Handbook for Sound Engineers

468 Chapter 15

The characteristics of typical detectors are shown in
Table 15-4.

15.6.1 Quantum Efficiency (K)

Quantum efficiency, another way of expressing a photo-
diode’s sensitivity, is the ratio of photons to the number
of electrons set flowing in the external circuit and is
expressed either as a dimensionless number or as a per-
centage. The responsivity can be calculated from the
quantum efficiency as follows:

(15-19)

where,
q is the charge of an electron,
h is Planck’s constant,
c is the velocity of light.

Since q, c, and h are constants, responsivity is simply a
function of quantum efficiency and wavelength.

15.6.2 Noise

Several types of noise are associated with the photode-
tector and with the receiver. Shot noise and thermal
noise are particularly important to our understanding of
photodiodes in fiber optics.
The noise current produced by a photodiode is called
shot noise. Shot noise arises from the discrete nature of
electrons flowing across the p-n junction of the photo-
diode. The shot noise can be calculated by using the
following equation

(15-20)

where,
q is the charge of an electron (1.6 × 10–19 coulomb),
Ia is the average current (including dark current and
signal current),

BW is the receiver bandwidth.

Dark current in a photodiode is the thermally gener-

ated current. The term dark relates to the absence of

light when in an operational circuit.

Thermal noise (itn), sometimes called Johnson or

Nyquist noise, is generated from fluctuations in the load

resistance of the photodiode. The following equation

can be used to calculate the thermal noise

(15-21)

where,

K is Boltzmann’s constant (1.38 × 10–23joules/K),

T is the absolute temperature in Kelvins,

BW is the receiver’s bandwidth,

Req is equivalent resistance, which can be approximated

by a load resistor.

Noise in a PIN photodiode is

(15-22)

where,

iTN is the thermal noise.

For an APD, the noise associated with multiplication

must also be added.

As a general rule, the optical signal should be twice

the noise current to be adequately detected. More

optical power may be necessary, however, to obtain the

desired SNR.

15.6.3 Bandwidth

The bandwidth, or operating range, of a photodiode can

be limited by either its rise time or its RC time constant,

whichever results in the slower speed or bandwidth. The

bandwidth of a circuit limited by the RC time constant is

(15-23)

where,

Req is the equivalent resistance offered by the sum of the

load resistance and diode series resistance,

Cd is the diode capacitance including any contribution

from the mounting.

A photodiode’s response does not completely follow

the exponential response of an RC circuit because

changes of light frequency or intensity change the

parameters. Nevertheless, considering the device

Table 15-4. Characteristics of Typical Detectors

Type Responsivity Response Time (ns)

PIN Photodiode 0.5 μA/μW5

0.6 μA/μW1

0.4 μA/μW1

APD 75.0 μA/μW 2

65.0 μA/μW0.5

IDP 4.5 mV/μW10

35.0 mV/μW35

Courtesy AMP Incorporated.

R KqO

hc

=----------

isn= 2 qIA BW

itn^4 KT BW^

Req

= -------------------------

in isn

2

iTN

2

+=

BW^1

2 SReqCd

----------------------=