Pergamon Compufers Herr. Engng Vol. 21, No. 2, pp. 143-146. 1995

Copyright 0 1995 Elsevier Science Ltd

00417!906(!34)OllO1~2 Printed in Great Britain. All rights reserved 00457906/95 $9.50 + 0.00

ANALYSIS OF DIGITAL RECEIVER BIPOLAR PREAMPLIFIER USING THE HAUS-ADLER

NOISE MEASURE

MAGDY M. IBRAHIM’ and A. M. IBRAHIM* ‘Department of Electronic Engineering, Ain-Shams University, Cairo I 1517, Egypt and *Department of

Electronics, DeVry Institute of Technology, Toronto, Ontario, Canada M9M 224

(Received for publication 6 October 1994)

Abstract-The noise performance of a bipolar preamplifier for digital optical receivers is expressed in terms of the Haus-Adler noise measure. A better estimation of the optimum collector current is thus obtained as compared to estimations reported using the common analysis technique.

Key words: Optical receiver, preamplifier noise, noise measure.

1. INTRODUCTION

Low noise preamplifiers for the front end of optical receivers have received considerable attention [l-12]. The typical performance optimization is based on minimizing the required input optical power for a given bit-error rate.

Bipolar transistors are used at high bit rates (exceeding 100 Mb/s) to provide better noise performance than FETS. An optimum value of the collector current is then required to provide the lowest input-noise current for the preamplifier, and hence the minimum circuit noise for the optical receiver. However, in many experimental designs the values used for the collector current are larger than the estimated optimum values to avoid any possible decrease in the current gain j? and the cut-off frequencyf, at low collector currents [7,8] the noise penalty due to operation at twice the optimum current is only 1 dB.

The noise figure F is a commonly used method to specify the noise performance of analog receivers [9]. It is limited to situations where the source impedance is resistive. For broad band amplifiers, an average noise figure is specified [13]. It seems advantageous to use the Haus-Adler noise measure M which takes into account both the noise figure and the gain of the amplifier. A cascade of two amplifiers has the lower overall noise figure if the first amplifier has the lower value of M [14]. The following analysis is based on minimizing M, rather than the usual approach.

2. ANALYSIS

Figure 1 shows a bipolar transistor preamplifier and its hybrid-pi model with the equivalent input voltage and current noise generators. The effective input noise current of the amplifier can then be written as [15]:

Z,B + ~KZ&,,(~~CC~~)~Z$~ + 2qZ,Z, B + 1 (1) where:

B = the operating bit rate Zb and Z, = base and collector bias currents

rbb’ = base spreading resistance of the transistor g, = I,/ VT = transistor transconductance VT = KTIq K = Boltzmann constant T = absolute temperature

143

144 Magdy M. Ibrahim and A. M. Ibrahim

R = source resistance C-r = total input capacitance C,, = photodetector and stray capacitance at the input

ZZ, ZJ = weighting functions which are dependent only on the input optical pulse shape and the equalized output pulse shape.

The noise figure F of the preamplifier is the ratio of the total output noise to the part of the output noise due to the source resistance, hence

F = (&)f(i;) (2)

where (it ) is the noise due to the source resistance

(if) = F12B. From equations (l))(3), the noise figure F can be written as:

(3)

where

and

u = 4KTr,, (2nC,,)‘I, B”

h = 2qI2 B!/&,,

(5)

(6)

c = 2qV+[BZz/R” + (27rC;)2B’1,]

& being the small-signal, low-frequency current gain of the transistor. The Haus-Adler noise measure M is given by [ 141

A4 = (F - I)/(1 - l/g,)

g, is the available gain of the amplifier and is given by

(7)

(8)

f, being the cut-off frequency of the transistor and is given by [13]

(10)

where rr is the forward transit time of the transistor, C,, is the emitter-junction space-charge

(a)

(b)

n 'hh H’ C’

1 c

i-

- A

i -’ .~

R 1: ’ h’c __ (‘h c R,,, l’h c RC

Fig. I. (a) Bipolar-transistor front-end receiver amplifier. (b) The hybrid-pi model with equivalent Input noise generators.

Analysis of digital receiver bipolar preamplifier 145

Table I. Typical characteristics of low-noise Si bipolar transistors

BFQ22 BFR90 BFY90

f,[GW 5 5 I .4 UmAl 30 14 25 CJPFI 2.5 I.2 -

C,, [PFI I.1 0.5 1.5 8, 50 90 5&100

rr[G%/mA] 0.6 0.9 0.6

0’ I I I I

250 500 750 IO00

B (Mb/s)

Fig. 2. Optimum collector current of bipolar transistor front-end amplifier. Solid line for minimum M, dotted line

for minimum (ii).

capacitance, and C, is the base-collector capacitance. At low values of Z, the terms involving C, and C, dominate and cause fT to fall as Z, as decreased leading to a dependence of the form:

fT=QZc. (11)

From equations (10) and (11) we get (for very small values of I,):

a = I/27rV,(Cj, + C,). (12)

When we apply equation (1 l), we take the average value of a for the possible current range as obtained from the data-sheets of the used transistors. Table 1 gives typical parameter values of various low-noise Si bipolar transistors that may be used in the preamplifier of a digital optical receiver.

From equations (9) and (11) and taking the bit rate B to be half the amplifier bandwidth, the gain g, can be written as

a2Z2 ga=$.

Substituting equations (4) and (13) into equation (8), we get

M=(a +bl,+$/(l -$)<i:>

(13)

(14)

where

d = 4B2/a2. (15)

The optimum collector current which minimizes the Haus-Adler measure A4 is obtained by equating the derivative of equation (14) with respect to Z, to zero. The optimum collector current satisfies the fourth-order equation:

61: - (c + 3bd)Zz - 2adZC - cd = 0 (16)

where coefficients a, 6, c and d are given by equations (5)-(7) and (15) respectively. For simplicity, we assume that g, is independent of Z, and hence the dependence of g, on Z, is not considered, d = 0, then, we get from equation (16):

co,, = Jclb or

‘f,,, = VT&

J

+2 + B2(27G)2~31~2

(17)

(18)

which is the optimum value obtained in previous studies that minimizes the effective input noise current (ii) [15].

146 Magdy M. Ibrahim and A. M. Ibrahim

In most practical cases, the effect of the base-spread resistance rbb. can be neglected, then a = o and the solution of equation (16) becomes:

Zf”,, = [c + 36d + J(c + 36d)’ + 4bcd]/26 (19)

or approximately

2. S. D. Personick, Receiver design for optical fiber systems, Proc. IEEE 65, 1670-1678 (1978). 3. S. D. Personick, P. B. Balaban, J. H. Bobsin and P. R. Kumar, A detailed comparison of four approaches to the

calculation of the sensitivity of optical fiber system receivers. IEEE Trans. Comm. COM-25, 541-548 (1977). S. D. Personick. Receiver Des&w in Ootical Fiber Telecommunications (Edited by S. E. Miller and A. G. Chynoweth). 4.

5.

6.

I. 8. 9.

10.

II.

12. 13. 14.

IS.

Academic Press; New York (1979). ’ I. Garrett and J. E. Midwinter, Optical Communication Systems in Oprical Fiber Communications (Edited by M. I. Howes and D. V. Morgan). Wiley, New York (1980). D. R. Smith and I. Garrett. A simplified approach to digital optical receiver design. Opt. Quanfum Electron. lo,21 l--221 (1978). T. V. Moui, Receiver design for high speed optical fiber systems. /. Light Wave Tech. LT-2, 243-267 (1984). R. T. Unwin, A high-speed optical receiver. Optical Quantum Electron 14, 61-66 (1982). Y. Takahashi, I. Nagano and Y. Takasaki. Optical receiver for VHF multichannnel video transmission. J. Select. Areas Comm. 8, 138221386 (1990). S. D. Walker, L. C. Blank, R. A. Garnham and J. M. Boggis, High electron mobility transistor lightwave receiver for broadband optical transmission system applications. J. Lightwave Tech. 7,454 (1989). Y. Archambault, D. Pavlidis and J. P. Guet, GaAs monolithic integrated optical preamplifier. J. Lightwave Tech. LT-5, 3555366 (1987). M. J. N. Sibey, Opfical Communications. McGraw-Hill, New York (1990). P. Gray and R. Meyer, Analysis and Design of Analog Integrated Circuit. Wiley, New York (1984). A. Carlson, Communications Sy.stems: An Inrroducrion to Signals and Noise in Electrical Communication. McGraw-Hill, New York (1975). H. Kressel. Semiconductor Devices,/& Optical Communications. Springer, New York (1982).

Ic”pi = J ; + 3d.

Comparing equations (17) and (20) leads to the finding that in order to minimize M, a value of & larger than that required to minimize (ii) is needed.

3. RESULTS

Consider a low-noise bipolar transistor preamplifier of a large source resistance R with the following parameters [7,8]

C., = 6pf, C,, = 4pj;

p” = 100, c1 = 1 GHZ/mA,

I2 = 0.5, and Z, = 0.03.

Then, from equation (I 9) we get

I+ = 4.3B PA

where B is expressed in Mb/s [lo]. Whereas:

I;,,, = 2.4B /LA.

These results are plotted in Fig. 2 together with some previously reported experimental values.

4. CONCLUSIONS

The most common method of specifying the noise and performance of the front-end of digital optical receivers is by specifying the equivalent input noise generators. However, when a bipolar preamplifier is used, minimizing the effective input noise current may require an unsuitable low value of the d.c. collector current I,. A better estimation for the optimum collector current may be obtained by minimizing the Haus-Adler noise measure. In the limit of a large source resistance, the optimum value is directly proportional to the operating bit rate.

REFERENCES

I. S. D. Personick, Receiver design for digital fiber optic communication systems, Part I and II. Bell Sysr. Tech. J. 52,843 (1973).