THE NOISE PENALTY IN APD RECEIVERS OPERATING WITH NON-OPTIMUM GAIN

LAWRENCE J MAYES,
Department of Electrical Engineering Science,
University of Essex,
Colchester,
Essex,
C04 5SQ,
England

ABSTRACT

Contours showing impairment in signal to noise ratio for avalanche optical receivers operating at non-optimum gain are presented.

The excess noise factor (F) for an avalanche photodiode (APD) is often approximated by:

F = m^x

(1)

where x » 0.3 for silicon APDs and » 1 for germanium. Using this expression the noise penalty suffered by a receiver using a diode operating at a non-optimum gain (m) rather than the optimum (m_o) can readily be found [l]:

S/N|	m		r2(1 + x/2)
		=
S/N|	mo		r2 + x + x/2

where: r = m/m_o

(2)

A closer approximation for F has been derived [2] which has been shown to be good experimentally [3]. In the model it is assumed that the ratio of ionisation coefficients of holes and electrons in the avalanche region of the diode is k (a constant, typically k = 0.02 in silicon and 0.5 in germanium). The resulting expression for F is of the form:

F  =  km + (1 - k)(2 - 1/m)

(3)

Therefore an improved indication of impairment may be obtained by repeating the procedure using equation (3). The impairment for non-optimum gain is now given by:

S/N|	m		r2[2mo(kmo + (1 - k)(2 - 1/mo)) + (k(mo2 - 1 ) + 1)]
		=
S/N|	mo		[2mor2(rkmo + (1 - k)(2 - 1/(rmo))) + (k(mo2 - 1 ) + 1)]

(4)

We note that both sensitivity expressions produce similar predictions for values of k and x close to unity; indeed, the expressions become equivalent when k = x = 1.

By way of example, contour plots showing lines of equal impairment (spaced at 1 dB intervals) are reproduced in figures 1 and 2; these apply to silicon APD receivers. The plots for germanium (for which values of k = 0.5 and x = 1 may be assumed) are almost identical (to within 0.2 dB) for moderate gain errors and consequently not reproduced here.

In summary, we can conclude that equation (2) predicts a lower sensitivity of signal to noise ratio to avalanche gain variation for practical silicon APD receivers than the more realistic prediction provided by equation (4) which is based on a more precise expression for the diode noise factor. In the case of APDs fabricated from germanium or materials with similar k values, differences between the two predictions may be small enough to be neglected and under these circumstances equation (2) is applicable.

1. M M IBRAHIM and M A ALHAIDER: 'Sensitivity of avalanche-photodiode optical receivers for avalanche gain'. AEU (Japan), February 1982, pp 153-155.
2. R J McINTYRE: 'Multiplication noise in uniform avalanche diodes'. IEEE Transactions on Electron Devices, vol ED-13 no 1, January 1966 pp 164-168.
3. J CONRADI: "The distribution of gains in uniformly multiplying avalanche photodiodes: experimental'. IEEE Transactions on Electron Devices, vol ED-19 no 6, June 1972, pp 713-718.

Acknowledgement: Financial support for the above work was provided by the SERC (UK).

This paper was published in PROCEEDINGS OF THE TWENTY-FIRST ALLERTON CONFERENCE ON COMMUNICATION, CONTROL, AND COMPUTING, UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN; OCTOBER 1983, pp 981-982

See the slide presentation given at the conference.