噪声系数测量

1RFMW 202: Noise Figure Basics Technical data is subject to change Copyright@2003 Agilent Technologies Printed on Dec. 4, 2002 5988-8495ENA 2Agenda Fundamental noise concepts How do we make measurements? What DUTs can we measure? What influences the measurement uncertainty? 3Fundamental Noise Concepts Fundamental noise concepts How do we make measurements? What DUTs can we measure? What influences the measurement uncertainty? Fundamental noise concepts 4What is Noise Figure? Imperfect Amplifier Signal larger But Noisier Agitation of Electrons adds noise to the signal Small Signal Fundamental noise concepts In this example, a perfect amplifier would add no noise, and the signal would be an amplified replica. However, in practice, noise is present, and can mask the wanted signal. The noise floor, as seen in a given bandwidth, limits the detection of weak signals. All electronic systems are subject to noise. Receiver systems have to process very weak signals and any noise added by the system will obscure these weak signals. 5Fundamental noise concepts DUT EMC Noise Power supply Noise Phase Noise DUT Noise V+ We will derive a figure of merit for this Causes of Noise Noise comes from a variety of sources. It can be picked up from the emissions of nearby electrical equipment, or from the phase noise of downconverting synthesizers. Noise can even come from the power supplies of active components in the receiver. In this presentation we will NOT be considering these types of noise although they are very important to understand and control. Instead, we will concentrate the type of noise caused by ordinary phenomena in active electrical circuitry caused by random fluctuations in charge carriers caused by thermal, shot and flicker noise. We will define a figure of merit called Noise figure which a unique way of characterizing systems and also the components within systems. When you know the noise figure of the system, you can easily calculate the system sensitivity from the system bandwidth. 6Noise Contributors Thermal Noise: (otherwise known as Johnson noise) is the kinetic energy of a body of particles as a result of its finite temperature Ptherm=kTB Shot Noise: caused by the quantized and random nature of current flow Flicker Noise: (or 1/f noise) is a low frequency phenomenon where the noise power follows a 1/fα characteristic Fundamental noise concepts Thermal noise is a function of the kinetic energy of a body of particles. The noise power available is equal to kTB and is the maximum rate at which energy can be removed from the body. Boltzmann’s constant is defined as the average energy per particle that can be coupled out by electrical means per degree of temperature. The power is related to temperature and that makes intuitive sense. Thermal noise is evenly distributed across the frequency spectrum (1% variation up to 100GHz) and therefore B specifies how much of the spectrum power is available. Shot noise occurs in active devices and is caused by the randomness of current flow. Shot noise is flat with frequency and a function of the current level. Flicker noise is a function of frequency and is a low frequency phenomenon. The value of alpha is close to unity. 7Noise Power at Standard Temperature R - j X R+jX L L Available Noise Power, Pav = kTB At 290K Pav = 4 x 10 -21 W/Hz = -174dBm / Hz k = 1.38 x 10-23 joule / k T = Temperature (K) B = Bandwidth (Hz) Fundamental noise concepts In deep space kT = -198dBm/Hz Here is a schematic representation of a noise source. Noise follows the normal power transfer laws. kTB is termed the available noise power. A conjugate match is needed for an optimum noise power transfer from the source to the load. This gives us the figure of -174dBm / Hz as the universal noise floor at standard temperature. Note that defining noise threshold at -174dB/Hz in space applications is not applicable because 290K is not the ambient temperature in deep space! In deep space the ambient temperature is around 4K and satellite earth station receivers the temperature 30K Noise power is not a function of the size (or resistance) of the body. Imagine if you connected a large body to a smaller one. If the larger one produced more power then there would be a net flow of energy to the smaller body and this does not happen! . 8What is Noise Figure ? Noise Out Noise in a) C/N at amplifier input b) C/N at amplifier output Measurement bandwidth=25MHz Fundamental noise concepts Nin Nout Here is an example of an amplifier connected to an antenna. Let us assume that the antenna and amplifier are perfectly matched. Let’s also assume that the measurement bandwidth is 25MHz - so add 74 to -174dBm. The noise at the input of the amplifier will be kTB which in log terms is -100dBm. The signal being picked up the input is -60dBm. The carrier to noise ratio at the input is 40dB. If the amplifier was perfect it would amplify the gain and noise by equal amounts and maintain the same C/N at the output. In reality the amplifier will add some gain of its own. It this example the gain of the amplifier is 20dB so the signal has risen from -60dBm to -40dBm. The noise however has risen by 30dB rather than 20dB. The C/N has dropped to 30dB because the amplifier has added 10dB noise of its own. Friis in 1944 defined noise figure as the ratio of signal to noise at the input to signal to noise at the output. I.e. 40dB minus 30dB. We can say the noise figure is 10dB. 9Definition of Noise Figure by equation - Friis 1944 Ga Rs Noise Figure NF (dB) Na + Nin .Ga Nin = kToB where To = 290K 10 log Nout = Na + Nin Ga Nin Nin . Ga 10 log Si / Nin So / Nout Fundamental noise concepts Noise figure = 10 . Log (noise factor) Na Lets look at what I’ve discussed algebraically and define some equations. Here is an amplifier with a noise generator connected to the input. The output noise consists of the input noise multiplied by the gain (that’s all of the input noise as the system is perfectly matched) added with a component of noise generated within the device under test. Remember a couple of slides back we defined noise in terms of signal to noise ratio. Here is the equation again. We can substitute So for G. Si - all the signal components cancel out and we are left with this equation Some people use the convention of defining noise factor as a pure ratio and noise figure as the same ratio logged i.e. noise figure is 10log(noise factor). In practice everyone uses the term noise figure and if it is expressed in dB then it has been logged 10 Precise definition of Noise Figure IEEE definition: Noise Factor, at a specified input frequency, is defined as the ratio of (1) the total noise power per unit bandwidth available at the output port when the noise temperature of the input termination is standard (290K) to (2) that portion of (1) engendered at the input frequency by the input termination Fundamental noise concepts Na + Nin .Ga Nin . Ga F = K.To.B *** Assumes noise source and DUT are conjugately matched *** Here is the IEEE definition of the noise which unless you read it very carefully may hide a couple of very important points about noise figure. First of all just read it. What ‘the noise engendered by the input termination’ means is that the definition assumes all the available power from the noise source passes through the DUT. This will only happen when the DUT is the conjugate match of the noise source. Agilent’s noise sources are matched to 50Ohm so if you are attempting to measure a device with a poor VSWR then you will be introducing measurement uncertainties. The other really important point to stress here is that noise figure is defined as a figure of merit when the input noise to the device is standard thermal noise i.e. -174dBm/ Hz. 11 Two examples of Noise Figure Example 1: In a receiver, the LNA is connected to an antenna which points to earth’s atmosphere (290K) and the LNA has 3dB NF and 10dB gain. Noise power at LNA output is: -174+10+3=-161dBm/Hz Example 2: In a transmitter the modulator noise floor is -140dBm/Hz. The modulator output is amplifier by a linear amp with 3dB NF and 10dB gain. Noise power at amplifier output is: -140+10+3=-127dBm/Hz Fundamental noise concepts -140dBm corresponds to a noise source with a temperature 700 million K, i.e. DUT input is not Standard Temperature and Example 2 is wrong Just to emphasize this point, noise figure only represents the noise added to the input noise referred to the DUT output when the noise into the device is thermal noise at the standard temperature. So the first example here is correct. In the second example, the noise going into the device is much higher and therefore the noise figure of the amplifier cannot be added to the noise out of the DUT from the modulator. In reality if the noise of the amplifier is only 3dB then it will add practically no noise to that generated by the modulator. 12 Ga , NaRs Nout = Na + kTB Ga Nin O ut pu t P ow er Noi se F ree Ch ara cter istic Na Slope=kBGa Source Temperature (K)Te-Te Fundamental noise concepts An Alternative Way to Describe Noise Figure: Effective Input Noise Temperature Let’s now plot the output noise power as a function of the temperature of the noise source. In the equation for Nout I have substituted Nin for kTB where T now varies from absolute zero upwards. It’s a linear curve as we are dealing with very low power levels so all devices are operating in their linear regions. Actually the line is a very standard ‘y=mx+C’. M is the gradient in this case kBGa and c is the point at which the curve intersects the y axis. C is equal to Na. What you can say at T=0 is that no power at the device output comes from the noise source. All the output power at this point is generated within the DUT. This gives us another figure of merit for describing the noise performance of active devices. If you look at the graph I have drawn the characteristic of a noise free device. If you transpose the added noise Na through this line on to the x axis you arrive at Te, the effective input noise temperature. When you multiply Te by the gain bandwidth product of the device you get the amount of noise added. It’s a useful figure of merit because it is independent of the device gain (unlike Na). 13 Effective Noise Temperature relation to NF Gain G Ts Te Na + kToBG kToBG F = kGBTe + kGBTo kBGTo Te + To To = = Therefore Te = (F-1) . To Fundamental noise concepts Assume Na = 0 Gain G Ts Na What is Te if the NF is 3dB? 14 Te or NF: which should I use? •Use either - they are completely interchangeable •typically NF for terrestrial and Te for space •NF referenced to 290K - not appropriate in space •If Te used in terrestrial systems and the temperatures can be large (10dB=2610K) •Te is easier to characterize graphically Fundamental noise concepts 15 Friis Cascade Formula F12 = F1 + F2-1 Ga1 Ga1 Ga2 F2F1 Fundamental noise concepts Σ FN+1 = Σ Fn + Fn+1 - 1 ΣGN Where Σ Fn is cumulative NF up to nth stage and Σ FN+1 is cumulative NF up to (n+1)th stage Noise figure can be used for much more than just characterizing a single stage. If you know the noise figure and gain of each stage you can calculate the noise figure of a cascade of devices. This equation is known as the cascade formula or Friis formula. F12 is the noise figure of the 2 stage system. G1 is the gain of the first stage, F1 is the NF of the first stage and F2 is the NF of the second stage. The formula clearly shows why you must put your best noise figure devices at the front of the chain. Also the higher the gain of the first stage, the less the noise figure contribution from subsequent stages. 16 stage 1 stage 2 stage 3 stage 4 TOTAL NF AMP1 AMP2 AMP3 AMP4 NF 4.00 2.00 5.00 10.00 gain 16.00 14.00 20.00 30.00 cummulative NF 4.00 4.03 4.03 4.03 cummulative gain 16.00 30.00 50.00 LOSS1 AMP1 AMP2 AMP3 NF 4.00 2.00 4.00 5.00 gain -4.00 14.00 16.00 20.00 cummulative NF 4.00 6.00 6.16 6.17 cummulative gain -4.00 10.00 26.00 10*LOG((10^(F22/10))+(10^(G20/10)-1)/10^(F23/10)) stage 1 stage 2 stage 3 stage 4 TOTAL NF AMP1 AMP2 AMP3 AMP4 NF 2.00 4.00 5.00 10.00 gain 14.00 16.00 20.00 30.00 cummulative NF 2.00 2.16 2.17 2.17 cummulative gain 14.00 30.00 50.00 AMP1 AMP2 AMP3 AMP4 NF 2.00 4.00 5.00 10.00 gain 9.00 16.00 20.00 30.00 cummulative NF 2.00 2.49 2.51 2.51 cummulative gain 9.00 25.00 45.00 Fundamental noise concepts 1 2 3 4 Receiver Modelling using Excel Here is an example of how useful the cascade formula is in the estimation of receiver sensitivity. I’ve used EXCEL to illustrate the example as EXCEL is a very simple and powerful way of performing linear calculations. Both examples have four system components. In the first one I have my low noise amplifier at the front followed by a linear gain block followed by 2 further gain stages. My best noise figure device is placed first as it will dominate the noise figure performance of the system. You can see that the overall noise figure performance is little more than the noise figure of the first stage. The second example is identical, except for the fact that the LNA has lower gain. This mean that the noise contribution of the following stages is more noticeable. The point to make here is that the noise figure of a device is important - but so is its gain. In the third one I have swapped the first two amplifiers around and you can see the difference his has made to the overall noise figure - although the cumulative gain is the same the noise figure is dominated by the first - and now poorer - noise figure performance. The last example is similar to the very fist one except that now4 dB of loss have been introduced. This is common in receiver systems and could represent the cabling between an antenna and the LNA or a front end duplexer. The noise figure of a passive lossy device is equal to its loss. Overall you just add front end losses to the system noise figure to get the overall noise figure The noise figure of a passive device can be seen to be same the magnitude of the insertion gain. For example, a 6dB attenuator will have a noise figure of +6dB, but an insertion gain of -6dB. This can also be seen from standard calculation as well. As an example : if Noise Factor = N out / Gain x N in, and if Noise_out = Noise_in for this case, and Gain = 1/4 then Noise Factor is 4 and the noise figure is the log of this at + 6dB I’ve shown the cascade equation in slightly modified form. This is what you would type into excel. Fn is the cumulative noise figure up to the nth stage and sigma Ga1 is the cumlative gain. 1 2 17 ERP = +55 dBm Path L osses : -200 dB Transmitter: ERP Path Losses Rx Ant. Gain Power to Rx Receiver: Noise Floor@290K Noise in 100 MHz BW Receiver NF Rx Sensitivity C/N= 4 dB + 55 dBm -200 dB 60 dB -85 dBm Why do we measure Noise Figure? Example... Choices to increase Margin by 3dB 1. Double transmitter power 2. Increase gain of antennas by 3dB 3. Lower the receiver noise figure by 3dB -174 dBm/Hz +80 dB +5 dB -89 dBm Power to Antenna: +40dBm Frequency: 12GHz Antenna Gain: +15dB Receiver NF: 5dB Bandwidth: 100MHz Antenna Gain: +60dB Fundamental noise concepts Here is an example of why we need to know the noise figure of a device. In this example, we have a satellite that transmits with an effective radiated power of +55dBm, and is transmitted through a path loss, of +200dB, to a receive antenna with gain of 60dB. The signal power to the receiver is -85dBm. The receiver sensitivity is calculated here using kTB is at -174dBm /Hz and the noise power in a 100 MHz bandwidth you add 80dB. The noise figure of the complete receiver is +5dB. So the receiver noise floor is at -89dBm. S we currently have a 4dB carrier to noise ratio in our 100MHz channel. If we wanted to double the link margin to get improved receiver reliability, then we could double the transmitter power. This would cost millions of dollars in terms of increased payload and /or higher rated, more expensive components and more challenging engineering issues. Another way is to increase the gain of the receiver. This would cost millions in terms of size and mechanical engineering, and the debates over local environmental issues and planning permissions. While lowering the Noise Figure of the front end would be a fraction of this, and is the more attractive economically. Noise figure is a $$$ figure. 18 •Not a figure of merit for different modulation techniques use BER instead •Not a quality factor for one port networks e.g. synthesizers, power supplies •Not a useful quality factor for high power stages use transmitter tester Fundamental noise concepts What Noise Figure is Not… We have discussed what noise figure is. It is maybe usefully to briefly describe what noise figure is not. It does not give any indication of the efficiency of the modulation scheme chosen. In digital receivers this is done by BER. BER and noise figure have a nonlinear relationship where as you gradually decrease the signal to noise ratio you will suddenly see a rise in BER as 1’s and 0’s become confused. Noise figure is a two port figure of merit. It does not describe one port networks such as terminations or oscillators. Oscillators do generate noise and will affect the sensitivity of receivers but noise figure is not a means of measuring oscillator quality. Here phase noise measurements would be more appropriate. High power stages imply nonlinearity and noise figure is a function of strictly linear systems. Also high power stages implies high levels of input noise, so the added noise of the of the high power stage is likely to be very small - remember noise figure is defined where the input power has an effective temperature of 290K. 19 •The Origins of Noise •Signal to Noise ratio •Definition of Noise Figure •Effective Noise Temperature •Friis Cascade Formula •Using Excel in Rx modeling •System Sensitivity Calculation Fundamental noise concepts Summary of Noise Fundamentals 20 How do we make measurements? Fundamental noise concepts How do we make measurements? What DUTs can we measure? What influences the measurement uncertainty? How do we make measurements? 21 Ga , NaRs Nout = Na + kTB Ga Nin O ut pu t P ow er Noi se F ree Ch ara cter istic Na Slope=kBGa Source Temperature (K)Te-Te How do we make measurements? To solve for Na: 1) establish 2 points on curve or 2) establish 1 point and gradient Na + Nin .Ga Nin . Ga F = Measuring Noise Figure To show how noise figure is measured, let’s look again at the graph that was first introduced to demonstrate the connection between noise figure and effective noise temperature. To find Na or Te in the graph we need to do two measurements. One way is to measure two sets of x:y points on the graph and from these, calculate the intersection of the Y-axis. Another method is to measure a single x:y point but also to establish the radiant of the curve and again this would give us the Y intersection point. We will concentrate on the first of these techniques. 22 Rs Nout = Nh or Nc Nin = kB(Th or Tc) O ut pu t P ow er Na Slope=kBGa Source Temp (K)-Te Nh Nc Tc Th How do we make measurements? •Physically hot/ cold source •avalanche diode Hot / Cold Techniques During the measurement, a hot noise source and a cold noise source are applied to the input of the DUT. We will get two output powers Nh and Nc for the two conditions. This is known as the hot/cold measurement technique and is also known as the Y-factor technique. The Y factor is the ratio of Nh to Nc. There are a number of ways of providing Th and Tc. Metrologists favour putting a noise source in an oven with an ambient of 373K for hot, and dipping the source in liquid Nitrogen at 77K for cold. Not the most convenient of sources and the time taken to make the measurement may mean the gain of the DUT or measurement system has drifted whic