where I _PHOTO is the photodiode output current, and the parallel combination of _RF and CF _sets the signal bandwidth. Ideally, all of the photodiode's output current passes through R _F , but all op amps have input bias currents that cause errors in their outputs. It is best to limit the input bias current of the op amp to a few pA and keep the input offset voltage low to minimize errors. The AD8065 has an input bias current of only 2 pA and an input offset voltage of only 400 μV.

This circuit is designed to provide a 5 V full-scale output with a maximum photodiode current of 200 μA. Determine the feedback resistor value from this:

The stable bandwidth achievable with this preamplifier is a function of: R _F , the gain-bandwidth product of the amplifier (65 MHz), and the total capacitance C _IN of the summing point of the amplifier . For this circuit, the diode SFH 2701 (OSRAM Opto Semiconductors GmbH) maximum capacitance value C _D = 5 pF. The AD8065 common-mode input capacitance is C _M = 2.1 pF and the differential-mode input capacitance is C _D = 4.5 pF. Therefore, the total input capacitance is C _IN = 11.6 pF.

The resulting signal bandwidth at a 45° phase margin f _{(45) can be expressed as:}

Since the maximum achievable bandwidth is greater than the required bandwidth, the AD8065 is well suited for this application, mostly due to its large f _CR to C _IN ratio.

R _F and C _IN create a pole in the amplifier's loop transfer function, which can cause peaking and circuit instability (see Figure 3)). Increasing C _F can create a zero in the loop's transfer function, which It can compensate for the effects of the above poles and reduce the signal bandwidth.

Selecting R _{F , the C F} value that produces a 2 MHz bandwidth can be expressed as:

By calculating the capacitance value required to obtain 45° phase margin, you can determine whether a 3.3 pF capacitor is sufficient to stabilize the system. The value of C _F that yields f ₍₄₅₎ can be expressed as:

Since the required 3.3 pF is higher than the minimum of 1.1 pF, increasing the capacitor value increases the phase margin, so the system is stable.

Noise analysis

After selecting a device, you must determine the resolution required to complete the signal conversion. As with most noise analyses, there are only a few key parameters to consider. Noise sources add up in RSS fashion; therefore, only consider any single noise source that is at least three to four times higher than other noise sources.

For photodiode preamplifiers, the main sources of output noise are the op amp's input voltage noise and feedback resistor noise. The input current noise of the FET input op amp is negligible. Due to the filtering effect of parasitic capacitance, the photodiode shot noise caused by reverse bias is negligible.

Resistor noise can be calculated according to the Johnson noise formula:

Among them:
k represents Boltzmann’s constant (1.38 × 10-23J/K).
T represents absolute temperature (unit K).
The factor 1.57 converts the approximate single-pole bandwidth to the equivalent noise bandwidth.

Note that the 0.1 μF capacitor at the positive input of the preamplifier cancels the high-frequency noise produced by the second _{RF resistor, which is used to offset the effects of the bias current.}

The output noise mainly originates from the input voltage noise and high-frequency noise gain peaking. The peaking phenomenon occurs between f ₁ and f _CR . If the output noise is assumed to be constant over the entire frequency range and the maximum value of the AC noise gain is used, then:

where V _N represents the input voltage noise of the amplifier (7 nV/√Hz).

The total rms noise referred to the output is the RSS value of the two devices:

The total output dynamic range of the preamplifier can be calculated by dividing the full-scale output signal (5 V) by the total output rms noise (67 μV rms) and then converting this to dB. The result is approximately 97dB.

ADC selection

Since the amplifier's noise output (that is, the maximum number of bits that can be resolved) can be calculated by dividing the full-scale output by the rms noise:

Therefore, the number of rms LSBs translates into effective resolution:

Subtract 2.7 bits from the effective resolution to get the noise-free code resolution

Depending on the final application, 13 bits may be much higher than the resolution actually required. Since the target application does not require such a high resolution, it can be determined that this system meets the 12-bit design requirements.

If the LSB value in terms of current is lower than the dark current, then as mentioned previously, a second photodiode of the same type can be used at the non-inverting input of the op amp to eliminate the dark current. For example, if 16-bit resolution is required, the amount of photocurrent detected is:

Since the maximum dark current rating through the SFH 2701 is 5 nA, dark current compensation is required in 16-bit designs.

This application uses a 12-bit ADC, so the LSB value is 49 nA and no dark current compensation is required.

If the bandwidth is 2 MHz, a sound design rule would be to select an ADC with a sampling rate of 10 times or higher. This means that the ideal ADC must have 12-bit resolution and a sampling rate of 20 MSPS.

The AD9629-20 is a 20 MSPS, 12-bit resolution ADC that can be used as an ideal replacement product. But it requires a differential input, and the 5 V pp single-ended input must be converted to a 2 V pp differential signal. This requirement is easily met using the AD8475 differential funnel amplifier. It simplifies single-ended to differential conversion and provides common-mode level translation and precision attenuation.

The AD8475 has a maximum output offset of only 500 μV, a differential output noise of 10 nV/μHz, and total harmonic distortion plus noise (THD + N) performance of −112 dB.

AD8475 AD8475 supports a maximum output voltage of 2 V pp and a maximum frequency of 10 MHz, fully complying with the 2 MHz design requirements.

The gain of the AD8475 is determined by the analog input range of the AD9629-20 (2 V pp) and the full-scale output of the AD8065 (5 V pp).

The AD9629-20 provides an on-chip common-mode voltage of 0.9 V through the VCM pin. This pin drives the VOCM pin of the AD8475 with a common-mode voltage of 0.9 V.

It is important to consider the noise contribution of the AD8475 in this system. First, the AD8065's noise contribution is calculated by multiplying the output noise of the AD8065 (67 μV rms) by the gain of the AD8475.

The output noise of the AD8475 can be calculated by multiplying the output noise density (10nV/μ Hz) by the square root of the bandwidth (set by the output filter).

AD8475 output noise after filtering =

The total noise at the filtered output of the AD8475 can be calculated using the RSS values ​​of the two devices:

Taking the noise contribution of the AD8475 into account determines the number of bits required for resolution and allows calculation of the total dynamic range.

Test Results

Use a laser diode to drive the D1 photodiode and generate a current. Photodiode D2 is used for dark current compensation and is covered with an optically opaque epoxy (EPO-TEK® 320) material that prevents D2 from generating output current when D1 is excited.

By forcing the photodiode to drive a higher current than expected, the AD8065's approximate maximum rise and fall times reach 72 ns (see Figure 4).

By changing the position of the laser diode so that it no longer overdrives the photodiode beyond 200µA, more practical system rise and fall times can be measured.

Figure 5 shows the AD8065 rise and fall measurements of 282 ns and 290 ns respectively. Note that due to sufficient phase margin, there is no ringing when the laser diode is turned off in both test cases.

Now that the system's response to bright light pulses has been tested, the system's response to high-speed changes in light intensity can also be measured. An Agilent 33250A function generator was used to drive the laser diode with a 2 MHz sine wave. Figure 6 shows that the AD8065 can correctly detect small light intensity changes, and Figure 7 shows a screenshot of the CN0272 evaluation software correctly obtaining the conversion data of the AD9629-20 ADC and displaying it graphically.

For the complete design support package for this circuit note, see http://www.analog.com/CN0272-DesignSupport .

Applications in Pulse Oximeter

A pulse oximeter is a medical device used to continuously measure the percentage of oxygen-saturated hemoglobin (Hgb) and a patient's pulse rate. Oxygen-carrying hemoglobin (oxyhemoglobin) absorbs light in the infrared spectral region (940 nm), while non-oxygen-carrying hemoglobin (deoxyhemoglobin) absorbs visible red light (650 nm). By calculating the ratio of these two light intensities, the percentage of oxygen content in the body can be obtained.

In a pulse oximeter, two LEDs (one emits red light, the other emits infrared light) are rapidly and sequentially excited by two current sources, and a photodiode detects the LED's light intensity. The circuit in Figure 1 can be synchronized with an LED current sink circuit (such as the CN-0125) to capture the light emitted by each LED as it passes through the tissue.