ADA4351-2ACPZ-R7 datasheet(30/36 Pages) AD

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Data Sheet

ADA4351-2

APPLICATIONS INFORMATION

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Rev. 0 | 30 of 36

Sticking with the Butterworth solution, a simple expression for the

maximum achievable gain given a target f−3 dB bandwidth and a CS

can be derived as follows:

RF,MAX= GBPf‐3 dB22πCS

(4)

Conversely, Equation 3 can be solved for the maximum f−3 dB for a

target RF to achieve a Butterworth response. Or, Equation 3 can be

used to solve for the minimum required GBP for the desired RF and

f−3 dB.

In general, to place P1 (the feedback pole) to get any Q for the

second-order closed-loop response, simply set P1 = Q × f0, which

is more applicable in designs where CS > 5 × CF. With a f0 largely

determined by CS and the GBP of the amplifier, the resulting f−3

dB for any Q is given by the following equation. Evaluating the

following equation at Q = 0.707 gives a ratio of 1. Evaluating the

following equation at Q = 0.62 and RF = 15 kΩ, CD = 100 pF, and

CF = 16 pF for the first example design gives 0.85, where then f−3 dB

= 0.85 × 926 kHz = 782 kHz ≈ 745 kHz (actual, see Figure 88).

f‐3 dBf0

= 1− 12Q2 + 1− 12Q2 2+1 (5)

These are approximate guidelines and making slight adjustments in

the CF value can tune a design into the desired frequency response

shape and/or pulse response.

NOISE CONTRIBUTIONS FOR

TRANSIMPEDANCE AMPLIFIERS

There are three main sources of noise in photodiode TIA applica-

tions that set the current noise floor (referred to the output). The

three noise sources include the following:

1. The Johnson noise of the feedback resistor

2. The current noise due to the input bias or leakage currents of

the amplifier

3. The effect of the input voltage noise on the output of the op amp

Figure 92. Noise Sources in the ADA4351-2

Each of these noise sources is referred to the output at the SW0

or SW1 pins. The spectral densities of these noise sources are

integrated over their respective noise bandwidths and then root

mean squared to provide the total output integrated noise.

►

The feedback resistor produces a temperature dependent John-

son noise given by

4kTRF,whichresultsinagaintothe

output of 1 V/V and is band limited by the feedback pole, P1.

Estimating a single-pole roll-off for this noise source gives a

noise power bandwidth (NPBW) of 1.57 × P1. A good starting

point for 4kT = 1.65 × 10−20 at 25°C.

►

The input current noise for the op amp itself has a shot noise

current term set by the DC input bias or leakage current, which

can be low. The current noise of the CMOS input devices rises

over frequency, and an estimate for the maximum current noise

over frequency is a flat 110 fA/√Hz density in the 10 kHz to 100

kHz region. This estimate for the input bias current noise term is

referred to the output by a factor of RF and has the same 1.57 ×

P1 noise power bandwidth as the resistor noise.

►

The noise gain of the input voltage noise of 7.3 nV/√Hz is the

same as the noise gain in the TIA loop gain plot (see Figure 87).

Hence, this noise starts out at a gain of 1 until Z1 (see Figure

87) and then rises with a one-zero response to the feedback

P1 pole. The noise gain then flattens out at 1 + CS/CF until the

roll-off of the GBP, which is normally the dominant integrated

noise term, and adding a post-output filter (REXT and CEXT) can

band-limit its contribution to the total output integrated noise.

Continuing with the overcompensated design example shown in

Figure 86, each output noise term can be estimated as follows.

Here, the feedback pole frequency, P1, is 1/(2π × 15 kΩ × 19 pF)

= 558 kHz, where its noise power bandwidth to use for some of the

terms is (π/2) × 558 kHz = 1.57 × 558 kHz = 877 kHz.

1. The 15 kΩ resistor noise has a gain of 1 to the SW0 or SW1

pins. Its 15.7 nV/√Hz term adds a 15.7 nV/√Hz × √877 kHz =

14.7 μV RMS output noise term.

2. An approximate 110 fA/√Hz input current noise is gained up by

15 kΩ RF and then has the same noise power bandwidth as the

resistor noise, which is a 15 kΩ × 110 fA/√Hz × √877 kHz = 1.5

μV RMS.

3. The input voltage noise adds three terms to the output RMS

noise total. The noise has a gain of 1 through the Z1 frequency

(= 1/(2π × 15 kΩ × 105.5 pF) = 101 kHz), then a rising region

following the noise gain peaking region (see Figure 87), then

a flat higher gain region from P1 to whatever higher frequency

pole is in the system. Here, a self-limited intersection with the

GBP is used.

a. The gain of 1 region adds a 7.3 nV/√Hz × √Z1 = 7.3 nV/√Hz

× √(101 kHz) = 2.3 μV RMS.

b. The rising region can be approximated by running an inte-

gral from Z1 to P1 and extracting a single-output voltage

noise value that integrates to the same power as the actual

response shape. This solution is given by en (2πRFCSP1)/

(√3) = en(P1/(Z1 × √3)), where P1 and Z1 are in Hz.

Evaluating this equation for the circuit shown in Figure 86

and the overcompensated response of Figure 96 gives an

equivalent flat spot noise voltage at the output of 23.5

nV/√Hz. Integrating that from Z1 to P1 gives an approxi-

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