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# RF Module Design - [Chapter 2] Noises

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### RF Module Design - [Chapter 2] Noises

1. 1. RF Transceiver Module Design Chapter 2 Noises 李健榮 助理教授 Department of Electronic Engineering National Taipei University of Technology
2. 2. Outline • Noise Sources in Electronic Components • Antenna Noise • Noise Temperature • Noise Figure • Non-frequency-converting Circuit Output Noise Power • Frequency-converting Circuit Output Noise Power • Output Noise Power of Cascaded Circuits • Sensitivity Department of Electronic Engineering, NTUT2/42
3. 3. Noise Sources in Electronic Components • The flow of charges(holes) in a electron tube or solid-state device has the thermal fluctuation in any component at a temperature above absolute zero. Such motions can be caused by any of several mechanisms, leading to various sources of noise, thermal noise, flicker noise, and shot noise. • Noises can be picked up by the antenna, which come from atmospheric noise, solar noise, galactic noise, ground noise, and man-made noise. Department of Electronic Engineering, NTUT3/42
4. 4. where is the Planck’s constant is Boltzman’s constant Thermal Noise • Johnson Noise, Nyquist Noise • Thermal agitation of charge carriers: v(t) is a open-circuit voltage across the resistor terminals Department of Electronic Engineering, NTUT ( ) ( ) ( ) 2 1 2 2 4 f n rms f v t V kT R f P f df= = ∫ ( ) 1hf kT hf kT P f e = − 34 6.546 10 J/sech − = × 23 1.380 10 J/Kk − = × ( )v t t ( )v tR ( )o KT For an electron in a conductor, the probability density function (PDF) obeys 4/42
5. 5. Shot Noise • Shot noise (Schottky noise) is first observed in vacuum tubes. • For example, the IV curve of the Schottky Contact (metal- semiconductor contact) is .The above results are applicable also to p-n junction diodes, bipolar transistors, metal-semiconductor (Schottky-barrier) diodes, and so on, where charges are carried across potential barriers. • In summary, shot noise has two characteristics: 1) White noise spectrum similar to that of thermal noise. This is very useful in measuring the noise temperature or noise figure of an amplifier or any linear receiver component for that matter. 2) The rms value of the shot noise can be easily calculated form the measured dc current IS. 0 ( 1)qV KT I I e= − Department of Electronic Engineering, NTUT5/42
6. 6. Flicker Noise • Flicker noise is a low-frequency phenomenon which is typically encountered in the device with a dc current flowing. It is a poorly understood phenomenon and seems to be related to surface properties of materials, and is also associated with imperfect contact between conductors. • Flicker noise has the interesting characteristic that its spectral density is inversely proportional to frequency. • Van der Ziel gives the following expression for the mean- square noise current per unit bandwidth: 2 a n I i K df f   =     where K : material constant, I : dc current, a : close to 2, and n : close to 1. This expression seems hold for a variety of cases, including semiconductors, carbon microphones, photoconductors, crystal diodes, and so on. Department of Electronic Engineering, NTUT6/42
7. 7. Antenna Noise • Generally speaking, antenna noise includes a total of the following noise sources: Atmospheric noise Solar noise Galactic noise Ground noise Man-made noise Department of Electronic Engineering, NTUT7/42
8. 8. Atmospheric Noise • This noise is greatest at the lowest frequencies and decreases with increasing frequency. Department of Electronic Engineering, NTUT • Below 30MHz, it is the strong source of antenna noise, generated mostly by lightning discharge in thunder storms. The noise level depends on the frequency, the time of day, weather, the season of the year, and geographical location. NoiseFigure(dB) 140 120 100 80 60 40 20 0 Frequency (MHz) 0.1 0.3 1 3 10 30 100 Galactic noise Atmospheric noise (Central United States) 8/42
9. 9. Solar Noise (I) • The Sun is a powerful noise source. • If a directional antenna is pointed at the Sun, it will see a large antenna noise temperature (also contributes to antenna noise through sidelobes). • During high levels of Sun spot activity, noise temperatures from 100 to 10,000 times greater than those of the quiet sun may be observed for periods of seconds in what is called solar bursts, followed by levels about 10 times the quiet level lasting for several hours Department of Electronic Engineering, NTUT9/42
10. 10. Solar Noise (II) • The Sun’s effective noise temperature seen by an antenna of gain Ga is: • For example, if the frequency is 1000 MHz and there are quiet sun conditions, the noise temperature is about . If we assume an antenna gain in the direction of the sun of 31 dBi and an atmospheric loss of 1dB, the antenna noise temperature will be 5 2 10 K× 6 5 4.75 10 1259 2 10 949.3 K 1.26 aT − × × × × = = Department of Electronic Engineering, NTUT 6 4.75 10 a s a A G T T L − × = AL : atmospheric loss (numeric) 10/42
11. 11. Galactic Noise • Typical antenna temperatures for frequencies above 100 MHz. • Galactic noise is the largest natural noise between 100~400 MHz, which is most intense in the galactic plane and reaches a maximum in the direction of the galactic center. • Above 400MHz, the other component dominate. Department of Electronic Engineering, NTUT AntennaNoiseTemperature(K) 3000 1000 300 100 30 10 3 1 Frequency (GHz) Cosmic noise from the galactic center Minimum noise 10000 0.1 0.3 1 3 10 30 100 NoiseFigure(dB) 10.5 6.5 3.1 1.3 0.4 0.15 0.04 0.015 15.5 Minimum noise Cosmic noise from the galactic pole 11/42
12. 12. Ground Noise • The Earth is a radiator of electromagnetic noise. • The thermal temperature of the Earth is typical about 290 K. • In radar systems and directional communication systems, the Earth will be viewed mainly through the sidelobes of the antennas. The average sidelobe antenna gain typically is about –10 dBi. A rough estimate of antenna noise temperature in that case is 29 K. Department of Electronic Engineering, NTUT12/42
13. 13. Man-made Noise and Interference (I) • Man-made noise is due chiefly to electric motors, neon signs, power lines, and ignition systems located within a few hundred yards of the receiving antenna. • There may be radiation from hundreds of communication and radar systems that may interfere with reception. • Generally this type of noise is assumed to decrease with frequency as shown in the following: where T100 is the man-made noise temperature at 100 MHz. Department of Electronic Engineering, NTUT 2.5 100 100 a MHz T T f   =     13/42
14. 14. Man-made Noise and Interference (II) • For an example of the formula, assume an operating frequency of 400 MHz and a man-made noise temperature at 100 MHz of 300,000 K (Fa = 30.2 dB above kT0B). The calculated antenna noise temperature would be The temperature is about 15.2 dB above kT0B. Department of Electronic Engineering, NTUT 2.5 100 300,000 9375 K 400 aT   = ⋅ =    14/42
15. 15. where is Boltzman’s constant Available Thermal Noise Power • Thermal Noise: 23 1.380 10 J/Kk − = × NAP kTB=Available noise power: Thermal noise source ,n rmsvR ( )KT + − Noisy resistor ,n rmsv Thevenin’s Equivalent Circuit Noise-free resistor R 2 , ?n rmsv = R R Matched Load 2 , 2 n rms NA v P kTB R      = = ,n rmsv , 2 n rmsv + − Available Noise Power 2 , 4n rmsv kTBR= Open-circuited noise voltage? Department of Electronic Engineering, NTUT15/42
16. 16. where is Boltzman’s constant Thermal Noise Equivalent Circuits • Thermal Noise: 23 1.380 10 J/Kk − = × NAP kTB=Available noise power: Thermal noise source ,n rmsv,n rmsvR ( )KT + − Thevenin’s Equivalent Circuit Noisy resistor Noise-free resistor Norton’s Equivalent Circuit Noise-free resistor R R 2 , 4n rmsv kTBR= ,n rmsi 2 ,2 , 4 4n rms n rms v kTB i kTBG R R   = = =    2 , 4n rmsv kTBR= Department of Electronic Engineering, NTUT16/42
17. 17. Thermal Noise Power Spectrum Density • Available noise power : • Thermal Noise at 290 K (17 oC): Department of Electronic Engineering, NTUT Ideal bandpass filter B R R ,n rmsv NAP kTB= PSD (W/Hz, or dBm/Hz) f (Hz) Bandwidth B (Hz) kT Integrate to get noise power 0 0NAP kT B=Available noise power: ( ) ( )21 0, 0 4 10 W Hz 174 dBm HzPSDN kT − × = −≜ ≃Power spectrum density: 17/42
18. 18. Equivalent Noise Temperature (I) • If an arbitrary source of noise (thermal or nonthermal) is “white”, it can be modeled as an equivalent thermal noise source, and characterized with an equivalent noise temperature. • An arbitrary white noise source with a driving-point impedance of R and delivers a noise power No to a load resistor R. This noise source can be replaced by a noisy resistor of value R, at temperature Te (equivalent temperature): Department of Electronic Engineering, NTUT oN R Arbitrary white noise source R oN RR eT o e N T kB = 18/42
19. 19. Equivalent Noise Temperature (II) • How to define the equivalent noise temperature for a two-port component? Let’s take a noisy amplifier as an example. • In order to know the amplifier inherent noise No, you may like to measure the amplifier by using a noise source with 0 K temperature. Is that possible? Noisy amplifier R oN aGR 0 KsT = This means that the output noise No is only generated from the amplifier. Noiseless amplifier R o a iN G N= aGR iN o i e a N N kT B G = =i o e a N N T kB G kB = = Department of Electronic Engineering, NTUT19/42
20. 20. Gain Method • Use a noise source with the known noise temperature Ts. Noiseless amplifier R o a iN G N= aGR i s eN kT B kT B= + sT eT Noisy amplifier R _o a i o addN G N N= + aGR i sN kT B= sT ( ) ( )o a s e a s eN G kT B kT B G kB T T= + = + o s e a N T T G + = o e s a N T T G = − Need to know the amplifier power gain Ga. Due to the noise floor of the analyzer, the gain method is suitable for measuring high gain and high noise devices. Department of Electronic Engineering, NTUT20/42
21. 21. The Y-factor Method • Use two loads at significantly different temperatures (hot and cold ) to measure the noise temperature. • Defined the Y-factor as Department of Electronic Engineering, NTUT 1 1a a eN G kT B G kT B= + 2 2a a eN G kT B G kT B= + 1 2 1 e T YT T Y − = − 11 2 2 1e e T TN Y N T T + = = > + R R 1T 2T aG B eT 1N 2N (hot) (cold) You don’t have to know Ga. The Y-factor method is not suitable for measuring a very high noise device, since it will make to cause some error. Thus, we may like a noise source with high ENR for measuring high noise devices. 1Y ≈ Sometimes, you may need a pre-amplifier to lower analyzer noise for measuring a low noise device . 21/42
22. 22. Noise Figure • The amount of noise added to a signal that is being processed is of critical importance in most RF systems. The addition of noise by the system is characterized by its noise figure (NF). • Noise Factor (or Figure) is a measure of the degradation in the signal-to-noise ratio (SNR) between the input and output: where Si , Ni are the input and noise powers, and So, No are the output signal and noise powers 1i i i o o o SNR S N F SNR S N = = ≥ ( )dB 10logNF F= Gain = 20 dB P (dBm) Frequency (Hz) −100 −60 SNRi = 40 dB NF = ? P (dBm) Frequency (Hz) −80 −40 SNRo= 32 dB −72 NF = 8 dB Noisy Amplifier Department of Electronic Engineering, NTUT22/42
23. 23. Noise Figure (NF) • By definition, the input noise power is assumed to be the thermal noise power resulting from a matched resistor at T0 (=290 K); that is, , and the noise figure is given as Department of Electronic Engineering, NTUT ( )0 0 0 1 1ei i e o i kGB T TSNR S T F SNR kT B GS T + = = = + ≥ 0iN kT B= ( ) 01eT F T= − Noisy Network G B eT R 0T R i i iP S N= + o o oP S N= + 23 1.380 10 J/ Kk − = ×where is Boltzman’s constant0NAP kT B= ( ) ( )21 0 4 10 W Hz 174 dBm HzTN kT − × = −≜ ≃ Use the concept of SNR Use the concept of noise only 0 0 0 0 0 1 1o add e e i N kGBT N kGBT kGBT T F GN GkT B GkT B T + + = = = = + ≥ 23/42
24. 24. Non-frequency-converting Circuit Output Noise A. Resistive-type passive circuits When a two-port network is a passive, lossy component (an attenuator or lossy transmission line). B. Reflective-type passive circuits Assume an ideal bandpass filter response with passband insertion loss of L (dB) and stopband attenuation of S (dB). C. Active circuit An active circuit is with noise figure NF and available gain G. Department of Electronic Engineering, NTUT24/42
25. 25. Resistive-type Passive Circuits (I) • The circuit is with a matched source resistor, which is also at temperature T. • The output noise power : • We can think of this power coming from the source resistor (through the lossy line), and from the noise generated by the line itself. Thus, Department of Electronic Engineering, NTUT 0P kTB= 0 addedP kTB GkTB GN= = + ( ) 1 1added e G N kTB L kTB kT B G − = = − = where is the noise generated by the line.addedN 25/42
26. 26. Resistive-type Passive Circuits (II) Department of Electronic Engineering, NTUT26/42 • The lossy line equivalent noise temperature : • The noise figure is where T0 denotes room temperature, T is the actual physical temperature (K). Note that the loss L may depend on frequency. • Output noise power : where input thermal noise power ( ) 1 1e G T T L T G − = = − ( ) 0 1 1 T F L T = + − ( )dB 10logNF F= ( ) ( ) ( )dBm dBm dBout inN N L NF= − + ( )WattinN kTB= ( )dBminN f ( )dBmoutN f inN L NF− +
27. 27. Reflective-type Passive Circuits (I) • Assume an ideal BPF response with passband insertion loss of L (dB) and stopband attenuation of S (dB). The filter is under an environment of T (K) • In the passband: Department of Electronic Engineering, NTUT ( ) 0 1 1 T F L T = + − ( )dB 10logNF F= 0 dB −L dB −S dB BW 27/42
28. 28. Reflective-type Passive Circuits (II) Department of Electronic Engineering, NTUT28/42 • Outside the passband, the noise, the same as the signal, is reflected back such that the output noise power is reduced by the stopband attenuation S (dB). ( ) 0 0 2 2 dBm in out in BW BW N L NF f f f N N S otherwise  − + − ≤ ≤ +  =   −   ( )dBmoutN inN L NF− + BW inN S− f ( )dBminN f
29. 29. Active Circuits • An active circuit is with noise figure NF and available gain G. (Note that NF and G are usually depend on frequency.) Department of Electronic Engineering, NTUT ( )dBmout inS S G= + ( )174 10log dBminN B= − + ( )dBmout inN N NF G= + + ( )dBminN f f ( )dBmoutN BW ( )dBminS f ( )dBmoutS f BW ( )dBmin inS N+ f ( )dBmout outS N+ f BW ( )dBG ( )dBNF 29/42
30. 30. Multiple Stages Cascaded • Multiple stages cascaded where Fi is the noise factor and Gi is the available power gain of each stage. Department of Electronic Engineering, NTUT 1 1 0 1 1 N i i i j j F F G − = = − = + ∑ ∏ 2 3 1 1 1 2 1 2 1 e e eN eT e N T T T T T G G G G G G − = + + + +⋯ ⋯ 1eT 1G 2G 2eT eNT NG g T addkT G N+gkT 1ekT 2ekT eNkT gkT ( )T g eTkG T T+ eTkT 1 2T NG G G G= ⋯ 1 1 1g ekT G kT G+ ( )1 1 1 2 2 2g e ekT G kT G G kT G+ + ( )1 2 1 1 2 2g N e N e N eN NkT G G G kT G G kT G G kT G+ + + +⋯ ⋯ ⋯ ⋯ 1 1 2 0 i T N j j G G G G G − = = = ∏⋯ ( ) 01eT F T= − Cascade System Equivalent System ( ) 32 1 1 1 2 1 2 1 1 11 1 1 N N F FF F F G G G G G G − − −− = + − + + + +⋯ ⋯ 1st stage dominate less significant 30/42
31. 31. Frequency-converting Circuit Output Noise • Image Noise : • LO Wideband Noise : Department of Electronic Engineering, NTUT Image noise fLO fLO fLO + fIFfLO − fIF fIF LO wideband noise LOf 2 LOf 3 LOf 31/42
32. 32. Output Noise Power of Cascaded Circuits (I) • The total mean-square noise voltage (Assume that the circuit is under the same physical temperature Tj=T) • The summed open-circuit mean-square voltage at a-a' is therefore given by ,where Department of Electronic Engineering, NTUT ( ) ( ) ( )2 1 1 1 4 4 4 4 N N N n j j j j j T T j j j v kT BR kB T R kBT R kBTR = = = = = = =∑ ∑ ∑ ( )2 2 2 2 1 2 3n T v v v v= + + +⋯ Noisy resistors in series 2 1ne 1R 2R 2 2ne NR 2 nNe 2 nTe a a′ ( ) 22 2 1 1 1nv v A f= ( ) 22 2 2 2 2nv v A f= ( ) 22 2 3 3 3nv v A f=, , and 32/42
33. 33. Example – T-network The total voltage at a-a' is the sum of the above, where the equivalent resistance Department of Electronic Engineering, NTUT ( ) ( ) ( ) 22 2 1 22 1 2 1 2 2 1 2 1 2 4n kTBR Rv R v R R R R = = + + ( ) ( ) ( ) 22 2 2 12 2 1 2 2 2 1 2 1 2 4n kTBR Rv R v R R R R = = + + 2 2 3 3 34nv v kTBR= = ( ) ( ) ( ) 2 2 2 1 2 2 1 1 2 3 32 2 1 21 2 1 2 4 4 4n eq T R R R R R R v kBT R kBT R kTBR R RR R R R     = + + = + =    ++ +     1 2 3 1 2 eq R R R R R R = + + 2 1ne 1R 2R 2 2ne 3R 2 3ne a a′ 2 nTe eqR a a′ ( ) 2 2 2 1 2 1 2 R A R R = + ( ) 2 2 1 2 2 1 2 R A R R = + 2 3 1A =, , and 33/42
34. 34. Output Noise Power of Cascaded Circuits (II) • When the noise temperature and gain of each stage are determined, the overall noise temperature and gain of the whole system can be obtained. • Use the following methods to calculate the output noise , (1) Cascade Formula (2) Walk-Through method (3) Summation method Department of Electronic Engineering, NTUT 1 1 dBL = 1 300 KT = 1 300 KT = 3 4 dBL = 2 150 KeT = 2 25 dBG = 4 700 KeT = 4 30 dBG = 50 KsT = oN′ stage1 stage2 stage3 stage4 oN′ 34/42
35. 35. Cascade Formula Method Department of Electronic Engineering, NTUT ( ) ( )1 1 11 1.259 1 300 77.7 KeT L T= − = − = ( ) ( )3 3 31 2.512 1 300 453.6 KeT L T= − = − = 150 453.6 700 77.7 275.42 K 0.794 0.794 316.23 0.794 316.23 0.398 eTT = + + + = × × × ( ) ( )23 21 1.38 10 50 275.42 =4.5 10 Watts Hz= 173.5 dBm Hzs eTk T T − − + = × × + × − 0 173.5 1 25 4 30 dBm HzN = − − + − + 1 1 dBL = 1 300 KT = 1 300 KT = 3 4 dBL = 2 150 KeT = 2 25 dBG = 4 700 KeT = 4 30 dBG = 50 KsT = oN′ stage1 stage2 stage3 stage4 Stage 1 Teff : Stage 3 Teff : System equivalent noise temperature and output noise : 35/42
36. 36. Walk-Through Method – Stage 1 • Calculate the noise signal from stage to stage. At first, calculate the noise density stage by stage: Antenna noise: Cable 1 noise: Department of Electronic Engineering, NTUT 23 19 1.38 10 50=6.9 10 mW Hz 181.6 dBm HzskT − − = × × × = − ( ) ( )1 1 11 1.259 1 300 77.7 KeT L T= − = − = 23 19 1 1.38 10 77.7=10.72 10 mW Hz 179.7 dBm HzekT − − = × × × = − 1 1 dBL = 1 300 KT = 1 300 KT = 3 4 dBL = 2 150 KeT = 2 25 dBG = 4 700 KeT = 4 30 dBG = 50 KsT = oN′ stage1 stage2 stage3 stage4 Stage Input A Input B Sum Output Noise Density (dBm/Hz) 1 −181.6 −179.7 −177.5 −178.5 2 −178.5 36/42
37. 37. Walk-Through Method – Stage 2 1 1 dBL = 1 300 KT = 1 300 KT = 3 4 dBL = 2 150 KeT = 2 25 dBG = 4 700 KeT = 4 30 dBG = 50 KsT = oN′ stage1 stage2 stage3 stage4 LNA Noise: 23 19 2 1.38 10 150=2.07 10 mW Hz 176.8 dBm HzekT − − = × × × = − Stage Input A Input B Sum Output Noise Density (dBm/Hz) 1 −181.6 −179.7 −177.5 −178.5 2 −178.5 −176.8 −174.6 −149.6 3 −149.6 Department of Electronic Engineering, NTUT37/42
38. 38. Walk-Through Method – Stage 3 Stage Input A Input B Sum Output Noise Density (dBm/Hz) 1 −181.6 −179.7 −177.5 −178.5 2 −178.5 −176.8 −174.6 −149.6 3 −149.6 −172.0 −149.6 −153.6 4 −153.6 1 1 dBL = 1 300 KT = 1 300 KT = 3 4 dBL = 2 150 KeT = 2 25 dBG = 4 700 KeT = 4 30 dBG = 50 KsT = oN′ stage1 stage2 stage3 stage4 Cable 2 Noise: ( ) ( )3 3 31 2.512 1 300 453.6 KeT L T= − = − = 23 19 2 1.38 10 453.6=6.26 10 mW Hz 172 dBm HzekT − − = × × × = − Department of Electronic Engineering, NTUT38/42
39. 39. Walk-Through Method – Stage 4 1 1 dBL = 1 300 KT = 1 300 KT = 3 4 dBL = 2 150 KeT = 2 25 dBG = 4 700 KeT = 4 30 dBG = 50 KsT = oN′ stage1 stage2 stage3 stage4 Gain amplifier noise: 23 19 4 1.38 10 700=9.66 10 mW Hz 170.2 dBm HzekT − − = × × × = − Stage Input A Input B Sum Output Noise Density (dBm/Hz) 1 −181.6 −179.7 −177.5 −178.5 2 −178.5 −176.8 −174.6 −149.6 3 −149.6 −172.0 −149.6 −152.6 4 −153.6 −170.2 −153.5 −123.5 Department of Electronic Engineering, NTUT39/42
40. 40. Summation Method • Each noise source is individually taken through the various gains and loses to the output, and the sum of all output noises is just the total output noise (Superposition). For stage1: For stage2: For stage3: For stage4: Department of Electronic Engineering, NTUT 181.6 1 25 4 30 131.6 dBm Hz− − + − + = − 179.7 1 25 4 30 129.7 dBm Hz− − + − + = − 176.8 25 4 30 125.8 dBm Hz− + − + = − 172 4 30 146 dBm Hz− − + = − 170.2 30 140.2 dBm Hz− + = − 1 1 dBL = 1 300 KT = 1 300 KT = 3 4 dBL = 2 150 KeT = 2 25 dBG = 4 700 KeT = 4 30 dBG = 50 KsT = oN′ stage1 stage2 stage3 stage4 oN′ Noise Contributor Output Noise Density (dBm/Hz) Environment −131.6 Stage 1 −129.7 Stage 2 −125.8 Stage 3 −146.0 Stage 4 −140.2 Total −123.5 40-I/42
41. 41. Noise Figure Method Department of Electronic Engineering, NTUT 1 1 dBL = 1 300 KT = 1 300 KT = 3 4 dBL = 2 150 KeT = 2 25 dBG = 4 700 KeT = 4 30 dBG = 50 KsT = oN′ stage1 stage2 stage3 stage4 Atten1 Amp2 Atten3 Amp4 Gain (dB) -1 25 -4 30 Gain 0.79432823 316.227766 0.39810717 1000 T 300 150 300 700 F 1.26785387 1.51724138 2.56402045 3.4137931 NF (dB) 1.03069202 1.81054679 4.08921484 5.33237197 Cumumlatvie Gain 0.79432823 251.188643 100 100000 Fcas 1.26785387 1.91902219 1.92524867 1.9493866 NFcas (dB) 2.89897976 Gcas (dB) 50 Ni (Ts=50 K) (dBm) -181.611509 No=Ni+Gcas+NFcas -128.7125-128.7125-128.7125-128.7125 Wrong!Since NF is defined@290 KSince NF is defined@290 KSince NF is defined@290 KSince NF is defined@290 K Fcas=1+(Te/T0) Te 275.322114 No=Gcas(kTsB+kTeB) 4.4894E-16 -123.47807 Correct! Department of Electronic Engineering, NTUT40-II/42
42. 42. Sensitivity • where is the on-channel noise, including thermal, shot, flicker, antenna noise. NIMG is the image noise, contributed from the mixing function NLO is the LO noise, down-mixing to IF signal due to the mixing function • The system overall noise figure is then obtained as where includes noise, phase jittering and channel fading effects. Department of Electronic Engineering, NTUT ( ) ( ) ( ) ( )_dBm dBm dB dBout RF system required S Sensitivity N NF N = + + out Channel IMG LON N N N= + + ChannelN Module Channel IMG LOF F F F= + + 41/42
43. 43. Summary • In this chapter, we’ve introduced the thermal noise and how to use thermal noise to define the equivalent noise temperature. • The measuring methods of the equivalent noise temperature (and thus the noise figure) are the practical procedure corresponding to the noise theory. Each method has its own pros and cons. • The calculation of a cascade system output noise was also introduced by using cascade formula, walk-through, and output summation methods. Department of Electronic Engineering, NTUT42/42