EE 414: Lab 3 Narrowband LNA Design G G G G G G

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1 Saket Voa Andy Chen Siddhath Panwa Intoduction EE 44: La 3 Naowand LNA Deign he naowand low noie aplifie (LNA) i a citical lock in the deign of a tanceive. It i often the lock that i cloet to the antenna (though a filte ight e in etween) and the naowand natue i needed o that puiou ignal ae not needlely aplified and paed though. he iplication of the aplification and noie chaacteitic of thi lock cacade down though the et of the tanceive. hi laoatoy exploation invetigate the deign and contuction of a low noie aplifie that povide ufficient gain at GHz with an acceptale noie figue. Noie igue Noie igue Input etun Lo ( S ) Output etun Lo (S ) Powe Gain (S ) Low.xx > db > db > db ale Specification equied fo LNA Noie figue (N) and the noie facto () ae elated a N log log SN SN input output. hi etic i ued to evaluate how uch noie the device unde tet (ou aplifie) add to an input ignal. he noie facto calculation i taken utilizing the availale noie powe fo the ouce, the availale powe gain of the aplifie, and the additional noie added y the aplifie. he IE accepted foulation i k BGav N k BG av a, whee k i Boltzann contant, i the efeence tepeatue 9K, B i the availale ickwall noie andwidth fo the ouce, G av i the availale gain fo the aplifie, and N a i the added noie fo the aplifie. A entioned aove, the deand fo low noie and acceptale powe gain on the LNA i high due to it effect on lock down the line. he ii equation fo total noie facto of a cacaded yte of lock with noie facto i and gain G i i: 3 4 G G G G G G av av av av av av3... A the equation aove deontate, the gain of the fit tage diinihe the noie ipact of the econd tage, and the noie facto of the fit tage i not educed at all. Now that otivation ha een povided fo a yte-level pepective, let u analyze the LNA itelf. It i a ingle NPN tanito (ohia SC33) in coon eitte configuation with a taniion line load at the collecto. A eitive netwok povide the DC ia condition, while locking capacito ae ued at the input and output pin (which ae tandad BNC connecto). he taniion line i AC gounded at one end to povide a λ/4 like condition, uch that the line i inductive in natue. At oe ditance fo the collecto, a atched taniion line i tapped off at a 9 degee angle and eve a the output of the LNA. hee ae eveal facto that influence the igue - Noie igue v I C (ouce: dataheet)

2 noie figue of the LNA and include iaing, oad deign, hielding, and input & output atching. Chooing a ia cuent I C i an ipotant deciion. A chat of noie figue veu collecto cuent (igue ) how that fo a given V CE, fequency, and tepeatue, the noie figue fit deceae then apidly inceae a collecto cuent I C i inceaed. he figue how that fo noie figue, an optial ia cuent i etween 3A and 5A. Howeve, a low ia cuent ight not povide ufficient g to achieve the equied S gain. hee will e a tadeoff. In contat to ealie laoatoy invetigation, thi LNA utilize dicete coponent uch a an NPN tanito in a platic package and uface ount eito and capacito. And given that we ae opeating in the icowave egion, oad deign take on a diffeent pepective. Geat cae ut e taken to contol fo paaitic and loe. Pope gound plane ut e povided and ditance etween ipotant coponent ut e kept vey all to avoid line loe. Extenal ouce of noie ut e conideed a well. Switching powe upplie intoduce ipple, o we choe to ue olde powe upplie that ely on linea egulato. Additionally, othe electonic device neay can add noie o they wee tuned off duing noie figue eaueent. avoale input and output atching aid in achieving the alance of gain and noie pefoance. it, a all ignal odel of the BJ tanito (with noie ouce included): igue Sall ignal odel of a NPN BJ with noie ouce. Depite the peence of and the paallel coination of C π and π, the input ipedance of the BJ i not high enough to atch the 5 oh eal ouce ipedance if the goal i to achieve axiu powe tanfe. Maxiu powe tanfe help inceae S and a alle ia cuent I C i needed, which aid in loweing the noie figue. Intead of intoducing a noiy eito in eie to atch the ouce ipedance, we utilize an inductive degeneation of the tanito to ceate an additional eal ipedance at the ae. In a geneal fo, the input ipedance i: Zin L L C, with L eing the eitte inductance. Anothe eie inducto at the ae could e then ued to eonate out any input capacitance een. he tanito ha a eitte inductance of.795ph and we etiated that the paallel coination of eitte lead (each lead at at.nh/) would add appoxiately.nh to the eitte inductance, leading to aound.9nh of eitte inductance. At a ia cuent of A, thi eult in a eal ipedance of ~ 9.7Ω, while at a ia cuent of 5A, thi eitance dop to 3.Ω (changing the ia cuent affect the tanit fequency). he ae ha an intinic inductance of.858nh, and the ae pin wa etiated to add anothe.nh in eie, inging the total ae eie inductance to aound.6nh. At GHz, thi inductance can eonate out 3.9 p. We decide we would adjut the eitte lead inductance in ode to oot the eal eitance een at the ae in ou cicuit, efoe attepting to eploy a lole ipedance tanfoe like an L-atch. A fo the output, we deie that the load at the collecto eonate at GHz. hi help axiize S. In the cae whee thee ae no paaitic at the load, we would iply utilize a quate wavelength taniion line a ou load. In eality, we ee a Milleized junction capacitance and the collecto-eitte

3 capacitance at the collecto node, CL Cce C.85 p. hi load capacitance can e A eonated out uing a taniion line load that i inductive in natue. We can calculate the inductance needed y equating eactance, L C ( e9).85 p v 3nH. We can then teat ou load a a taniion line hoted to gound, thu, we can find the length that give u the neceay eactance. he inductance of a taniion line vaie a L Z tan( z ), whee < z < λ/4 and Z =5 oh, and i the ditance fo the hot cicuit end of the taniion line. We find that z = 34. will povide u the inductance we want. Afte deteining the length of the line, we need to find whee to tap the line to connect to the output load. Gaining a quantitative inight into thi wa vey difficult in the ealy tage of the deign, ecaue it i influenced y o any facto. We decided to fit expeientally deteine a uitale tap point and gain a ette undetanding of how the tapping point election affect the S-paaete y oeving the change on the VNA. It hould e noted that having the LNA ee a 5 oh ouce eitance i not neceaily optial fo noie figue. o a ia cuent I C = A, the optial ouce eitance fo low noie pefoance can e calculated uing: ( ) ( g g ( / ) ( 7 / ) 49 and ).338 g g, with ) (, ( ) (5.) 7. 4,. o dataheet and odel inpection, we ue f to e 5. GHz, = 7Ω, β = 8, and g = 4 S. hi eult in a S 9.7 Ω. If needed, an ipedance tanfe can e ued to ake thi the ouce eitance that the LNA ee, a ove that would help educe the noie figue. On the uject of noie, what i a typical noie figue one would expect fo thi LNA? he noie facto fo an LNA of ou topology can e found with: z ( ) z g g We know C i lagely doinated y diffuion capacitance. Hee z i given y the paallel coination of C and. C V I C, peak whee,pk i the peak value of tanit fequency of the tanito and i appoxiately equal to 5.8 GHz fo the SC33 tanito. So fo I C = A, C i oughly equal to.37 p and =β/g =. ogethe the two give Z =(.975- j3.9). he S we ue i 5 oh, the actual ouce eitance ued in the LNA. z ( ) g.4,. 455, and. 6, z g which give a noie facto =.755 and a noie figue of.44 db. 3

4 Contuction & Siulation It wa expected that we would iteate though eveal LNA deign. A fit pa aic LNA wa ceated uing the following ia point paaete: V CE = V and I C = A. hi tating point wa deteined y exaining the dataheet and though wod of outh a to peviou expeience with the SC33 tanito. We expected the choen cuent to e too high fo an optial noie figue, ut we wanted to enue eeting othe pecification a well. he figue elow contain the cicuit that we contucted. We alo etiated paaete V BE =.8V, β = 8. wa choen a 8Ω uch that the input eitance of the BJ would doinate in the paallel coination of and the input eitance of the BJ een fo the input pot. We etiated thi input eitance would e elow 8Ω, o we choe a ten tie lage. Uing thi infoation, I A V I 5 A I.5A I I I.5A 5 A.5A C BE B B 8 he taniion line load at the collecto i a hot at DC, o the V CE voltage i een at the top of. o V.8V.5A 798 have a I =.5A, the calculated value hould e. hee i flexiility in chooing 3 a it deteine the V CC upply voltage. We choe 3 = Ω o that V CC would not e vey high. V ( ).3 CC 3 I IC V. When actually contucting the cicuit, lagely due to pat availaility, we choe value of = 86 Ω, = 86 Ω. 3a Vcc 3 C_ac_gound Clock Clock load V igue 3 Cicuit cheatic fo LNA Blocking capacito wee ued at the input and output, and ized to equal n (each capacito in paallel i n). wo capacito wee ued in paallel o that thei width would e appoxiately the width of the 5 oh taniion line, o that it ette atching fo a phyical tandpoint. he line i teinated in a paallel coination of capacito to povide an AC gound. One capacito wa intended to e of a all value (on the ode of to 8 p) to povide a high fequency gound, while the othe wa e lage (nh to nh) to povide a low fequency gound. We choe value of 4p and nh, epectively. 4

5 Gound OU Gound DC BIAS n 4p Ω n 5 8Ω 8kΩ n IN DC ia path Eitte oldeed to ackplane igue 4 Contuction of the LNA, fit iteation. Contuction he fit iue addeed in the LNA contuction wa the ounting of the tanito. We oeved the Liu-Cheng tea dill a hole in the 4 oad and olde the eitte pin diectly to the gound plane while the ae and collecto lead paed though the hole and to the othe ide. Inpied y thi choice, we extended it y ceating all end in the lead which allowed the tanito to it in the iddle of the hole. hough thi lightly lengthened the eitte lead, it helped educe the length (and thu paaitic inductance) of the ae and collecto lead. Both eitte lead wee oldeed the gound plane, uch that the paallel coination of the lead would educe the paaitic eitte inductance. aniion line wee laid at full length, then late vey all ( wide) cut wee ade in the and idged with the equied coponent, e the eito o capacito. Wide tip of coppe line wee ought ove fo the gound plane and oldeed in ultiple point to enue a good gound. Becaue of the taniion line lo ove ditance (ee la ) we iniized thee ditance. he,, and C lock wee oldeed vey cloe the ae. A all length of line wa left etween the C lock and the input pin to allow oo fo a atching netwok, ut no atching netwok wa ultiately ued. With egad to the taniion line load length, we decided to fit tat at a λ/4 (~37 to 38 fo GHz) then tweak the line y hifting the location at which we connect the AC gounding capacito. hi deciion wa lagely infoed y ou expeience in ealie laoatoie, when oe light vaiaility in eonant fequency wa oeved with thee kind of hand-cut taniion line. he ipedance of the taniion line eonant load at the collecto deceae in a quadatic fahion fo the collecto to the AC gound. We initially etiated that the tapping point would occu elow the halfway ak cloe to the collecto, and attached a BNC connecto at a ditance of 7 to 8 fo the taniion line. We expected that ight angle end would e needed to hift the pecie the tapping point fo the line. A ou initial tapping point, we iply tied a 5 oh line diectly to the load. eting Afte a DC hot (too uch olde at a junction) wa olved and the ia point wee veified uing a ultiete, we teted the LNA on the HP 897B Noie igue ete and eaued a noie figue of 3.5 db. We then ued a pe-caliated VNA (HP 8753ES) to eaue the S, S, and S paaete. We found that each of thee paaete et pecification, having value of db o geate. 5

6 hee wee nueou pole with thi initial caual eaueent the intuent wee not popely caliated and the output powe of the VNA did not atch that of the noie figue ete. he dataheet of the HP 897B howed an pot output powe of - db, and the default output pot powe of the VNA wa db. he following day, uing feedack fo othe goup and the A, we added a lage ypa capacito (uh) fo V CC to gound. Geate cae wa ued to enue pope caliation. he new noie figue eaued wa.5 db. he VNA eult fo S-paaete alo indicated that we wee till eeting pecification, with a agin of.5db to.5db. ankly, we wee upied. Ou tapping point wa not igoouly calculated, we had no input atching netwok. he eult fo thee eaueent fo ou LNA ae hown elow in igue 5. igue 5A S log agnitude igue 5B S Sith chat igue 5C S log agnitude igue 5D S Sith chat 6

7 ale Meaueent fo the nd pa teting Seeing that we had a decent agin fo the db pecification fo S, S, and S, we then attepted to ipove the noie figue futhe. he iplet adjutent we could ake wa to deceae the ia cuent. A een in igue, a deceaing the ia cuent I C ipove the noie figue to an extent. hi could e achieved y loweing the upply voltage. While igue 5E S log agnitude the LNA wa on the noie figue ete, V CC wa loweed and the noie figue deceaed to.85 db. Supecting that the ia cuent wa too low to eet the S-paaete pecification, we eaued the LNA on the VNA (uing a conitent output powe of -db) and found the S-paaete 3 to 4 db lowe than equied. inal eult GHz (in db) e{z} I{Z} S -.8 db 4Ω 3.56nH S -.6 db 8.3Ω 47p S.5 db - - N.5 db - - We adjuted the upply voltage until the S-paaete wee et and the noie figue wa a good value at etween.93 db and.95 db (we ued the aveaging featue on the 897B to ettle the nue down).he final S-paaete eult, noie figue, and ia point eaueent ae hown elow. igue 6A S log agnitude igue 6B S Sith chat he input ipedance Z in i given oe igoouly y the following equation: Z in ( j ) j C j L L( j L Z L ) o the Sith Chat we ee that S tat out capacitive and a fequency inceae the paaitic inductance egin to inceae and the ipedance appoache a puely eitive one. At eonance we 7

8 ee that the eitance looking into the input i aound 5. If we aue that the output eitance i lage copaed to the load and the coupling of the load to the input though the collecto-ae capacitance C (accoding to the genealized Mille effect given y the equation Z C ( g Z ) ) i alo negligile, then the eitance een at the input i uppoed to e the u of and the eitance L e eflected to the ae fo the eitte. he Mille effect can e doinant when, fo exaple, due the peence of a eonato a chiefly inductive load i een at the collecto at a paticula fequency. hat load will then poduce a negative eitance at the ae of tanito. Auing i aound 7-8 and the effect of finite o i negligile in educing Z in, then the eitte degeneation inductance L e i a low.3 nh fo inpecting the Sith chat in igue 6B. hi i on the ode of what we etiated fo ou contuction technique, ut we ae unue whethe o i indeed negligile. At the GHz opeating point, the S i -.95 db and the Sith chat how a eitance of 3.45 Ω and an inductance of.3 nh. hi eitance i vey iila to what calculation pedicted (6.9 Ω fo a I C ~ 5.7A), and the additional eie inductance (intinic plu etiated lead inductance pedicted ~ nh) could e explained y additional inductance picked up due to the BNC input connecto. Additionally, the dicepancy in the etiated and eaued eitance value could e do the effect that the output loading ha on the input ipedance. Back to the S Sith chat, we ee that a fequency i inceaing (counte-clockwie) and we ove eyond eonance, the iatch i educing ut thee i a hap tun outwad on the Sith chat at aound.3 GHz in ou eaueent and a iila one in the ADS iulation plot (ee elow) at aound.3 GHz and fo oth cae we ee in the log plot the S deteioate. In ADS we wee ale to deteine thi atifact coe afte incluion of the icotip at the collecto that i ued a a eonato. hi could ecaue of the genealized Mille effect een at the input a the load vaie with the fequency. L igue 6C S log agnitude igue 6D S Sith chat he S eaueent in igue 6C and 6D how a S of -. db at the GHz opeating point and a eitive coponent of 3.38 Ω and eactive coponent of ~.6 p. he hap dip in the log agnitude plot coepond to the ae fequency (etween 55 MHz and 65 MHz) a the dip in the ae S plot hown in igue 6A. he local iniu in S at ~.5 GHz alo coepond to a iila occuence in the S plot. hi help eveal the coupled natue of the input and output pot due to eonant ehavio. While the eitive coponent i not peciely atched to 5 Ω, it povide ufficient S. Adjuting the tapping point could e ued to ipove the eitive pat, and pehap uing an inductive notch in the 8

9 taniion line leading to the output pin could e ued to cancel out the ~.6 capacitance. hi appea a little iky howeve, ecaue of how the peence of a new inductive coponent ight eflect ack to the input. igue 6E S log agnitude igue 6 Noie igue eult A faint andpa ehavio can e een in the S plot in igue 6E. At the GHz opeating point, a gain of.55 db wa otained at the ia point. hi gain could e inceaed a V CC inceae, at the expene of noie pefoance. A noted in the S plot ection aove, thee ae egion of exteely poo pefoance aco all S-paaete. hi could e explained due to tange ipedance ehavio in which the eitive coponent of the input ipedance fall daatically and caue a evee input iatch, which pevent ufficient powe tanfe. igue 6 how the eult fo the 897B noie figue ete and how oth noie figue and S ove a fequency pan of 98 MHz to GHz. Both the noie figue and gain i faily flat ove thi hot ange. he full eult ae hown elow. GHz (in db) e{z} I{Z} S -.95 db 3.45 Ω.3 nh S -. db 3.38 Ω.5 p S.55 db - - N.95 db - - ale 3 eult fo final tet he noie figue epoted a S gain of ~. db, which i 6.% highe than the VNA eult. We elieve thi i due to the auption that the 897B ake egading the input and output atch; it aue that the DU i atched to 5 oh. Ou LNA doe not atch to 5 oh, ut conulting with the A aued u that ou etun loe of ~ -db fo S and S put u into a egion in which the 897B till povide eliale eult. Bia Point he final V CC, I CC, V CE, and V BE wee eaued expeientally. Othe ia calculation wee then calculated a hown elow. 9

10 V.79 V VBE I 98 A I.7A BE CE I I I 6.8A.7A 5.75A C CC I 5.75A IC 5.75A I I I.6A 98 A 8 A 7 g 3S I 8 A V 5V C B B V CC.7 V V CE 9.34 V I C 5.75A β 7 I CC 6.8 A V BE.79 V I B 84 μa g 3 S he eonant Collecto Load ale 4 Suay ia point and elected all ignal paaete eult In ou actual LNA, the length of ou taniion line i ~37.5 (depending on edge o cente-point eaueent), o the inductance een y the collecto i likely uch lage than 3nH. We can calculate an appoxiate value of the inductance: Z L tan( z) 55nH. he highe inductance of the load eult in a eonant fequency that i lowe than GHz and i at aound o f LC 74MHz hi i in ageeent with ou VNA oevation, which aw a weak eonance at appoxiately 8 MHz. Note that thi i likely diffeent than the phenoenon decied aove with egad to the egion of poo pefoance. We hould e ale to ipove ou gain y educing the length of ou taniion line and oving the S eonant point cloe to GHz. We can teat thi netwok a a tapped inducto atching netwok a hown elow: A pope tapping point would tanfo the output eitance of the BJ to the ipedance of ou 5oh load. he output eitance of ou BJ i o V I A C 8.7 k. o find the coect tapping point, we need to find L and then olve fo the length of line equied to ee that inductance. o olve fo L, thee ae 6 equation we need to ue:. igue 7 - apped inducto netwok o ( L L ) Q Q Q Q t Q Q L L L L L Q Q Q ol igue

11 Afte tuning the cank though thee equation, we find L =.4nH. A efoe, we can olve fo the appopiate length of line that will give u thi inductance, z L tan o 7.5 Z. In ou actual LNA, the tapping point i actually 3 fo gound; thi eult in an inductance of 9.7 nh. We can aue then L i appoxiately.3 nh. We iply ued thi point ecaue it wa good enough in the expeient. Since ou cicuit i not a pue ideal eonant netwok, it i difficult to apply the iple eie to paallel tanfoation. We can olve fo the ipedance looking into the output of the LNA y doing all ignal analyi at the output pot. he appopiate equation ae: Z L L L j LZ c j ( L L ) Z, whee Zc c o j C. Afte plugging in nue, we get Z L = 83 5j, o o 83 oh and.7 p. he actual ipedance we ee looking into the output of ou LNA i 3.4 oh and.6 p. Depite the enoou eo, it hint that at leat that we hould expect the output to e eitive and capacitive. hee ae a nue of eaon why ou actual nue don t atch hand calculation. o one, the capacitance and output eitance of the BJ ued in the odel file, which i whee we got ou nue, could e vey diffeent fo the actual value. Anothe eaon i that it eally difficult to know exactly what inductance L and L i. In the end, we can only follow cetain tend. If we want to inceae the ipedance looking into the output node, we hould inceae L, i.e. inceae the ditance etween the tap point and gound. Optial Souce eitance Becaue ou final ia point diffe fo the initial point, we e-calculated what the pedicted optial ouce eitance fo ou cicuit would e. he calculation fo optiu ouce eitance value to achieve et noie figue have een hown elow, uing the ia point value in ale 5 aove. ( ) ( g g ( / ) ( 7 / ) 49 and ).79 with ( ) (4.45) 9.8, g g ( ) 8.5, he aove value when utituted in the equation give = 35.8 a the optiu ouce eitance. Noie igue We now copute an etiate of noie facto fo ou cicuit uing ou ia point value with a 5 eitance. ouce z z g ( ) g Uing the ae ethodology fo finding C π and π a explained ealie, fo I C = 5.75 A, C i oughly equal to 6.3 p and =β/g = 38. ogethe the two give Z =(.5-j5). Again, auing = 7 with =5, the individual te of the aove ae coputed a follow:

12 .4, z.8 z g and ( ) g.. he eulting noie facto i.53 which in te of noie figue i.85 db. Ou actual cicuit ha a noie figue of.95 db, which i. db highe. hi 5% dicepancy can e accounted fo in the appoxiation ued fo C π o f, ut alo in nd ode effect uch a noie coupling into the LNA due to extenal intefeence ouce. ADS Siulation In an effot to ette explain the eult we wee eauing, we attepted to iulate ou cicuit in the Advanced Deign Syte (ADS) tool. he figue elow how how we odeled ou cicuit. he 4 utate wa included, a well a the 5 oh taniion line path (oth length and width) fo the input pin to the ae junction and fo the tapping point to the locking capacito at the output pin. he two paallel paaitic eitte lead inductance, ae lead inductance, and collecto lead inductance wee odeled a ideal inducto with a value aed on the etiate of the etal lead having a elfinductance of.nh/. he taniion line load wa oken into thee ection the line fo the collecto to the tapping point, the line fo the tapping point to the AC gound, and the junction etween thee two line and the 5 oh tapping taniion line. igue 7 ADS Scheatic fo LNA o a DC opeating point, the ADS and ou eaued eult wee not ignificantly diffeent. ADS epoted an I CC appoxiately.6a lowe than what wa actually eaued, which i likely due to

13 S(,) S(,) db(s(,)) db(s(,)) nf() db(s(,)) deviation fo the value uch a β in the BJ odel. A uay of the vaiou ia point value ae hown elow in ale 7. Paa Meaued ADS % Eo* V CC.7 V.7 V I CC 6.8 A 6. A +.6% V CE 9.34 V 9.48 V +.5% V BE.79 V.84 V +3% I C 5.75A 5.3 A -.5% I B 84 μa 65.7 ua -.7% β 7 8* +.7% g 3 S S -.6% I.7 A.8 A +.93% I 98 A. A +3% ale 7 Copaion of ADS and Meaued Value. *elative to Meaued value. he iulation of the cheatic had the following eult een in the figue elow feq, GHz feq, GHz feq, GHz feq, GHz 3

14 S(,) S(,) db(s(, db(s(, feq, GHz feq, GHz feq (.MHz to 3.5GHz) igue 8 ADS fequency epone eult feq (.MHz to 3.5GHz) ADS iulation evealed an unuual ehavio in that iila patten could e oeved that atched what we oeved on the LNA, ut thee only occued a we inceaed the fequency ange that wa wept. A the plot how, the iulation eult ae ignificantly off the value that we eaued. A uay of the eult at GHz and the pecent eo can e found in ale 8 elow. Paa Meaued ADS % Eo* S -.95 db db +8% S -. db -4.4 db +6% S.55 db 4.3 db +6% N.95 db.67 db +37% ale 8 Copaion of paaete, eaued v ADS iulation. *elative to eaued value he go eo etween ADS and eaued value povided oe validation to ou expeientcontuction focued appoach. Concluion hi wa an unuual laoatoy invetigation due to the fankly iaculou natue of the fit LNA we contucted. We wee planning eveal iteation, paticula with egad to the output tapping point, ut ou initial contuction ought u vey cloe to achieving all pecification with only vey light adjutent. We achieved a noie figue of.95 db, while aintaining a.5 db to. db agin on the S- paaete equieent. hee wee piaily achieved y adjuting the upply voltage and tuning the ia point of the tanito. hi laoatoy alo einded u of the cae and attention-to-detail needed with egad to taking laoatoy eaueent: alway check fo good caliation, atch key paaete uch a pot output powe aco intuent, and popely account fo loe whee applicale. Ou goup poceeded with LNA contuction and iulation in paallel, ut due to the eakale ucce of ou contuction effot, uch of the iulation and hand calculation wok wa done in ode to ette undetand why ou LNA woked a it did, without thing uch a additional feite ead inducto o atching netwok needed. It i appaent that the paaitic inheent in the way we contucted the LNA helped get ou paaete cloe to acceptale value. hee ae till ipoveent left to exploe fo ou LNA piaily adjuting the output tapping point to ove it cloe to a 5 oh atch. We hope to continue efining ou LNA a we uild additional lock fo ou tanceive. 4