Electromag Compatibility ECE 4391
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Date Created: 11/02/15
Comparison of the JFET and the BJT An exact comparison of the BJT and the FET is impossible in general because the noise perfore mance of each is so dependent on device parameters and bias currents The JFET exhibits only Un noise whereas the BJT exhibits both Un and in noise For a low source resistance the BJT Un noise is its dominant noise In this case the BJT usually has a lower noise than the JFET For a high source resistance the BJT in noise can cause it to exhibit more noise than the FET This assumes that the BJT bias current remains xed as the source resistance is increased 1f the BJT is biased for minimum noise the collector bias current must be decreased as the source resistance is increased In this case the FET may not be the better choice device for the lowest noise To make an example comparison of the noise performance of the BJT and the JFET typical numerical values for device parameters must be assumed Although the conclusions may not be applicable to speci c devices such an example serves to illustrate the differences between the devices Because icker noise is so device dependent it will be neglected For the BJT we will assume that M 40 9 VA 00 and 5 500 For the JFET we will assume the parameters 5 5 X 10 4 AVg A 0 and VTO 72 V For these values the drainetoesource saturation current is IDSS ngo 2 mA Let the BJT be connected as a commoneemitter ampli er with its emitter connected to ac ground We calculate the noise both for a constant collector bias current and for the optimum collector bias current Copt Let the JFET be connected as a commonesource ampli er with its source connected to ac ground We calculate the noise for a constant drain bias current For the constant current cases we will assume that both the BJT and the JFET are biased at 1 mA so that the devices are compared at the same power dissipation This assumes the same bias voltage across each device Let R5 be the source resistance For C 1 mA the BJT spot noise voltage in VxE is 2 Uni 135 V 2 12 Af 4kTRsTm2qIBR5Tm22q10lt r 1 C 12 353 X 1044130 X 107 R5 40 500 R5 402 R5 130002 1 For C Copt it is U ygu 7 r 1 12 A f 7 4kTR1TmR2AfXW 132 X 1040413 40 2 For ID 1 mA the JFET spot noise voltage is U72 7 4kTR HM 12 7 1 29 X 1040413 471 3 A f 5 3m 39 5 Figure 1 shows the plots of HugiAf versus R5 for the three cases Curve a is a plot of Curve b is a plot of Curve c is a plot of For R5 small the two BJT cases give the lowest noise Although the curves almost coincide the noise is slightly lower for the BJT biased at Copt For R5 large the JFET and the BJT biased at Copt give the lowest noise Although the curves almost coincide the JFET noise is slightly lower than the BJT noise For R5 in the 3 to 4 k9 range the JFET and the BJT biased at C 1 mA give approximately the same noise while the BJT biased at Copt gives slightly lower noise 1 T iwiuu H STP Zonmh WonAhu 4r L Zenmn J YNE 5on2 w wPSburPu U YP ltOVSWDS Kayla 0 Nghpklxacrv S rmavoltr 41v Pv ox Syllor am D9cMFV u Y ltltrnri PSPltWU 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model with a Th venin input source where V5 is the source voltage Z5 R5 sz is the source impedance Vts is the thermal noise voltage generated by the source and Vn and In are the noise sources representing the noise generated by the ampli er The output voltage is given by Z L AZi ZL V0 AV V V V Z 1 ZoZL Z5ZiZoZL ST T 7LT n 5 where A is the voltage gain and Z5 is the input impedance The equivalent noise input voltage Vm is de ned as the voltage in series with V that generates the same noise voltage at the output as all noise sources in the circuit It consists of the terms in parenthesis in Eq 1 and is given by Note that this is independent of both A and Z5 It is simply the noise voltage across Z5 considering Z to be an open circuit ZL V0 Z8 Vs Vn Amplifier 20 was Figure 1 Dy 7 in ampli er model with Thev nin source The meanesquare value of Vm is solved for as follows VnV 2Re MM 2 125 szg 4mm 25 Ar M Re W 3 where 39y 7 j39yi is the correlation coe icient between Vn and In and it is assumed that V25 is independent of both Vn and In The correlation coef cient is given by V 1 7 4 072 2 Effect of a Series Impedance at the Input Figure 2 shows the input circuit of an ampli er with an impedance Z1 added in series with a Th venin source The noise source th models the thermal noise generated by Z1 As is shown above the equivalent noise voltage in series with the source can be solved for by rst solving for the openecircuit input voltage ie the input voltage considering Z to be an open circuit It is given by v10 V5V25V21Vn1nzszl V5Vm 5 where Vni is the equivalent noise voltage in series with the source It is given by Vni VtsVt1 Vn1nZsZ1 W V Luz 6 where VnS and InS are the new values of Vn and In on the source side of Z1 It follows from this equation that Vns ltl Vn Inzl InS In 8 Note that VnS consists of all terms which are not multiplied by Z and InS consists of the coefficient of Z in the term that is multiplied by Z5 Figure 2 Ampli er input circuit with Thevenin source and series impedance added at input It follows that the addition of a series impedance at the input of an ampli er increases the Vn noise but does not change the In noise If Z1 is not to increase the noise7 lle should be as small as possible If Z1 is lossless7 it generates no noise itself so that V 0 The meanisquare values and the correlation coefficient for VnS and InS are given by 4M Re 21 Ar a Rewz W 9 27m E 10 1 E 2 2 7221 1ng ZELS The meanisquare equivalent noise input voltage is given by 73 4kTReZ5 Z1Af E 2xT xEReMZ ZI Elzszmg 12 Effect of a Shunt Impedance at the Input Figure 3 shows the input circuit of an ampli er with an impedance Z2 added in parallel with the source The noise source Itg models the thermal noise generated by Z2 The openicircuit input voltage is given by V2100 Vs W5 Vn B2 In ZsllZ2 A Z5Z2 i V V39 Z2 13 5 mZZg where Vni is the equivalent noise voltage in series with the source It is given by Vni z Vt Vn 1 12 17 Z 2 Vt Vm IMZS 14 where VnS and InS are the new values of Vn and In on the source side of Z2 It follows from this equation that Vns Vn V Ins It2 l 7 l In 2 Note that VnS consists of the term which is not multiplied by Z and InS consists of the sum of the coef cients of Z in the terms that are multiplied by Z5 Z8 Vts V11 I e Zi Figure 3 Ampli er input circuit with Thevenin source and shunt impedance added at input s It follows that the addition of a parallel impedance at the input of an ampli er increases the In noise but does not change the Vn noise If Z2 is not to increase the noise7 lZQl should be as large as possible If Z2 is lossless7 it generates no noise itself so that Im 0 The meanisquare values and the correlation coef cient for VnS and InS are given by I n 17 T 1 0 5 2 7 Y 7 2m4kTRe 72 AfW2 Un ane 72 2 18 2 2 vxvU Z Z2 75 r 1ng ZELS The meanisquare equivalent noise input voltage is given by 19 lZsl2 A 2 Z 6 2 vgRe 7 1 ZS 2 lZSlg 20 Dc bias networks and rf matching networks usually consist of series and parallel elements at the input to an ampli er One method of analyzing the effect of these elements on the ampli er noise is by transforming the Vn and In sources from the ampli er input back to the source by use of the above relations This is illustrated in the following example 4kTRe 25 Z52 1 Z2 Example 1 Figure 4shows the input circuit of an ampli er It is given that R 75 9 R1 1 k9 C 10 nF R2 100 Q a 2 nV HE 15 12A 7 02j01 The noise speci cations are for a frequency f 100th and a bandwidth Af 1 Hz Calculate 11 in series with the source by transforming Vn and In back to the source with Eqs 9 through 11 and 1 7 through 19 Vts C V71 AAA ll 39quot l l lt 1 Vs R1I1t1 R2It2ll lln Vi Zi Figure 4 Ampli er input circuit xEav n nv 4kTAf 472 v T2Eg2xugReltfg 23 2 vxUg R2 7aT xviaxiia The capacitor impedance is Z0 1j27TfC 7j159 9 To the left of C 12 quib via 24ng igm Re yazg 2 ZCF 43 nV ME 4 24pA 02 iTZC 7b l mem 0394 710335 V ibv ii iu Ew 1U ib 43 nV 12 4 112 4kTA f V 2 Rig R1 if 263 pA 2 2 U g 4 n In Unb an E Yc 2 2 V Unc V ch Solution To the left of R2 12 24 pA 47 lmi 0347 1626 X 103 To the left of R1 0523 710807 The equivalent noise voltage in series with the source is 12 569 nV The following example illustrates the calculation of HI 2 for the circuit of Fig 4 by rst calcui lating the openicircuit input voltage due to all sources in the circuit factoring out the coe icient of V and assigning all remaining noise terms to Vm Example 2 For the circuit of Erample I calculate Hui by calculating the openicircuit input voltage factoring out the coe icient of V5 and assigning all remaining noise terms to Vm Solution The equivalent source impedance seen by the ampli er is given by 1 Z R R 6867 294 sq R2HltWC 1H J The thermal noise voltage generated by R5 R1 and R2 has a meanisquare value of 4hT Re Zeq Denote the phasor value of this voltage by Vteq The openicircuit input voltage is given by V V 1 L we SR1 3 R2R1lle11WC 0292 10273 V mm Vn 12eel we Vi 172 0292 10273 Weq Vn InZeq 0292j0273 V5 It follows that the equivalent noise input voltage is given by 12 U2 7 4kT Ream 03 21uRe39yzeq 22 zeql m 292 10273 2 569 nV This is the same as that found in Example 1 Note that the method used in this example is more straightforward because it is necessary to transform only one source through the network That source is the signal source V5 Noise Factor and Noise Figure The noise factor F of an ampli er is de ned as the ratio of its actual SNR and the SNR if the ampli er is noiseless where the temperature is taken to be the standard temperature To When it is expressed in dB it is called noise gure and is given by NF 1010g Consider the ampli er model in Fig 1 If the ampli er is noiseless the signalitonoise ratio given by SNR U gUtgs where 11 is the meanisquare source voltage and 11 55 is the meanisquare thermal noise voltage generated by the source i aedance When the ampli er noise is included the signalitoinoise ratio is given by SNR Thus the noise factor is given by viv5 r2 712 2 U1Re v22 st 7 21 1 21 U 4kT0R5Af It follows from this expression that a noiseless ampli er has the noise factor F 1 A useful relation which follows from the de nition of F is EFXEFx4kTOReZs 22 This relation is used below in the method for measuring F Example 3 Calculate F and NF for the ampli er in Eacample 1 for which R5 75 Q and 569 nV Assume Af 1 Hz and T To 290 K Solution The meanisquare thermal noise voltage of the source is 11725 AUCTRS 120 X 10 18 V2 Thus the noise factor and noise gure are 569 X 1092 F 12 X 10 18 270 NF 10log 270 143 dB When Af 1 Hz7 as in this example7 F is called the spotinoise factor and NF is called the spotinoise gure Measuring the Noise Factor This method is the most general one because it does not require knowledge of either the ampli er gain or its noise bandwidth Consider the noise model of an ampli er given in Fig 5 Consider the source to be a white noise source having the spectral density 5v VSV Af The total noise voltage at the output can be written V0 A 9 tsvn InZsllZi AZr ZS V Vt V7 InZ 23 Z2 Z5 Z5 The meanisquare value is given by Z Z5 HMVEM v29 1242 i AZi 2 57 f Bn 4hT0 Re Z5Bn 11 2 2 Z5Zi ls fBquot ml Z5 Z5 2 lSv f B F X 4kT0 Re Z5 Bu where Bn is the ampli er noise bandwidth and Eq 22 has been used to relate to the thermal noise vo ge of the source Let 1131 be the value of U with the noise source at the input set to zero7 ie 5v 0 Now7 let S7 be increased until the rms output voltage increases by a factor 7 ie 11 3 THU 21 It follows by taking the ratio of the two meanisquare voltages that r2 1 F X 4kT Re Z5Bn F X 4kT0 Re Z5
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