in the VHF band (here, 37–59 MHz) that employs a narrowband antenna with a direct sampling receiver that continuously captures the full bandwidth. Instrumentation performing similar measurements has been in existence for decades, but has experienced renewed interest due to recent developments in radio astronomy [1], as well possible applications in surveillance and dynamic spectrum applications [2]. The Galactic synchrotron noise background provides a useful performance baseline in this frequency range. Because of its extraterrestrial origin, it is ubiquitous and irreducible; therefore a radiometer which is able to accurately measure this background has achieved the maximum useful sensitivity [3]. A sensitive broadband measurement of the Galactic noise spectrum using a narrowband dipole was reported in [4]. Recent developments in radio astronomy have lead to the development of exquisitely accurate broadband VHF radiometers employing broadband antennas exhibiting very precise impedance matching [5]. However applications exist for VHF radiometers employing simple wire antennas in order to facilitate compact portable form factors and as elements in large arrays, in either case with interference-robust receivers. In most locations interference from Citizen’s Band (CB) radio (≈ 27 MHz) and FM broadcast radio (88–108 MHz) make sensitive broadband radiometry intractable without notch filtering to prevent these signals from overloading low-noise amplifiers. Notch filtering introduces an additional degree of impedance mismatch which must be taken into account in order to properly recover the spectrum of interest. The relevant analysis is reported here, along with a demonstration.

Fig. 1. System model.

II. T HEORY Figure 1 shows a model for the radiometer. The connecting network (CN) between the antenna and analog receiver (ARX) consists of an impedance transformer (in this case, 2:1) followed by notch filters for 27 MHz and 94 MHz, respectively. The CN is characterized in terms of its transducer power gain GT . The ARX is modeled by its power gain GRx and noise temperature TRx , and is assumed to be both input and output matched to the CN output impedance Z0 . The measured power spectral density (PSD) is then given by  Sout = kGRx GT Tant + TRx (1) where k is Boltzmann’s constant and Tant is the antenna temperature. Contributions to Tant include the Galactic noise Tsky and noise radiated by the ground, Tgnd . Although Tsky varies slightly as a function of sidereal time, a sufficientlyaccurate approximation for low-gain antennas is −2.55

Tsky ≈ (9120 K) (f /39 MHz)

(2)

where f is frequency in MHz. This model is obtained as a fit to Eq. 6 of [3]. Tgnd is roughly 150 K (i.e., 300 K physical temperature filling half the antenna pattern), which is at least an order of magnitude less than Tsky over the frequency range of interest. The antenna temperature is then given by Tant = ηTsky + ηTgnd where η accounts for ground loss.

(3)

Fig. 2. Antenna and receiver impedances Zant (solid) and ZRz (dash).

Fig. 3. (solid:) Measured PSD from the ARX with 1.3 s integration. The large signal occupying 60–66 MHz is a digital TV station. (dash:) PSD by forward modeling. (dot:) PSD by forward modeling, using incorrect GT .

GT is defined in the customary manner as the power PR delivered to the ARX relative to the power PA that the antenna would deliver to a conjugate matched load: GT ,

4Rant RRx PR = PA |Zant + ZRx |2

(4)

where Zant = Rant + jXant is the antenna impedance and ZRx = RRx + jXRx is the radiometer input impedance. GT may alternatively be expressed in terms of the “power wave e ant [6]: reflection coefficient” Γ ∗ e ant |2 , where Γ e ant = Zant − ZRx GT = 1 − |Γ Zant + ZRx

(5)

Note an easy-to-make mistake: The above result is invalid e ant : when the voltage reflection coefficient is used in lieu of Γ GT 6= 1 − |Γant |2 , where Γant =

Zant − ZRx Zant + ZRx

(6)

unless either Xant = 0 or XRx = 0. III. D EMONSTRATION The antenna used in this demonstration is a 3.048 m long, 2.5 cm diameter, straight copper dipole positioned parallel to and 1.524 m above grass-covered earth ground. Figure 2 shows Zant obtained from the lumped-element circuit model for a free-space dipole from [7]. Moment method (NEC2) simulations indicate the earth ground is expected to modify Zant by less than 1% with respect to the free-space value assumed. ZRx for the CN of Fig. 1 is also shown in Fig. 2. The ARX provides peak gain of 75 dB, 27-60 MHz 3 dB bandwidth, and input-referred equivalent noise temperature TRx ≈ 720 K, all taken as a priori information. Figure 3 shows the measured PSD at the output of the ARX. This is compared to a forward model result assuming Tsky from (2) and η = 1. The forward model is also computed using GT erroneously calculated using (6). Figure 4 shows Tsky obtained from the measurement using   Sout TRx 1 − ηTgnd − (7) Tsky = η kGT GRx GT

Fig. 4. Estimates of Tsky determined assuming η = 0.8 (solid), η = 1 (dash), and Equation 2 (dot). Dash-dot: Using GT from Eq. 6 with η = 1.

where a frequency-independent value of η = 0.8 was determined by minimizing the mean square error between (2) and (7). The residual error is primarily attributed to the dipole impedance model. Note that this result was achieved without internal power calibration. Also shown in Fig. 4 is the result using (6) for GT , which is seen to result in very large error which increases with proximity to the notch frequency. R EFERENCES [1] R. H. Tillman and S. W. Ellingson, “Active Antennas for 20-90 MHz: Examples and Practical Limits,” in 2013 IEEE Int. Symp. Ant. Prop., Jul. 2013, pp. 1266–1267. [2] S. W. Ellingson, “Spectral Occupancy at VHF: Implications for Frequency-Agile Cognitive Radios,” in 2005 IEEE Veh. Technol. Conf., Sept. 2005, pp. 1379–82. [3] ——, “Antennas for the Next Generation of Low-Frequency Radio Telescopes,” IEEE Trans. Antennas Propag., vol. 53, no. 8, pp. 2480– 2489, Aug. 2005. [4] S. W. Ellingson, J. H. Simonetti, and C. D. Patterson, “Design and Evaluation of an Acive Antenna for a 29-47 MHz Radio Telescope Array,” IEEE Trans. Antennas Propag., vol. 55, no. 3, pp. 826–831, Mar. 2007. [5] A. E. E. Rogers and J. D. Bowman, “Absolute Calibration of a Wideband Antenna and Spectrometer for Accurate Sky Noise Temperature Measurements,” Radio Science, vol. 47, no. 6, Jun. 2012. [6] K. Kurokawa, “Power Waves and the Scattering Matrix,” IEEE Trans. Microw. Theory Techn., vol. 13, no. 2, pp. 194–202, Mar. 1965. [7] T. G. Tang, Q. M. Tieng, and M. W. Gunn, “Equivalent Circuit of a Dipole Antenna using Frequency-Independent lumped elements,” IEEE Trans. Antennas Propag., vol. 41, no. 1, pp. 100 –103, Jan. 1993.

Broadband VHF Radiometry with a Notch-Filtered ...

spectral density (PSD) is then given by. Sout = kGRx(GT Tant + ... [4] S. W. Ellingson, J. H. Simonetti, and C. D. Patterson, “Design and. Evaluation of an Acive ...

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