D. Receiver Dynamic Range

Transcription

1 10/29/2007 Receiver Dynamic Range note 1/1 D. Receiver Dynamic Range Q: So can we apply our new knowledge ab noie power to a uper-het receiver? A: Example: Receiver Ga and Noie Figure Q: What ab the put ignal power? You aid it can be very large or very mall. Are there any limit to the ignal power? A: Ye! If the ignal power i too mall, it cannot be accurately demodulated due to ignal noie. HO: The Mimum Detectable Signal Likewie, if the ignal power i too large, the receiver will urate! HO: Receiver Compreion ot The ratio of the larget to mallet ignal power defe the dynamic range of a receiver. HO: Receiver Dynamic Range

2 10/29/2007 Example Receiver Ga and Noie Figure 1/5 Example: Receiver Ga and Noie Figure We cam now determe the overall ga and noie figure of a uper-het receiver! Conider the followg example: Let look at each device dividually: Antenna - We aume that the antenna noie temperature i T = T = 290 K, therefore N = 174 dbm Hz. Alo, the antenna A o couple a deired ignal with power A. 1. LNA - Thi device ha a ga G 1 = (10 db) and a noie figure F 1 = 15. (1.76 db). 2. reelector Thi device ha an ertion lo of 1 db. Therefore:

3 10/29/2007 Example Receiver Ga and Noie Figure 2/5 ( ) G db = 10. G = ( ) F db = 10. F = Mixer - Thi device ha an converion lo of 6 db. Therefore: G db = 60. G = 025. ( ) 3 2 ( ) F db = 60. F = IF Amp - Thi device ha a ga G = 10 (30 db) and a 4 noie figure F 4 = 40. (6 db). 5. IF Filter - Thi device ha an ertion lo of 2 db. Therefore: G db = 20. G = 063. ( ) 5 2 ( ) F db = 20. F = The total ga of the receiver i eay to determe, it imply the product of the ga of all device: or, GR x = G G G G G = ( 10)( 08. )( 025. )( 1000)( 063. ) = 1260

4 10/29/2007 Example Receiver Ga and Noie Figure 3/5 R x ( ) = ( ) + ( ) + ( ) + ( ) + ( ) G db G db G db G db G db G db = = 31 Note that: 10 [ ] 10log 1260 = Now, determg the noie figure of the receiver i a bit more challengg. F R x Therefore: F 1 F 1 F 1 F = F G1 GG 1 2 GGG GGGG = ( 10) ( 10)( 08. ) ( 10)( 08. )( 025. ) ( 10)( 08. )( 025. )( 1000) = = 20. R x ( ) = 30 F db. Note then that the noie power at the receiver put i: = F G kt B n Rx Rx A IF = ( 2)( 1260) = B IF W kt B A IF

5 10/29/2007 Example Receiver Ga and Noie Figure 4/5 Now, let e what happen if we move the LNA to the end of the receiver! We fd the ga i unchanged! R x ( ) = ( ) + ( ) + ( ) + ( ) + ( ) G db G db G db G db G db G db = = 31 But not the noie figure: F R x F3 1 F4 1 F5 1 F1 1 = F G GG GGG GGG G = ( 08. ) ( 08. )( 025. ) ( 08. )( 025. )( 1000) ( 08. )( 025. )( 1000)( 063. ) = = 20 0.

6 10/29/2007 Example Receiver Ga and Noie Figure 5/5 The receiver noie figure ha creaed to 13 db 10 db larger than before! A a reult, the noie put power ha likewie creaed by a factor of 10 time! = F G kt B n Rx Rx A IF = ( 2)( 1260) = B IF W kt B A IF Thi example demontrate how important the LNA i to effective receiver deign.

7 10/29/2007 Mimum Detectable Signal 1/6 Mimum Detectable Signal,N SNR A Rx Rx, SNR n Rx = SNR D Let review what we have dicovered! The noie power at the put of a receiver (i.e., the put of the demodulator) i: = F G kt B n Rx Rx o IF while the ignal power at the receiver put i: = G Rx Thu, the SNR at the receiver put (the detector put) i: SNR Rx = = n G Rx F G kt B Rx Rx o IF = = SNR F kt B Rx o IF D

8 10/29/2007 Mimum Detectable Signal 2/6 Q: OK, o the expreion above provide a method for determg the value of SNR ; but what hould thi value Rx be? What value i conidered to be ufficiently large for accurate ignal detection/demodulation?? A: It depend! It depend on modulation type, demodulator deign, and ytem accuracy requirement. From all thee conideration we can determe the mimum m required SNR (i.e., SNR D ) a value that mut be exceeded at the detector/demodulator put order for an ufficiently accurate demodulation to occur. I.E., SNR Rx > SNR m D for accurate demodulation The value of thi mimum SNR can be a mall a -20 db (or even lower), or a large a 40 db (or even greater), dependg on the application and it requirement. Q: How can we ure that SNR Rx > SNR?? m D A: Of coure, we do need to make the noie figure of the receiver a mall a poible. However, the value SNR Rx ultimately depend on the ignal power if thi ignal power drop toward zero, o too will SNR Rx! m Thu, the requirement SNR D ultimately tranlate to a mimum ignal power any ignal above thi mimum can be accurately detected, but ignal power below thi value cannot.

9 10/29/2007 Mimum Detectable Signal 3/6 Make ene! If the put ignal power i too mall, it will be buried by the receiver noie. We call thi mimum put ignal power the Mimum Detectable Signal (MDS) a.k.a the Mimum Dicernable Signal. I.E., > MDS for accurate demodulation Thi Mimum Dicernable Signal thu determe the enitivity of the receiver. Q: What i the value of MDS? How can we determe it? A: We know that for ufficiently accurate demodulation: SNR R x = SNR F kt B > R o IF x m D Thu: > F kt B SNR m R o IF D x And o it i evident that: MDS = F kt B SNR m R o IF D x

10 10/29/2007 Mimum Detectable Signal 4/6 Radio engeer often expre MDS a dbm! The above expreion can written logarithmically a: m FR kt x o BIF SNRD MDS ( dbm ) = 10log10 1mW m FR kt 1 x o BIF SNRD Hz = 10log10 1mW 1Hz 1Hz = 10log10 FR + 10log x 10 kto 1 mw B IF + 10log log10 SNR 1Hz Recall that we earlier determed that : m D 1Hz 10log10 kto = mw And o the enitivity of a receiver can be determed a: m B IF MDS ( dbm ) = FR ( db ) + SNR ( ) 10 x D db + log10 1Hz

11 10/29/2007 Mimum Detectable Signal 5/6 Every radio engeer worth hi or her own alt ha thi expreion committed to memory. You do the ame, or I ll become even more grumpy and diagreeable than I already am! Now, let do an example! Say a receiver ha a noie figure of 4.0 db and an IF bandwidth of 500 khz. The detector at the receiver put require an SNR of 3.0 db. What i the enitivity of thi receiver? m B IF MDS ( dbm ) = FR ( db ) + SNR ( ) 10 x D db + log10 1Hz 3 = log = = Q: Yike! The value -110 dbm i 10 femto-watt! Jut one percent of one billionth of one milli-watt! Could thi receiver actually detect/demodulate a ignal whoe power i thi fantatically mall?

12 10/29/2007 Mimum Detectable Signal 6/6 A: You bet! The value ued thi example are fairly typical, and thu an MDS of -110 dbm i hardly unuual. It a good thg too, a the ignal delivered to the receiver by the antenna are frequently thi ty!

13 10/29/2007 Receiver Compreion ot 1/14 Receiver Saturation ot Given the ga G Rx of a receiver, we know that the put ignal power (i.e., the ignal power at the demodulator) i: = = G D Rx Of coure, limited! can theoretically be any value; but i Q: Limited by what? A: Many of the device a receiver have compreion pot (e.g., mixer and amplifier)! In other word, a creae, one of the device the receiver will eventually compre (i.e., urate). A we creae the ignal power beyond thi pot, we fd that the receiver put power will be le than the value G. Rx reciely the ame behavior a an amplifier or mixer! Accordgly, we can defe a compreion pot for our receiver.

14 10/29/2007 Receiver Compreion ot 2/14 We can approximately determe the compreion pot of our receiver if we know both the ga (attenuation) and compreion pot of each and every one of it component. Q: Thi ound very much like how we determed the overall noie figure of a receiver (i.e., with knowledge of G and F for every component). Give me the equivalent equation o I can get buy calculatg the compreion pot of my receiver! A: Not o fat! The procedure for determg the compreion pot of a receiver i quite a bit more complex than fdg it noie figure. The problem i that the compreion pot of a receiver i not ome function of the all the compreion pot of each device. Intead, it i dependent only on the compreion pot of the device that urate firt a creae. Big problem we do not know what device will urate firt! Q: Won t it imply be the device with the lowet 1 db compreion pot? A: Nope! The ga (or attenuation) of all of the device that precede a component will likewie determe the value of receiver put power at which that component urate.

15 10/29/2007 Receiver Compreion ot 3/14 Thu, we mut dividually determe the value of receiver put power that will caue each of the component our receiver to urate. The mallet of thee value will be the compreion pot of the receiver! erhap thi i bet explaed by an example. Conider a imple uper-het receiver with the followg component: Device G m m m=1 10 db +10 dbm m=2-1.0 db m=3-6.0 db 3 dbm m=4 15 db +14 dbm m=5-2 db

16 10/29/2007 Receiver Compreion ot 4/14 Here the value G m repreent the ga of the m-th component, m the compreion pot of the m-th component, and i the amount of receiver put power required to caue that particular component to urate. Now, let look at each component, and determe it particular value for. m=1: LNA Recall the 1 db compreion pot of an amplifier i pecified term of put power. Thu, when thi amplifier urate, the put power will be: or equivalently: 1 1 = G1 db ( ) = ( ) ( ) dbm dbm G db = = 0 dbm Q: Wait! Shouldn t we add 1 dbm to thi anwer?? A: Theoretically ye, a when the device ha compreed by 1 db, the ga i effectively 1 db le (i.e., G1 = 9dB). However, we typically do not conider thi fact when computg compreion pot, a:

17 10/29/2007 Receiver Compreion ot 5/ dbm i generally not large enough to be numerically ignificant, particularly when coniderg all the other approximation and uncertatie our deign! 2. By not addg the 1 dbm to the olution, we have a bit more conervative etimate of receiver performance. After all, our goal i to avoid receiver uration! Now, ce the put to the LNA i likewie the put to the receiver, we can conclude that the LNA will urate when the receiver put power i 0 dbm. Thu, accordg to our firt component: = 0dBm However, thi very well may not be the put value at which the receiver urate, a ome other component may compre at an even lower receiver put power. Let fd if there i uch a component! m=2: reelector Filter Q: Wait a econd! I don t recall ever hearg ab a filter compreion pot!? A: True enough! A filter, ce it i a paive and lear device, ha no compreion pot. Of coure, if we put too much power to the device, it will damage (e.g. melt) it, but thi power i typically very large compared to mot amplifier or mixer compreion pot.

18 10/29/2007 Receiver Compreion ot 6/14 Thu, we can conclude that the compreion pot of a filter i effectively fity, a i the put receiver power required to urate it (i.e., = ). Q: I ee! Filter make no difference determg the uaration pot of a receiver. Can we ignore them altogether? A: Abolutely not! Although filter will not urate, they will help determe the uration pot of a receiver. The reaon i that filter have ertion lo. Note the ga of thi filter i 1.0 db, which dicate an ertion lo of +1.0 db. Thi lo will affect the put power of all the component further down the receiver cha, and thu may affect the receive uration pot! m=3: Mixer Don t forget that the compreion pot of a mixer (unlike an amplifier) i pecified term of it put power! Thu, from the mixer compreion pot, we can immediately conclude that: db ( ) ( ) dbm dbm dbm 1 3 = 3 = 3 In other word, we do not have to remove the mixer converion lo to fd the put power, the way we had to

19 10/29/2007 Receiver Compreion ot 7/14 ubtract the LNA ga from the LNA (put) compreion pot. However, ce the mixer i not directly connected to the put of the receiver, we mut remove the ga of the precedg component order to determe what put receiver power will caue the mixer to urate. Sce the power to the mixer i imply the power to the receiver time the ga of the LNA and preelector filter: = GG we can conclude that: 3 = GG 1 2 or equivalently: ( ) = 3 ( ) 1( ) 2( ) = 3 10 ( 1) dbm dbm G db G db = 60. dbm

20 10/29/2007 Receiver Compreion ot 8/14 Note here that the ertion lo (i.e., G 2 = 10. db) of the filter wa volved our computation, and thu affected the value of thi uration pot! m=4: IF Amp Thi IF amplifier urate when it put power i 4 =+ 14 dbm. The receiver put power that would caue thi much put power at our IF amp can be (approximately) determed by removg the ga of each precedg device, cludg the ga of the amplifier itelf (do you ee why?): ( ) = 4 ( ) 4( ) 3( ) 2( ) 1( ) = ( 6) ( 1) 10 dbm dbm G db G db G db G db = 4dBm Note that the ga of the mixer i -6 db; meang that the mixer converion lo i +6 db. It i now evident that we can write a general equation for determg the put receiver power that will caue an amplifier to urate, when that amp i the m-th component of a receiver: ( ) = ( ) ( ) ( ) ( ) dbm dbm G db G db G db m m m 1 1 = m ( dbm) Gn ( db) m n = 1 (for amplifier)

21 10/29/2007 Receiver Compreion ot 9/14 Note the expreion for mixer will be lightly different, given their defition of compreion pot: ( ) = ( ) ( ) ( ) ( ) dbm dbm G db G db G db m m 1 m 2 1 m 1 = m ( dbm) Gn ( db) ( for mixer) n = 1 m=5: IF Filter A we determed earlier, the compreion pot of a filter i effectively fity, and o for thi device: = So, let ummarize our table what we have found: Device G m m m=1 10 db +10 dbm 0 dbm m=2-1.0 db m=3-6.0 db 3 dbm -6 dbm m=4 15 db +14 dbm -4 dbm m=5-2 db

22 10/29/2007 Receiver Compreion ot 10/14 Q: Wait a econd! We have determed four different anwer for the receiver put power that will urate our receiver. Can they all be correct? A: Abolutely not! There i one, and only one, anwer for receiver uration pot. The receiver uration pot i the mallet of all of our calculated value! Thu, for thi example, the receiver compreion pot i: = 6 dbm Q: Why do we conider the mallet of all the value a the receiver compreion pot? Why not the larget? Why not the average? A: A receiver i conidered urated when any of it component are uration. Remember, uration caue our ignal to ditort, and thu it may not be accurately demodulated. A a reult, an put ignal power that caue the uration of even one receiver component i unacceptable.

23 10/29/2007 Receiver Compreion ot 11/14 Thu, by choog the mallet of the put uration power, we have elected a value that will unambiguouly defe the pot where even one component i urated if the receiver put power i le than even the mallet of our calculated, then none of the receiver component will be urated. Q: In thi example, it i the mixer that urate firt. I thi alway the cae? A: It i deed often the cae that the mixer i the device that determe the receiver uration pot. However, the LNA can likewie be the component that urate firt. Q: What can we do to improve (i.e., creae) the uration pot of a receiver? A: Coniderg the dicuion of thi hand, it hould be quite evident how to accomplih thi. We can do two different thg: 1. Fd a different component part with a higher uration pot m Thi trategy at firt eem very imple. However, a component deigner of mixer or amplifier i faced with the ame deign conflict and trade-off that typically face all other deign engeer. If he or he improve the compreion pot, it will undoubtedly me-up ome other

24 10/29/2007 Receiver Compreion ot 12/14 important parameter like ga, or bandwidth, or noie figure, or converion lo. Thu, a receiver deigner that attempt to replace a mixer or amplifier with another exhibitg a higher compreion pot will almot certaly caue ome degradation ome other receiver performance parameter, like ga, or noie figure, or bandwidth. The election of receiver component part i typically a compromie between competg and conflictg component parameter. You will never fd a perfect microwave component, only a component which bet uit the receiver pecification and deign goal. 2. Decreae the ga (creae the attenuation) of the component part precedg the component that urate. Decreag the ga and or creag the lo of component a receiver will generally improve (i.e, creae) the receiver uration pot. However, it will alo me-up the receiver noie figure and MDS! Aga, we are faced with a deign trade-off! Note however, that we only need to decreae the total ga of the component precedg the device that i uratg. Another way to accomplih thi i imply to rearrange the order of the device the receiver cha.

25 10/29/2007 Receiver Compreion ot 13/14 For example, we might move an amplifier from a location precedg the uratg component, to a location after the uratg component thi of coure reduce the ga of the component precedg the device, but doe not alter the overall receiver ga! Likewie, we might move a loy component from a location after a uratg component, to a location precedg the uratg component thi aga reduce the ga of the component precedg the device, but aga doe not alter the overall receiver ga! Thu, we can conclude that the compreion pot of a receiver will typically improve if we move loy component to the front and amplifier to the back! However, we mut keep md two thg: * The order of ome device cannot be changed. For example, we cannot put the mixer before the preelector filter! * Although rearrangg the order of the component a receiver will not change the receiver ga, it can play havoc with receiver noie figure and MDS! In fact, it hould be evident to you that the receiver noie figure typically improve if we move loy component to the back and amplifier to the front exactly the oppoite trategy for improvg receiver uration!

26 10/29/2007 Receiver Compreion ot 14/14 We fd that very often, receiver uration pot and receiver enitivity are direct conflict improve one and you degrade the other! Saturation ot Senitivity

27 10/29/2007 Receiver Dynamic Range 1/1 Receiver Dynamic Range We now know there i a mimum put ignal power that a receiver can accurately demodulate. The Mimum Detectable Signal (MDS) defe the enitivity of the receiver We alo know there i a maximum put ignal power that a receiver can accurately demodulate. The receiver 1 db compreion pot defe the uration pot of the receiver. The ratio of the put uration pot and the mimum detectable ignal i defed a the total dynamic range of the receiver. total dynamic range MDS Note dynamic range i a unitle value, therefore dynamic range i mot often expreed db: ( ) ( ) MDS ( ) total dynamic range db dbm dbm