PSD6407 datasheet(12/16 Pages) ETC

12 / 16 page

Noise currents are calculated below, assuming that the

feedback resistance Rf of the current-to-voltage conversion

circuit is sufficiently greater than the PSD interelectrode

resistance Rie. In this case, 1/Rf can be ignored since it is

sufficiently small compared to 1/Rie. Position resolution as

listed in our PSD data sheets is calculated by this method.

1) Shot noise current Is originating from photocurrent and

dark current

2) Thermal noise current (Johnson noise current) Ij generated

from interelectrode resistance (This can be ignored as Rsh

>> Rie.)

3) Noise current Ien by equivalent noise input voltage of

operational amplifier

By taking the sum of equations (5-4), (5-5) and (5-6), the

PSD noise current can be expressed as an RMS value

as follows:

If Rf cannot be ignored versus Rie (as a guide, Rie/Rf >

0.1), then the equivalent noise output voltage must be

taken into account. In this case, equations (5-4), (5-5)

and (5-6) are converted into output voltages as follows:

The thermal noise from the feedback resistance and the

equivalent noise input current of the operational amplifier

are also added as follows:

The equivalent noise input voltage of the operational am-

plifier is then expressed as an RMS value by the following

equation.

Figure 5-3 shows the shot noise current plotted along the

signal photocurrent value when Rf >>Rie. Figure 5-4

shows the thermal noise current and the noise current by

the equivalent noise input voltage of the operational

amplifier, plotted along the interelectrode resistance value.

When using a PSD with an interelectrode resistance of

about 10 k

W, the operational amplifier becomes a crucial

factor in determining the noise current, so a low-noise-

current operational amplifier must be used. When using a

PSD with an interelectrode resistance exceeding 100 k

the thermal noise generated from the interelectrode

resistance of the PSD itself will be predominant.

As explained above, PSD position resolution is determined

by interelectrode resistance and light intensity. This is the

point in which the PSD greatly differs from discrete type

position detectors.

The following methods are effective for increasing the PSD

position resolution.

· Increase the signal photocurrent Io.

· Increase the interelectrode resistance Rie.

· Shorten the resistance length L.

· Use a low noise operational amplifier.

The position resolution listed in our PSD data sheets is

measured under the following conditions.

· Photocurrent: 1 µA

· Circuit input noise: 1 µV (31.6 nV/Hz1/2)

· Frequency bandwidth: 1 kHz

Is =

2q . (Io + ID) . B [A] ............ (5-4)

q : Electron charge (1.60 × 10-19 C)

Io: Signal photocurrent (A)

ID: Dark current (A)

B : Bandwidth (Hz)

k : Boltzmann constant (1.38 × 10-23 J/K)

T : Absolute temperature (K)

Rie: Interelectrode resistance (

en: Equivalent noise input voltage of operational amplifier

(V/Hz1/2)

Ij =

[A] ............ (5-5)

4 kTB

Rie

Ien =

B [A] ............ (5-6)

Rie

In =

Is2 + Ij2 + Ien2 [A] ............ (5-7)

Vs = Rf .

2q . (Io + ID) . B [V] ............ (5-8)

Vj = Rf .

[V] .............................. (5-9)

4 kTB

Rie

Ven = 1 +

. en .

[V] .............. (5-10)

Rie

VRf = Rf .

[V] ............................ (5-11)

4 kTB

Vin = Rf . in .

[V] ............................ (5-12)

Vn =

Vs2 + Vj2 + Ven2 + VRf2 + Vin2 [V] ............ (5-13)

Characteristic and use

Figure 5-3 Shot noise vs. signal photocurrent

Figure 5-4 Noise current vs. interelectrode resistance

KPSDB0083EA

KPSDB0084EA

SIGNAL PHOTOCURRENT (µA)

(Typ. Ta=25 ˚C)

0.1

0.01

0.1

110

INTERELECTRODE RESISTANCE (k

Ω)

(Typ. Ta=25 ˚C)

100

0.01

0.1

1000

Thermal noise current Ij generated from

interelectrode resistance

Noise current (en=10 nV) by equivalent

noise input voltage of operational amplifier

Noise current (en=30 nV) by equivalent

noise input voltage of operational amplifier

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