Noise in Transistors

Wireless World, July 1970 www.keith-snook.info 339 Noise in Transistors A short explanation of noise performance of bipolar and field effect transistors at frequencies of a few kHz to a few MHz by F. N. H. Robinson. * M.A., D.Phil. At low frequencies, below a few kHz, the The strengths of the two current genera The optimum source resistance is chief source of transistor noise is flicker, or tors are given by (2) and (3) and they are Ilf noise, and no simple, generally valid, uncorrelated. This circuit is valid up to fre (9) theory exists. Above a few hundred MHz quencies approachingfTlft!. If fT = 2 GHz the noise behaviour, like the signal be and this can be as high as p = 100 200 Since the input impedance is approximately haviour, becomes quite complicated and MHz. Ilg.. IJlb we see that our initial assumption cannot profitably be discussed in simple If the transistor is used in the common that Rs � Zi was justified. The optimum terms. In the intervening region, i.e. about emitter connection it will have a mutual noise figure is now 5 decades in frequency, noise in both bi conductance T !f:b polar and field effect transistors is remark F = 1+- - (10) ably simple. (4) 1'. le In bipolar transistors the current injected If for example T 1'. and the d.c. current into the base by the emitter consists of elec = and we can transfer the current generator gain is 100 we have F = 1·1 or about t dB. trons which had enough thermal energy to ie to the input as a voltage generator If the collector current is I mA we have surmount the potential barrier at the deple v .. = ielg . Its strength is therefore I/g.. = 250 and Rs = 2500 compared tion layer. It is therefore completely random with Zi = 2,500 n. and displays full shot noise. In a bandwidth (5) Notice first of all that a good low-noise dfthe mean square fluctuations in the emit transistor must have a high d.c. current gain ter current le are given by In Fig. 2 is shown an equivalent circuit for and secondly that Rs is quite low. Fortu d i/ = 2ele df (I) a common-emitter stage connected to a nately an error of a factor 2 in Rs only in signal source ofintemal impedance R,. The creases to H25 so that there is no point where e is the electronic charge. In the base, F in attempting to be too precise in designing some electrons recombine and constitute input stages. the base current, the remainder reach the c If Rs is fixed then le (and thus g.. ) should collector. This random division, of a ran be adjusted to satisfy (9). If Rs is high dom current, leads to two uncorrelated sets e.g. 50 kQ and the d.c. current gain is 400 it of fluctuationsin the base current Ib and the is easy to see that the optimum le is 10 f.lA. collector current le. Their magnitudes are For this reason low-noise transistors should dib 2 = 2elb df (2) also have high current gain at low currents. This is not usually compatible with good and die 2 = 2ele df (3) e Fig. 2. An equivalent circuit for a common Lf. response. Provided that the input capa and, because they are uncorrelated, d (ibie) emitter stage. citance of the transistor is tuned out, the = O. formula for the optimum value of Rs is Because any equivalent circuit for a tran circuit includes the two noise generators ib valid up to about tfT but the noise figure sistor must lead to the relation ie = ib + i" and v and the thermal noise generator VI begins to deteriorate appreciably at about we do not need to consider ie separately. associated with the source at a temperature fTIPt. At very high frequencies, the effect Thus the noise properties are completely T. of base series resistance becomes appreci specified by ib and ie• A complete noise able and, in any case, F exceeds 1 +flfT + dv/ = df (6) equivalent circuit for the transistor is shown 4k1'.Rs (flfT)2. in Fig. 1. www.keith-snook.info If we assume that the input impedance Zi In f.e.ts noise arises from thermal noise in the channel. When allowance has been • Clarendon Laboratory. University of Oxford. of the transistor is large compared with the source impedance R. the total noise input is made for the distributed nature of the noise given by source, the effect is equivalent to a current c generator whose strength is 2kTdf dV2 = 4kT.R.df + -- + 2elbR.2 df (7) g.. di/ = �. 4kTg.. df b --.......---+-L The noise figure F is the ratio of this total connected between drain and source. This is noise to the noise due to the source alone equivalent to a voltage generator of strength (the first term in (7)), so that �4kT � (_I_ elbR.) dv2 = df (11) F = I + + 3 g.. 21'. g.. R. kT in the gate lead. e We can also write this as At low frequencies there is also current noise in the gate lead due to leakage Ig Fig. 1. Noise equivalent circuit for a bipolar T Ilb ) F= 1+- --+-g.. R s (8) transistor, valid up to 200 MHz. 21'. G..Rs le d V = 2eIg df (12) 340 www.keith-snook.info Wireless World, July 1970 but at high fr equencies this is swamped by induced current noise, produced by fluc Domestic video records tuations ir, the channel under the gate. This noise is to all intents uncorrelated with the drain noise and is of magnitude W2C2 di2= ! 4kT df (13) 4 gm where C is the input capacitance. The com plete equivalent circuit is shown in Fig. 3. Drain Gate_...... __ _t- ---....-i Machines for playing recorded VISIOn version, justifying the name, will record programmes into domestic television sets as well as reproduce, and for recording Fig. 3. An equivalent circuit for afield are arriving from all directions. Some are broadcast television programmes it obtains effect transistor. players only, for reproducing programme the video signal by means of a built-in tuner materifll on records supplied by outside which receives its r.f. signal from the aerial The optimum source resistance and noise organi�ations. Others will, in addition, connection on the home television set. figure at low fr equencies are record and reproduce television program This machine will cost about £230. mes (broadcast or closed-circuit) selected Each cassette contains enough tape for d�: t 4kT t ' R= (14) by the user. The two latest are the Video an hour's running. It can be put into or s ) =( ) (dig 3el�m Cassette Recorder, from Philips (Holland), taken out of the machine very easily and at shown below, and the Cartrivision system, any required moment, regardless of the artd fr om Avco (U.S.A.). position of the tape. Programme material 8elg )t The Philips machine (called VCR, may be erased and fr esh material recorded F= I + (15) ( 3kTgm perhaps for its convenient euphonic in its place, as with a sound tape recorder. relationship with EVR) was demon No rewinding is required. If =10-9 A and =5 millimho, we la gm strated in the U.K. at a convention of The cassettes are interchangeable in have R ::::: lOO kQ and F:::::1·005. s the Film Industry Organization at the sense that, provided they are of the right At high fr equencies the optimum values Brighton. As the name indicates the type to fit the VCR, they can come are machine uses cassettes to hold the recording from any source. Also, colour and medium, which is t-inch magnetic tape. I monochrome cassettes are compatible, R=_ _ � (16) The recorded material, colour or mono in that either type can be played on • wC './3 chrome, is reproduced on a domestic monochrome machines and colour and television receiver, and connection to the machines. On the t-inch tape two sound set is made via the aerial socket. record tracks are available, and these can C f Two versions of the machine have been -W be used, say, for stereophonic sound or F=I+o -:::::1+- (17) gm A3 fT produced. The first is a player only, in for spoken commentaries in two languages. tended for reproducing programme Other domestic video reproducing where fT =gm/2nC is the gain bandwidth material supplied in cassettes by outside systems already launched or announced product. Obviously good low-noise rJ. am organizations-hence the interest of the have the trade names: EVR (Electronic plifiers require f.e.ts with a high gain band film industry. This is expected to cost about Video Recording), Vidicord, Selectavision width product. £ 120 for a monochrome machine and about and Sony. Domestic v.t.r. machines are Insulated gate fe.ts tend to have high £140 for a colour machine. The second already on the market. flicker noise and these results are only valid above about I MHz., but, for junction fe. ts, they are often valid down to low audio fr equencies. Perhaps the most important part to bear in mind is that there is an optimum source impedance, and that for bipolar transistors this is much less than the input impedance. If the source impedance is high, an fe.t. will usually be the most suitable input stage. Conversely for low source impedances it will be a bipolar transistor. Finally it should be noted that the use of negative feedback, or other connections (e.g.

Load more