Periscope Ant. NF Degradation?

To:   The Microwave Group
From: Dick, K2RIW          10/07/03.
Re:   "Periscope Ant. NF Degradation?" and Antenna Noise Temperature.

Subsequent parts will be added as Dick makes them available.

WARNING -- This treatise is quite long-winded, but contains some of the information that a number of the serious microwavers have been requesting. This submission provides some definitions, and Radiometry examples, before directly addressing the Periscope Antenna Noise question.

1.0 INTRODUCTION -- There has been a good thread of comments on this subject from W6GHV, K2TXB, N4HY, WA2SAY, WA1MBA, AL7EB, N5GDB, AA1YN, and I will add mine.

You may find that each technologist has his own favorite equations and methods of evaluating System Noise Power, and its effects. Most of these methods can give the correct answers, as long as the details are properly considered. My method attempts to display the Noise Power and its detriment at each stage of the system. I believe this method illuminates the critical stages.

2.0 ANTENNA NOISE TEMPERATURE -- and the Gain-to-Temperature Ratio (G/T) of an antenna system are concepts that many microwave engineers have trouble with. The concepts are often counter-intuitive. Here are some examples of the apparent paradox:

(1) Does a Periscope Antenna System have more Antenna Noise Temperature than a conventional "Dish at the top of the tower system"? With a good design, I say it can be significantly better -- for at least three reasons that are described later. You would have to coat the Flyswatter Reflector with a layer of carbon granules that are almost a 1/4 wave thick in order to substantially change this condition. As you will see, you'd have to really work at destroying the great Antenna Noise Temperature capability of a good Periscope Antenna system.

(2) If my Radio Astronomy Dish antenna is in direct sunlight (but aimed away from the sun) the aluminum reflecting surface will get quite hot. Will the hot reflector increase the Antenna Noise Temperature? I say essentially no, for the reasons (explained below).

(3) If the aluminum elements of my Yagi antenna get hot from sun exposure, will that increase the Antenna Noise Temperature? I say no.

(4) My EME antenna sidelobes look at the ground and pick up some Antenna Noise Temperature. Will that noise be worse in Summer versus Winter? I say the difference is quite small (not including the presence of "lossy" summer foliage). ............

(5) If I spread wire screening on the ground around my EME antenna, will that improve the Gain-to-Temperature (G/T) ratio? I say yes. Quite a few satellite ground stations are doing this, and they think the improvement is worth the effort.

2.1 WHERE DOES ANTENNA/SYSTEM NOISE TEMPERATURE COME FROM? -- In many of those situations, the underlying causes are not always obvious. Here is my partial list, in approximately the descending order:

(1) Noise Figure of the Low Noise Amplifier (LNA).
(2) Loss in the feed line between the antenna and the LNA.
(3) The cascaded Noise Figure of the rest of the RCVR system.
(4) The G/T Design of the antenna.
(5) Antenna VSWR that makes the LNA's working NF greater than it was tuned for.
(6) Water in the feed line system.
(7) Noise/Jamming entering the sidelobes of the antenna.
(8) Man-made noise.
(9) Reflectivity/Absorptivity of the "earthy" materials in the vicinity of the antenna's back lobes and sidelobes (trees, grass, bare earth, screening, etc.).
(10) Signal-to-Noise degradation in the RCVR system caused by excessive gain in the earlier stages causing partial limiting in the rest of the RCVR. This causes Signal-Crossed-Noise components to be created in the RCVR system. This factor can decrease the SNR in a very subtle way that's hard to detect (a CW signal is assumed).
(11) Physical temperature of the <> Antenna-plus-feedline components of the antenna system.
(12) Electronic Noise from the voltage regulators used within the RCVR system.
(13) RCVR LO Synthesizer Spectral Purity Noise.
(14) Earth temperature of the Ground Noise Power that enters the antenna sidelobes.


ANTENNA NOISE QUALITY -- What follows are slightly complicated examples that help illustrate some interesting principles that directly affect the Periscope Antenna Noise Figure question. If the (I^2)*R Loss within an antenna system is kept low, and the ground-looking sidelobes are controlled, then the Antenna Temperature will also be kept low -- regardless of the antenna's layout. I'm going to use a 1 dB cable loss to illustrate a Radiometry Principle. Bear in mind that the 1 dB loss could be located anywhere within, or in front of, the Receiving Antenna system (but, before the LNA), and it will have a similar impact on the SNR. But, the word "loss" has to be used carefully. There are technologists who believe that if they use a Yagi antenna that's mistuned so that it has 1 dB less gain (but good VSWR), they believe it has 1 dB of excess loss, and that it suffers the Antenna Noise temperature detriments that are about to be described -- this is usually not so.

3.1 DEFINITIONS -- What is Noise Figure (NF), Noise Power Density (NPD), and Noise Temperature (NT) of an antenna system? Some of the definitions are:

(1) NF(dB) = 10*LOG[SNR(out)/SNR(in)].
(2) NF(dB) = 10*LOG[Te/290+1].
(3) NPD(dBm/MHz) = -114 + 10*LOG[Te/290].
(4) NPD(dBm/MHz) = 10*LOG[10^{(NF-114)/10}-10^{-11.4}].
(5) NT(Kelvins) = 290*(10^{NF/10}-1).
(6) NT(Kelvins) = 290*10^{(NPD+114)/10}.
The next equation is referenced to the Amplifier input, Simply add the Gain (in dBs) to obtain the output NPD:
(7) Amplifier NPD(dBm/MHZ) = 10*LOG[(10^{(NF-114)/10})-10^(-11.4)].
(8) Pad(output) NPD(dBm/MHz) = 10*LOG[(1-10^{-L/10})*10^{-11.4}+10^{(NPDi-L)/10}].
(9) Cooled Pad(output) NPD(dBm/MHz) = 10*LOG[(1-10^{-L/10})*(Tp/290)*10^{-11.4}+10^{(NPDi-L)/10}].
(10) Adding Noise Powers, Psum(dBm/MHz) = 10*LOG[10^{P1/10}+10^{P2/10}].

NF = Noise Figure in dB units.
SNR(out) =The Signal to Noise Ratio at the output of the stage being measured.
SNR(in) = The Signal to Noise Ratio at the input of the stage being measured.
Both SNR's are a Ratio (not dB's).
Te = Equivalent Receiver System or Amplifier Noise Temperature, in Kelvins.
NPD = Noise Power Density in dBm/MHz.
NPDi = Noise Power Density (in dBm/MHz) at Pad input.
L = pad loss in positive dB units.
Tp = Pad Physical Temperature in Kelvins.
Kelvins = 273.15 + Degrees Celsius.
P1 & P2 = NoisePower(1) & NoisePower(2), in units of dBm/MHz.

3.2 A ZERO dB NOISE FIGURE EXAMPLE -- If my "Perfect LNA" had 20 dB of Gain, and added no Noise Power during the amplification process, then the amplifier's output would simply be an amplified version of everything that was applied to its input. That means that the input Signal would become 20 dB louder, and the input Noise Power would also become 20 dB louder. But, here's the kicker -- for that "Perfect LNA" the output Signal-to-Noise ratio would be the SAME as the input Signal-to-Noise ratio. Thus, the SNR(out)/SNR(in) would = 1, and the 10*LOG of this would be 0.0 dB (Equation 1). We would call that a 0.0 dB Noise Figure amplifier, a very desirable device.

3.3 THE LOSSLESS CABLE'S NF -- By the above definition, a really good piece of LOSSLESS coaxial cable (or Wave Guide) that's 3 feet long would have a Noise Figure of 0.0 dB, even if I heat it up with a blow torch to 500 degrees Fahrenheit (assuming I didn't melt the dielectric). A truly LOSSLESS component that the signal flows through (like a cable or an antenna) does not have the ability to add RF Noise Power, regardless of its physical temperature -- see Equations (8) or (9), and plug in Loss = 0 dB. This is true for a transmission line, the other components of an antenna system, as well as the atmosphere that the signal flows through during an EME QSO (if its lossless at your frequency). Only components that have a kind of I^2R loss (heating loss) are capable of generating RF Noise Power, which is usually quantified by Noise Power Density (NPD) in units of dBm/MHz, or dBm/kHz.

3.4 HERE'S THE TEST FOR A PERISCOPE ANTENNA, OR A COMPONENT -- If you can put a lot of RF power through a component in question, and if it would run ice cold, it then has no ability to generate RF Noise Power. By comparison, a 1 dB pad can generate considerable RF Noise Power, unless it's cryogenically cooled. In a well-designed Periscope Antenna System there are no components that would run hot with high powered RF. The improved illumination taper of the "Flyswatter" portion (compared to a normal dish) causes it to run slightly higher in gain, and slightly higher in sidelobe levels. The two factors almost balance, but they often display an improved G/T performance.

3.5 YOU MAY NOT "SEE" THAT NOISE -- Bear in mind that most room temperature, passive, lossy, components (with the exception of a Noise Diode) can not generate any more than -114 dBm/MHz (-144 dBm/kHz) of Noise Power Density (NPD). Therefore, if your system's LNA has a Noise Figure (NF) much above 3 dB, you may be quite unaware of the detriment of the Passive Noise Sources; their Noise is almost below your system's detectability, without the use of a Radiometer. Only the Integration Factor of a Radiometer is capable of resolving a small fraction of a dB of Noise change.

3.6 THE LOSSY CABLE'S NF -- If that 3 foot piece of coaxial cable had an insertion loss of 1.0 dB, things change considerably. At so-called room temperature (290 Kelvins, 16.85 C, or 62.33 F) by the IEEE definition, that piece of cable has a Noise Figure of 1.0 dB. But, if I had the resources to cryogenically cool that cable to 0.0 Kelvins (-273.15 C, -459.67 F), that same 1 dB loss cable would have a Noise Figure of 0.0 dB (Equation 1). With the right selection of non-superconducting materials, that cable (or a 1 dB pad) could still attenuate the signal by 1.0 dB, and it would also attenuate the input Noise Power by 1.0 dB, but there would be no Noise Power generated within the cable itself (that's because of its cryogenic physical temperature, Equation 9). Thus, the SNR(out)/SNR(in) = 1. That's a 0.0 dB Noise Figure (Equation 1).

3.7 BUT, IT STILL HAS A SYSTEM IMPACT -- A naive technologist might think that a 0.0 dB Noise Figure component could not have an impact on the operation of his RCVR system -- that's usually not so. If the LNA that follows that 1 dB cable has a NF of 0.0 dB, then there's no impact. But, if my more-realistic LNA had any other NF, that cooled cable will still hurt my overall system SNR. That cryogenically cooled cable will still attenuate the signal by 1.0 dB, and that weakened signal must now compete with the Noise Power generated by the Power Sum of the LNA Noise plus the attenuated Antenna Noise Temperature. A numeric example will illustrate this.

4.0 A VERY GOOD DISH -- Assume that my VERY GOOD 10 GHz Parabolic Dish antenna is aimed at cold sky and has an Antenna Noise Temperature of 15 Kelvins. That's a Noise Power Density (NPD) of -126.86 dBm per MHz (Equation 3), or -156.86 dBm per kHz of RCVR bandwidth. Assume that my VERY GOOD LNA is first mounted at the dish, and has a NF of 0.4 dB. The LNA is generating an input-referenced NPD of -124.16 dBm per MHz (Equation 4), or -154.16 dBm per kHz. My total RCVR Noise is the power sum of -156.86 dBm/kHz and -154.16 dBm/kHz = -152.29 dBm/kHz (Equation 10). Assume that I'm listening to a CW satellite signal of -149.29 dBM. That gives me a Signal-to-Noise-Ratio (SNR) of +3.0 dB in a 1 kHz RCVR Bandwidth. By the way, that same signal would also yield a 4.76 dB of Signal-Plus-Noise-to-Noise Ratio ( [S+N]/N ); that's the Delta dB you would see when sweeping the dish across that satellite source.

4.1 DISH PLUS WARM CABLE -- First, I'll add the room temperature 1 dB cable between the dish and the LNA. The dish is providing a NPD of -156.86 dBm/kHz to the cable, and the cable's NPD output will be -150.08 dBm/kHz (Equation 8) -- note the 6.79 dB of NPD increase (there's more explanation in the Conclusion). When that Noise Power (really NPD) is applied to the LNA, the total system Noise Power will be power sum of -150.08 dBm/kHz and 154.16 dBm/kHz = -148.64 dBm/kHz (Equation 10). The -149.29 dBm satellite signal has been attenuated by the cable to -150.29. Now the SNR is 148.64 - 150.29 = -1.65 dB. The SNR was +3.0 dB; I've lost 4.65 dB of SNR due to the 1 dB room temperature cable that's been added to my cryogenic antenna system.

4.2 DISH PLUS COOLED CABLE -- Next I'll cool the 1 dB cable to 0.0 Kelvins. The dish supplied a NPD of -156.86 dBm/kHz to the cable. This time the cable output will be -157.86 dBm/kHz (Equation 9). When added to the LNA's NPD the system NPD is the power sum of -157.86 dBm/kHz and -154.16 dBm/kHz = 152.61 dBm/kHz. The -150.29 dBm signal applied to the LNA yields a SNR of +2.32 dB. Cryogenically cooling the 1 dB cable has improved the SNR from -1.65, to +2.32, an improvement of +3.97 dB.

4.3 COOLED CABLE PLUS PERFECT AMPLIFIER -- As the NF of the LNA gets better (goes down to 0.0 dB), the improvement caused by cooling the -1 dB cable increases even more. The room temperature cable had a NPD output of -150.08 dBm/kHz. The cooled cable had a NPD output of -157.86 dBm/kHz. That's a change of 7.78 dB. An LNA with a NF of 0.0 dB will add nothing to these Noise Powers (really NPDs), therefore such a system will see the full 7.78 dB of SNR improvement, which is caused by cooling the cable.

4.4 IS IT REAL? -- Of course, we don't presently have access to an LNA with a NF of 0.0 dB at 10 GHz, but this example is intended to demonstrate what kind of improvements are possible. In approximately 1965 the Bell System Technical Journal described an early Satellite Ground Station design where there was an unavoidable 3 foot piece of wave guide between the dish and the LNA. The Bell System people cryogenically cooled the wave guide in order to lessen the NF impact on the Parametric Amplifier LNA that followed that wave guide.

5.0 PART 1 CONCLUSION -- A VERY GOOD Parabolic Dish Antenna, or a VERY GOOD Periscope Antenna that's aimed at cold sky (by tilting the Flyswatter) is really a cryogenic system that could have an Antenna Temperature as low as 15 Kelvins (-126.86 dBm/MHz or -156.86 dBm/kHz). That's the same NPD that would be generated by a 50 ohm load that's cooled to 15 Kelvins (-258.15 Celsius). When a room temperature Pad (our 1 dB cable, for instance) is added to such a system, it only takes a small number of dBs of loss to "warm up" our system's Antenna Temperature toward 290 Kelvins (room temperature). Paragraph (4.1) and Equation (8) displays how the 1 dB cable raised the 15 Kelvin (-156.86 dBm/kHz) Antenna Temperature to -150.08 dBm/kHz, which is the same as 71.56 Kelvins (by Equation 5). A 2 dB cable would bring it up to 116.49 Kelvins; a 3 dB cable would bring it up to 152.17 Kelvins; and a 10 dB cable would bring it up to 262.5 Kelvins.

5.1 PAD EQUATIONS -- The Pad Equations (8 and 9) are difficult to memorize and understand. However, they can be re-derived (with your favorite variables), if the concept of operation is understood. An attenuating component always does three things within a Low Noise Receiving System:
(1) It attenuates the Input Noise and the Input Signal by the same number of dBs.
(2) It creates Additional Noise that's a product of the Absorptivity (1-Loss Factor) and its Physical Temperature (in Kelvins).
(3) At the output it adds the Noise Power of step(1) and step(2); they are two independent Noise Sources.

IN THE NEXT INSTALLMENTS -- I'll use the 1 dB cable example to show how this relates to the superior Antenna Noise Temperature capability of a Periscope Antenna System, and I'll discuss the relationship between the Periscope Antenna Sidelobes, and the very low sidelobes of the W4RNL Antenna Study. A future submission will discuss a more scientific way of calculating the proper Antenna Stacking Distances; for both one band, and multiple bands.

Feel free to correct the math errors.

      73 es Good VHF/UHF/SHF/EHF Optical DX,
      Dick K2RIW.
      Grid FN30HT84DC27