CN0272

Component Selection

Photodiodes are high impedance sensors used to detect the intensity of light. Photodiodes do not have internal gain but can operate at much higher light levels than other light detectors.

Photodiodes operate either with zero bias (photovoltaic mode) or with a reverse bias (photoconductive mode). The most precise linear operation is obtained in the photovoltaic mode, while higher switching speeds are realizable when the diode is operated in the photoconductive mode at the expense of linearity. Under these reverse bias conditions, a small amount of current called dark current flows even when there is no illumination. The dark current error can be cancelled using a second photodiode of the same type in the noninverting input of the op amp as is shown in Figure 1.

Three factors influence the response time of a photodiode

• The charge collection time of the carriers in the depleted region of the photodiode
• The charge collection time of the carriers in the undepleted region of the photodiode
• The RC time constant of the diode circuit combination

Because the junction capacitance is dependent on the diffused area of the photodiode and the applied reverse bias, faster rise times are obtained with smaller diffused area photodiodes and larger applied reverse biases. The junction capacitance for the SFH 2701 PIN photodiode used in the CN-0272 circuit note is 3 pF typical, 5 pF maximum for 0 V bias. The typical capacitance is 2 pF for 1 V reverse bias and 1.7 pF for 5 V reverse bias. Measurements in the circuit were all taken with a reverse bias of 5 V.

Figure 2 shows an I/V converter with an electrical model of a photodiode. The basic transfer function is

Where I_PHOTO is the output current of the photodiode, and the parallel combination of R_F and C_F sets the signal bandwidth. Ideally, all of the output current from the photodiode passes through RF, but all op amps have input bias currents that introduce errors on the output. Op amps with picoamps of input bias current and low input offset voltages are preferred to minimize the error. The AD8065 has only 2 pA of input bias current and only 400 μV of input offset voltage.

The circuit is designed to have a full scale output of 5 V with a maximum photodiode current of 200 μA. This determines the value of the feedback resistor to be

The stable bandwidth attainable with this preamp is a function of R_F, the gain bandwidth product of the amplifier (65 MHz), and the total capacitance at the amplifier’s summing junction, C_IN. For this circuit, the SFH 2701 diode (OSRAM Opto Semiconductors GmbH) has a maximum capacitance of 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.

It can be shown that the signal bandwidth resulting in a 45° phase margin, f₍₄₅₎, is defined by

Because the maximum attainable bandwidth is larger than the intended bandwidth, the AD8065 is a good candidate for the application, which is largely due to its large ratio of f_CR to C_IN.

R_F and C_IN produce a pole in the loop transfer function of the amplifier that can result in peaking and instability (see Figure 3). Adding C_F creates a zero in the loop transfer function that compensates for the effect of the pole and reduces the signal bandwidth.

The value of C_F that produces 2 MHz of bandwidth with the selected value of R_F is

To determine if 3.3 pF is enough capacitance to stabilize the system, calculate the amount of capacitance needed to obtain 45° of phase margin. The value of C_F that produces f₍₄₅₎ can be shown as

Because the intended value of 3.3 pF is larger than the minimum value of 1.1 pF, the system is stable because increasing the capacitance increases the amount of phase margin.

Noise Analysis

Now that the components are selected, how much resolution is needed to convert the signal must be determined. As in most noise analyses, only the key contributors need to be identified. Noise sources combine in an RSS manner; therefore, any single noise source that is at least three-to-four times larger than any of the others dominates.

In the case of the photodiode preamp, the dominant sources of output noise are the input voltage noise of the op amp and the feedback resistor noise. The input current noise of the FET-input op amp is negligible. The shot noise of the photodiode (caused by reverse bias) is negligible because of the filtering effect of the shunt capacitance.

The resistor noise is calculated using the Johnson noise formula.

where:
k is Boltzmann’s constant (1.38 × 10-23J/K).
T is the absolute temperature in Kelvin.
The factor of 1.57 converts the approximate single-pole bandwidth into the equivalent noise bandwidth.

Note that the 0.1 μF capacitor on the positive input of the preamp eliminates the high frequency noise produced by the second R_F resistor used to cancel the effects of bias current.

The primary source of output noise is due to the input voltage noise and the high frequency noise gain peaking that occurs between f₁ and f_CR. If it is assumed that the output noise is constant over the entire range of frequencies and the maximum value for the ac noise gain is used, then

where V_N is the input voltage noise of the amplifier (7 nV/√Hz).

The total rms noise referred to the output is then the RSS value of the two components

The total output dynamic range of the preamp can be calculated by dividing the full scale output signal (5 V) by the total output rms noise (67 μV rms) and converting it to decibels, yielding approximately 97 dB.

ADC Selection

Because the amount of noise output by the amplifier is known the maximum number of bits that can be resolved can now be calculated by dividing the full scale output by the rms noise.

The number of rms LSBs can be converted into effective resolution.

Noise-free code resolution can be obtained by subtracting 2.7 bits from effective resolution.

Depending on the end application, 13 bits may be more resolution than is actually needed. Because the intended application does not require this amount of resolution, it has been confirmed that the system meets the design requirements with 12 bits.

If the LSB size (in current) is smaller than the amount of dark current, as mentioned earlier, the dark current can be canceled using a second photodiode of the same type in the noninverting input of the op amp. For example, if 16 bits of resolution is needed, the amount of photocurrent detected is

Since the maximum amount of dark current that flows in the SFH 2701 is specified at 5 nA, dark current compensation is needed in a 16-bit design.

This application uses a 12-bit ADC; therefore, the LSB size is 49 nA, and it does not require dark current compensation.

If the bandwidth is 2 MHz, a reasonable guideline is to select an ADC with a sampling rate 10 times greater or more. This means the ideal ADC must sample at a rate of 20 MSPS with 12 bits of resolution.

The AD9629-20 is a good candidate because it is a 20 MSPS ADC with 12 bits of resolution. However, it requires differential inputs, and the 5 V p-p single-ended signal must be converted to a 2 V p-p differential signal. This is easily accomplished by using the AD8475 differential funnel amplifier, which simplifies the single-ended-to-differential conversion, and provides common-mode level shifting and precision attenuation.

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

The AD8475 can support a maximum output voltage of 2 V p-p up to 10 MHz, which is well within the design requirement of 2 MHz.

The gain of the AD8475 was determined by the analog input span of the AD9629-20 (2 V p-p) and the full scale output of the AD8065 (5 V p-p).

An on-chip, common-mode voltage of 0.9 V is included in the AD9629-20 and is available from the VCM pin. This pin drives the VOCM pin of the AD8475 with the common-mode voltage of 0.9 V.

It is important to include the noise contribution of the AD8475 in this system. This is calculated by first multiplying the output noise of the AD8065 (67 μV rms) by the gain of the AD8475 to get the contribution due to the AD8065.

The output noise due to the AD8475 is calculated by multiplying the output noise density (10nV/√Hz) by the square root of the bandwidth set by the output filter.

The total noise at the output of the AD8475 after the filter is calculated by taking the RSS value of the two components is

With the noise contribution of the AD8475 incorporated into the calculations, the number of bits that can be resolved can be confirmed, and the total dynamic range can be calculated.

Test Results

A laser diode was used 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) to prevent output current from D2 when D1 is excited.

By forcing the photodiode to drive a larger than expected current, the approximate maximum rise and fall time of the AD8065 was 72 ns (see Figure 4).

A more realistic rise and fall time of the system can be measured by moving the position of the laser diode so that it does not overdrive the photodiode current beyond 200 μA. Figure 5 shows the measured rise and fall time of the AD8065 to be 282 ns and 290 ns, respectively. It is important to note that there is no ringing after the laser diode has turned off in both test cases because there is sufficient phase margin.

Now that the response of the system to a pulse of bright light has been tested, how the system responds to high speed changes in light intensity can be tested. An Agilent 33250A function generator was used to drive a laser diode with a 2 MHz sine wave. Figure 6 shows that the output of the AD8065 was able to successfully detect the small changes in light intensity, and Figure 7 shows a screenshot of the CN0272 Evaluation Software successfully receiving conversion data from the AD9629-20 ADC and plotting the data in a chart.

A complete design support package for this circuit note can be found at http://www.analog.com/CN0272-DesignSupport.

Applications in Pulse Oximetry

A pulse oximeter is a medical device used for continuously measuring the percentage of hemoglobin (Hgb) saturated with oxygen and the pulse rate of a patient. Hemoglobin carrying oxygen (oxyhemoglobin) absorbs light in the infrared region (940 nm) of the spectrum; hemoglobin that is not carrying oxygen (deoxyhemoglobin) absorbs visible red light (650 nm). The percentage of oxygen in the body is determined by calculating the ratio between these two intensities of light.

In a pulse oximeter, two LEDs (one emitting red light and the other emitting infrared light) are rapidly and sequentially excited by two current sources and a photodiode is used to detect the intensity of the light from the LEDs. The circuit shown in Figure 1 can be synchronized with an LED current sink circuit, such as CN-0125, to capture the light from each LED as it transmits through the tissue.