Antenna and Noise Concepts

Antenna and Noise Concepts 1 Antenna concepts 2 Antenna impedance and efficiency 3 Antenna patterns 4 Receiving antenna performance Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 1 / 31

I. Antenna concepts Antennas are devices which convert currents into electromagnetic waves and vice-versa Any current carrying structure is an antenna, but usually very inefficient Far away from an antenna (or source), fields appear to be spherical (approximately plane) waves spreading from a point source Conditions to get to far field: r > 2(D + d) 2 /λ r > 1.6λ r > 5(D + d) (1) where D and d are the dimensions of the transmitting and receiving antennas respectively Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 2 / 31

Fields radiated by a time harmonic current J can be found through the vector potential and A(r) = µ 4π ds J(r ) e jk r r r r (2) H = 1 µ A (3) Conditions for the far field can be derived from this, and it can be shown that in the far field. E(R, θ, φ) = [ˆθf θ (θ, φ) + ˆφf φ (θ, φ)] e jkr R (4) Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 3 / 31

Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 4 / 31

We will focus on three basic parameters of antennas Impedance, Z A : ratio of antenna terminal voltage to current, includes both circuit and radiation effects Efficiency, υ: ratio of power radiated by antenna to the total power delivered to the antenna terminals Directional pattern: describes how much power antenna radiates in a given direction θ, φ Note that we are coupling circuit and field models here - we should be aware that fields will involve all an antenna s external environment, not usually thought of in circuit theory Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 5 / 31

II. Antenna impedance and efficiency Measurements of antenna impedance seem simple, but care must be taken to insure external environment effects and interfering signals are not significant Z A = R A + jx A (5) Real part, R A, indicates power lost from the circuit model, imaginary part, X A, indicates energy storage in fields and capacitances. So we can define an antenna loss resistance and the radiation resistance as P = 1 2 I 2 R A = P r + P l (6) R l = 2P l / I 2 (7) R r = 2P r / I 2 (8) Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 6 / 31

Antenna efficiency, υ, indicates the ratio of power radiated by the antenna to that input υ = P r /P = R r /R A = 1 R l R A (9) Of course, higher efficiency antennas are more desirable! Power lost in wires of antenna reduces efficiency. Methods for measuring efficiency Measure radiated power at sufficient distance and input power Measure antenna impedance in free space, surround by conducting shell and repeat. First measurement gives R A while second gives R l Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 7 / 31

Calculation of P r given known fields E(R, θ, φ) = [ˆθf θ (θ, φ) + ˆφf φ (θ, φ)] e jkr R (10) P r = lim R = lim R 1 π = lim R dθ 2η 0 ds ˆn < S(t) > ( 1 ds ˆn 2 Re [ E H ]) 2π 0 dφr 2 sin θ E 2 (11) We can also talk about the power in a particular polarization by only considering that component of E Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 8 / 31

III. Antenna patterns The fact that E(R, θ, φ) = [ˆθf θ (θ, φ) + ˆφf φ (θ, φ)] e jkr R (12) in the far field shows that an antenna can radiate different field strengths in different directions. Basic rule: small antennas in terms of a wavelength tend to have broad patterns, larger antennas become more directive. Pattern measurements can be made by Moving a measurement antenna around the test antenna and measuring relative or absolute signal strength in a given direction Fixing a measurement antenna and rotating the test antenna - usually done in pattern measurement ranges Scale models at different frequencies can also be used Care must be taken to eliminate environmental effects and to insure measurement is in the far field Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 9 / 31

Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 10 / 31

Standard way of reporting patterns is through the directional gain, defined as D(θ, φ) = power radiated by antenna at (θ, φ) power radiated by an isotropic antenna at (θ, φ) = P θ (θ, φ) + P φ (θ, φ) P r /4πR 2 = P θ (θ, φ) + P φ (θ, φ) υp in /4πR 2 (13) Gain, G(θ, φ) of an antenna is defined as υd(θ, φ), and thus includes losses in the antenna wires We can also talk about directional gain and gain in specified polarizations (rather than the sum as in the notes) Results are often presented in dbi - db relative to an isotropic antenna Directivity = maximum value of directional gain Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 11 / 31

IV. Receiving antenna performance Field of a dipole is E = j η 0 2λ I e jkr (h sin θ)ˆθ (14) r Introduce the concept of an effective length, h e (θ, φ) for all antennas: E = j η 0 2λ I e jkr h r e (θ, φ) (15) Flux density radiated by an antenna can thus be calculated as or S(θ, φ) = E 2 from power considerations. Thus, 2η 0 = I 2 h 2 e(θ, φ)η 0 /(8λ 2 r 2 ) (16) S(θ, φ) = I 2 R A υd(θ, φ)/(8πr 2 ) (17) h e (θ, φ) = λ [R A υ/(πη 0 )] 1/2 [D(θ, φ)] 1/2 (18) Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 12 / 31

Model an antenna receiving a signal with a circuit and voltage generator, V TH, where so that power delivered to the receiver is V TH = E(θ, φ) h e (θ, φ) (19) P R = E h e 2 R R 2 Z A + Z R 2 (20) This is a sufficient model, but it is possible to relate this to more familiar antenna parameters through our previous equation. We obtain P R = E 2 (θ, φ) λ2 D(θ, φ) υ â 2η 0 4π E â h 2 4R A R R Z A + Z R 2 (21) Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 13 / 31

P Receiver = V TH Z A Z R Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 14 / 31

Our previous equation can be rewritten as P R = S(θ, φ)a em (θ, φ)υpq (22) where the maximum effective aperture or area A em is given by A em (θ, φ) = λ2 D(θ, φ) 4π the polarization mismatch factor by (23) and the impedance mismatch factor by p = â E â h 2 (24) q = 4R A R R Z A + Z R 2 (25) The name effective aperture of area and symbol A e is given to the product A e = υa em = υdλ2 4π = Gλ2 4π Effective aperture does not necessarily have a direct relationship to physical aperture area of antenna (26) Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 15 / 31

Antenna Noise 1 Noise considerations 2 Internal noise 3 External noise 4 Brightness temperatures 5 Atmospheric noise Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 16 / 31

I. Noise considerations All electronic systems are subject to the influence of randomly varying signals - noise! When desired signal strengths are small compared to the noise level in a given system, signals will not be received Thus adding gain to a receiver does not necessarily help! Noise originates from both internal and external sources Non-random, i.e. man-made, signals can also be classified as external noise, usually called interference instead Understanding noise effects is important in system design and performance Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 17 / 31

II. Internal noise All electronic devices produce small randomly varying electrical signals primarily due to thermal motions of their constituent atoms Standard equation for the thermal noise emitted from a resistor at absolute temperature T in bandwidth B is N i = k B TB (27) where N i is the emitted noise power and k B = 1.38 10 23 Joule/K is Boltzmann s constant This equation can also be used to relate an equivalent noise temperature T to any noise power source Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 18 / 31

Standard characterization of noise performance of an amplifier is the noise figure F: F = S i/n i S 0 /N 0 (28) where the measurements are done with N i = k B T 0 B and T 0 = 290 K (approximately 63 degrees F). Defining available power gain as the noise figure can be written as Note F 1, an ideal amplifier has F = 1 G A = S 0 /S i (29) F = N 0 G A N i (30) Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 19 / 31

The output noise consists of amplified input thermal noise plus some additional noise which we will call N N : F = G AN i + N N G A N i (31) It is sometimes useful to refer the additional noise to the input N N /G A, resulting in a quantity known as the excess noise N e. F = N ig A + G A N e G A N i = N i + N e N i (32) S 0 /N 0 = G AS i FG A N i = G A S i FG A k B T 0 B = S i Fk B T 0 B (33) under standard input conditions. Note that in receivers containing several amplifier stages, most of the internal noise comes from the first amplifier stage Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 20 / 31

More generally when the input noise N i is not k B (290)B, we have S 0 /N 0 = S i N i + (F 1)k B T 0 B (34) The input noise in realistic situations comes from noise signals received by the system antenna (external noise) as discussed next. Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 21 / 31

III. External noise Planck s blackbody radiation law tells us that any object at non-zero absolute temperature will radiate noise power Thus there is noise power in all external environments, this power will be received by our antennas Usually smaller than internal noise, so it can be neglected, but not at higher frequencies Passive sensors (radiometers, radio astronomy) measure this noise to determine properties of the observed scene External noise power is usually distributed over both frequency and angle, so a new quantity, brightness, is used to describe it Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 22 / 31

The received external noise power at the output of a receiver is given by P N,out = 0 { Ω=4π H(f ) 2 q(f )υ(f ) B s (f, Ω)A em (f, Ω)p(f, Ω)dΩ+ Ω=0 k B [1 υ(f )] T p } df (35) The second term accounts for antenna lossiness! If we assume things are constant in frequency and refer the noise power to the input, we get { λ 2 P N = B 4π Ω=4π Ω=0 B s (Ω)G(Ω)p(Ω)dΩ + k B [1 υ] T p } (36) Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 23 / 31

IV. Brightness temperatures Source brightness is often related to a source brightness temperature through Planck s law B s = 2hf λ 2 1 e hf /k BT 1 where h is Planck s constant, which can be approximated as (37) k B T B (Ω) = λ 2 B s (Ω)p(Ω) (38) for microwave and lower frequencies. Our equation for external noise power is now { 1 Ω=4π } P N = k B B T B (Ω)G(Ω)dΩ + [1 υ] T p 4π Ω=0 (39) Planck s law only applies for blackbodies, but we can define a brightness temperature of a given source as being the physical temperature of a given source that would radiate the same amount of noise power. Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 24 / 31

We can then write the external noise power as P N = k B T A B (40) or as an equivalent standard receiver noise factor F ext P N = F ext k B T 0 B (41) where T 0 = 290 K is a standard reference temperature, and T A = 1 4π Ω=4π Ω=0 T B (Ω)G(Ω)dΩ + [1 υ] T p (42) When the source brightness is constant over the entire antenna beam and Ω=4π Ω=0 G(Ω)dΩ = 4πυ (43) Three distinct concepts of temperature! T A = υt B + (1 υ)t p (44) Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 25 / 31

If the source subtends such a small angle at the receiver that it cannot be resolved, G(Ω) and p(ω) can be held constant in the integration with respect to Ω and B s (Ω)dΩ = S N(Ω 0 ) (45) B Thus Ω P N = B S N(Ω 0 ) B A noise field strength E N can be defined by λ 2 G(Ω 0 ) p(ω 0 ) + k B BT p (1 υ) (46) 4π S N = E 2 N /η 0 (47) where η 0 is the impedance of free space, resulting in P N = E N 2 (Ω 0) λ 2 G(Ω 0 ) p(ω 0 ) + k B BT p (1 υ) (48) η 0 4π Treats noise which arrives as a plane wave from a single direction just as a signal smeared over the receiver bandwidth! Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 26 / 31

We can thus describe external noise either through its brightness or brightness temperature Radio astronomy and passive remote sensing measure brightness temperatures of scenes It is possible to infer many interesting things - sea surface temperature, wind speed, atmospheric composition, etc. Sensors (radiometers) must be very high gain and with long integration times Knowing average brightness temperatures of external environment allows us to compute external noise contribution to system S/N Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 27 / 31

V. Atmospheric noise Many measurements are available - be careful about situations under which data were obtained Sferics (noise due to lightning) is dominant atmospheric noise source below 10 MHz Atmospheric thermal noise becomes significant at higher frequencies Galactic sources also produce significant noise at lower than 1 GHz frequencies Again, all this usually matters only with very sensitive receivers Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 28 / 31

Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 29 / 31

Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 30 / 31

Levis, Johnson, Teixeira (ESL/OSU) Radiowave Propagation August 17, 2018 31 / 31