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Download this article in PDF format. (193 KB) Programmable-Gain Transimpedance Amplifiers Maximize Dynamic Range in Spectroscopy Systems By Luis Orozco
Transimpedance amplifiers are essential building blocks in any system that measures light. Many chemical analysis instruments, such as ultraviolet-visible (UV-VIS) or Fourier transform-infrared (FT-IR) spectroscopes, rely on photodiodes to accurately identify chemical compounds. These systems must measure a wide range of light intensity. For example, a UV-VIS spectroscope can measure opaque samples, such as used motor oil, or transparent substances, such as ethanol. In addition, some substances have strong absorption bands at certain wavelengths, while remaining almost transparent at other wavelengths. Instrument designers often add several programmable gains to the signal path to increase the dynamic range.
Figure 2 shows the transfer function for a typical photodiode. The curve looks very similar to that of a normal diode, but the entire curve moves up and down as the photodiode is exposed to light. Figure 2b shows a close-up of the transfer function around the origin, where no light is present. The output of the photodiode is nonzero as long as the bias voltage is nonzero. This dark current is typically specified with a 10-mV reverse bias. Although operating the photodiode with a large reverse bias (photoconductive mode) results in a faster response, operating with zero bias (photovoltaic mode) eliminates the dark current. In practice, the dark current does not disappear completely, even in photovoltaic mode, as the amplifier’s input offset voltage will result in a small error across the photodiode’s terminals.
When operating a photodiode in photovoltaic mode, a transimpedance amplifier (TIA) keeps the bias voltage near 0 V while converting the photodiode current to a voltage. Figure 3 shows the most basic form of a TIA.
_{f}. With one end of R_{f} at virtual ground, the output voltage is simply R_{f} × I_{d}. In order for this approximation to hold true, the op amp’s input bias current and input offset voltage must be small. In addition, a small input offset voltage will minimize the photodiode’s dark current. A good amplifier choice is the AD8615, which specifies 1-pA maximum leakage and 100-μV maximum offset at room temperature. In this example, we choose R_{f
}= 1 MΩ to provide the desired output level with the maximum light input.Unfortunately, designing a photodiode amplifier is not as simple as selecting an op amp for the circuit shown in Figure 3. If we simply connect R
Note that R
Each pole causes a 90° phase shift in the open-loop transfer function, for a 180° total phase shift well below the frequency where the open-loop amplitude response crosses 0 dB. As shown in Figure 4b, the lack of phase margin makes it almost certain that the circuit will oscillate. To ensure stable operation, we can add a zero to the transfer function by placing a capacitor in parallel with R
where This value for C Figure 5 shows the open-loop frequency response after adding the feedback capacitor. The phase response dips below 30°, but this occurs several decades away from where the gain goes to 0 dB, so the amplifier will remain stable.
_{f}, and the compensation capacitor, C_{f}. Using the specifications from the stability example, the resulting closed-loop bandwidth is
To convert the 3-dB bandwidth to ENBW in a single-pole system, multiply by π/2:
Now that we have the ENBW, we can find the rms noise due to the feedback resistor and the op amp’s current noise. The resistor’s Johnson noise will appear at the output directly, and the op amp’s current noise will appear as an output voltage after going through the feedback resistor.
where k is Boltzmann’s constant, and T is the temperature in kelvin. The final contributor is the op amp’s voltage noise. The output noise is the input noise multiplied by the noise gain. The best way to think about the noise gain for a transimpedance amplifier is to start with the inverting amplifier shown in Figure 7.
For this circuit, the noise gain is
Using the photodiode amplifier model from Figure 4a, the noise gain will be:
where Z This transfer function contains several poles and zeroes, and hand analysis would be tedious. However, using the values from the previous examples, we can make some rough approximations. At frequencies near dc, the resistors will dominate, and the gain will be near 0 dB, as the diode’s shunt resistance is two orders of magnitude larger than the feedback resistance. As the frequency increases, the impedance of the capacitors will decrease and start to dominate the gain. Since the total capacitance from the inverting pin of the op amp to ground is much larger than the feedback capacitor, C Figure 8 shows the amplifier’s noise gain behavior over frequency and the location of each pole and zero in the transfer function.
Just as with the resistor noise density, the most accurate way to convert the output noise density of Figure 8 to voltage noise in V
The noise will peak at
Note that With this assumption in mind, the output noise is equal to the input noise density multiplied by the plateau gain and by the ENBW, which is
Now that we have the output referred noise from all three sources, we can combine them to get the overall system output noise. The three noise sources are independent and Gaussian, so we can root-sum-square (RSS) them rather than adding them. When combining terms using RSS, one term will dominate the result if it is more than about three times larger than the others.
The response of Figure 8 makes it obvious that the noise bandwidth of the op amp is much larger than its signal bandwidth. The additional bandwidth does nothing but contribute to the noise, so we can add a low-pass filter on the output to attenuate the noise at frequencies outside the signal bandwidth. Adding a single-pole RC filter with 34-kHz bandwidth reduces the voltage noise from 254 μV
To calculate the total noise of the system, we can again root-sum-square the TIA’s noise contribution and the PGA’s noise contribution as shown in Table 3. For this example, assume that the PGA includes a 34-kHz filter. As we can see, for a gain of 10, the TIA’s noise contribution will appear at the PGA’s output multiplied by the PGA gain.
As we would expect, the output noise is slightly more than ten times as large when operating with a gain of ten than when the PGA is set for a gain of one.
and the total output noise is
Adding a single-pole RC filter with a bandwidth of 34 kHz at the output results in lower noise, for a total system noise of Table 4 shows a summary of the noise performance for both amplifier architectures. For a transimpedance gain of 10 MΩ, the total noise will be about 12% lower than with the two-stage circuit.
The circuit in Figure 10 avoids these problems by using two switches in every transimpedance leg. Although this requires twice as many switches, the on resistance of the switches on the left is within the feedback loop, so the output voltage depends only on the current through the selected resistor. The switches on the right look like an output impedance and will contribute negligible error if the amplifier drives a high-impedance load, such as an ADC driver.
The circuit of Figure 10 will work for dc and low frequencies, but the parasitic capacitance across the switches in the off state presents yet another challenge. These parasitic capacitors, labeled C
Depending on the desired bandwidth and feedback resistor, the parasitic capacitance could result in a significant difference between the expected and measured behavior of the amplifier. For example, assume the amplifier of Figure 11 uses the same 1 MΩ and 10 MΩ values as in our previous circuit, with their respective capacitors of 4.7 pF and 0.47 pF, and we select the 10 MΩ gain. If each switch has approximately 0.5 pF of feed-through capacitance, Figure 12 shows the difference between the ideal and actual bandwidths, taking into account the parasitic path.
One way to address this problem is to replace each switch with two switches in series. This reduces the parasitic capacitance by half at the expense of additional components. Figure 13 shows this approach.
If the application requires even more bandwidth, a third alternative is to use SPDT switches to connect every unused input to ground. Although the parasitic capacitance from each open switch is still in the circuit, Figure 14b shows how each parasitic capacitor appears to be connected from the output of the op amp to ground or from the end of the unused feedback leg to ground. Capacitance from the amplifier output to ground tends to be associated with instability and ringing, but in this case, the total parasitic capacitance of just a few picofarads will not have a significant effect on the output. The parasitic capacitance that appears from the inverting input to ground will add to the photodiode’s shunt capacitance and the op amp’s own input capacitance and will represent a negligible increase when compared with the photodiode’s large shunt capacitance. Assuming
As with everything, however, the approach of Figure 14 has trade-offs. It’s more complex and can be difficult to implement for more than two gains. In addition, the two switches in the feedback loop will introduce dc errors and distortion. Depending on the value of the feedback resistor, the additional bandwidth may be important enough to warrant these small errors. For example, with a 1-MΩ feedback resistor, the on resistance of an ADG633 will contribute about 50 ppm gain error and 5 μV offset error at room temperature. If the application calls for maximum bandwidth, however, this may be a reasonable trade-off.
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