ADI teaches you how to achieve high bandwidth and low noise while ensuring stability!
Precision instrumentation systems that measure physical properties using photodiodes or other current-output sensors often include a transimpedance amplifier (TIA) and a programmable gain stage to maximize dynamic range. This article uses a practical example to illustrate the advantages and challenges of implementing a single-stage programmable gain TIA to minimize noise while maintaining high bandwidth and high accuracy.
Transimpedance amplifiers are the basic building blocks of all light measurement systems. Many chemical analysis instruments, such as UV-VIS or Fourier transform infrared (FT-IR) spectrometers, rely on photodiodes to accurately identify chemical components. These systems must be able to measure a wide range of light intensities. For example, a UV-VIS spectrometer 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 and are nearly transparent at other wavelengths. Instrument designers often add multiple programmable gains to the signal path to increase the dynamic range.
Before discussing photodiode amplifiers, a quick review of photodiodes is in order. Photodiodes generate a voltage or current when light strikes their PN junction. Figure 1 shows the equivalent circuit. This model represents a typical device used in a spectrometer and consists of a light-dependent current source in parallel with a large shunt resistor and a shunt capacitor, which can range in value from less than 50 pF (for small devices) to more than 5000 pF (for very large devices).
Figure 1. Photodiode model.
Figure 2 shows the transfer function of a typical photodiode. The curve looks very similar to a normal diode, but the entire curve moves up and down as the photodiode is exposed to light. Figure 2b is a close-up of the transfer function near the origin, where no light is present. As long as the bias voltage is non-zero, the output of the photodiode is non-zero. This dark current is usually specified with a 10mV reverse bias. While operating the photodiode with a large reverse bias (photoconductive mode) results in a faster response, operating the photodiode with zero bias (photovoltaic mode) eliminates the dark current. In practice, even in photovoltaic mode, the dark current does not completely disappear because the input offset voltage of the amplifier produces a small error at the photodiode leads.
Figure 2. Typical photodiode transfer function.
When operating the photodiode in photovoltaic mode, a transimpedance amplifier (TIA) allows the bias voltage to approach 0 V while converting the photodiode current to a voltage. Figure 3 shows the most basic form of a TIA.
Figure 3. Transimpedance amplifier.
For an ideal op amp, its inverting input is at virtual ground, and all the current of the photodiode flows through the feedback resistor Rf. One end of Rf is at virtual ground, so the output voltage is equal to Rf×Id. For this approximate calculation to be valid, the input bias current and input offset voltage of the op amp must be small. In addition, a small input offset voltage can reduce the dark current of the photodiode. A good amplifier choice is the AD8615, which has a maximum leakage current of 1pA and a maximum offset voltage of 100μV at room temperature. In this example, we choose Rf = 1MΩ to provide the required output level under maximum light input conditions.
However, designing a photodiode amplifier is not as simple as selecting an op amp for the circuit shown in Figure 3. If Rf = 1MΩ is simply connected across the feedback path of the op amp, the shunt capacitance of the photodiode will cause the op amp to oscillate. To illustrate this, Table 1 shows Cs and Rsh for a typical large area photodiode . Table 2 lists the key features of the AD8615, whose low input bias current, low offset voltage, low noise, and low capacitance make it ideal for precision photodiode amplifier applications.
Table 1. Photodiode Specifications
Table 2. AD8615 Specifications
Figure 4a is a good model for a photodiode amplifier. The open-loop transfer function of this system has a pole at 28Hz due to the open-loop response of the op amp (see the data sheet) and another pole due to the feedback resistor and the parasitic resistance and capacitance of the photodiode.
Figure 4. Photodiode amplifier model (a) and open-loop response (b).
For the component values we chose, this pole occurs at 1kHz, as shown in Equation 1.
Note that Rsh is two orders of magnitude larger than Rf, so Equation 1 simplifies to:
Each pole causes the open-loop transfer function to shift by 90°, for a total phase shift of 180°, well below the frequency at which the open-loop amplitude phase shift crosses 0 dB. As shown in Figure 4b, the lack of phase margin will almost certainly cause the circuit to oscillate.
To ensure stable operation, a capacitor can be placed in parallel with R f , adding a zero to the transfer function. This zero reduces the slope of the transfer function from 40 dB/decade to 20 dB/decade when it crosses 0 dB, resulting in a positive phase margin. The design should have at least 45° of phase margin to ensure stability. Higher phase margins result in less ringing, but the response time is increased. The zero that the capacitor adds to the open-loop response becomes a pole in the closed-loop response, so the closed-loop response of the amplifier degrades as the capacitance is increased. Equation 2 shows how to calculate the feedback capacitor to provide a 45° phase margin.
where fu is the unity-gain frequency of the op amp.
This C f value determines the highest practical bandwidth over which the system can operate. Although a smaller capacitor can be chosen to provide lower phase margin and higher bandwidth, the output may oscillate excessively. In addition, all components must have margin to ensure stability under the worst-case condition. In this example, C f = 4.7pF is chosen, which corresponds to a closed-loop bandwidth of 34kHz, which is typical of many spectroscopy systems.
Figure 5 shows the open-loop frequency response after adding feedback capacitance. The phase response has a low point below 30°, but this is several dozen octaves away from the frequency where the gain becomes 0dB, so the amplifier will remain stable.
Figure 5. Photodiode amplifier open-loop response using 1.2 pF feedback capacitor.
One approach to designing a programmable-gain photodiode amplifier is to use a transimpedance amplifier with a gain that keeps the output in the linear region, even for the brightest light inputs. In this way, a programmable-gain amplifier stage can boost the output of the TIA in low-light conditions, achieving a gain close to 1 for high-intensity signals, as shown in Figure 6a. Another option is to implement the programmable gain directly in the TIA, eliminating the second stage, as shown in Figure 6b.
Figure 6. (a) TIA first stage followed by a PGA; (b) programmable gain TIA
There are three main noise sources for transimpedance amplifiers: the op amp’s input voltage noise, input current noise, and the Johnson noise of the feedback resistor. All of these noise sources are typically expressed as noise density. To convert the units to V rms , find the noise power (the voltage noise density squared) and then integrate it over frequency. An accurate but much simpler method is to multiply the noise density by the square root of the equivalent noise bandwidth (ENBW). The closed-loop bandwidth of the amplifier can be modeled as a first-order response dominated by the feedback resistor, R f, and the compensation capacitor, C f . Using the specifications from the stability example, the closed-loop bandwidth is found to be:
To convert the 3dB bandwidth to ENBW in a single-pole system, multiply by π/2:
Once ENBW is known, the rms noise caused by the feedback resistor and the current noise of the op amp can be calculated. The Johnson noise of the resistor appears directly at the output, and the current noise of the op amp appears as the output voltage after passing through the feedback resistor.
Here, k is the Boltzmann constant and T is the temperature (in K).
The final source is the voltage noise of the op amp. Output noise is equal to input noise multiplied by noise gain. The best way to think about the noise gain of a transimpedance amplifier is to start with the inverting amplifier shown in Figure 7.
Figure 7. Inverting amplifier noise gain.
The noise gain of this circuit is:
Using the photodiode amplifier model shown in Figure 4a, the noise gain is:
Where Zf is the parallel combination of the feedback resistor and capacitor, and Zin is the parallel combination of the op amp input capacitance and the photodiode’s shunt capacitance and shunt resistor.
This transfer function contains many poles and zeros, and it would be very tedious to calculate by hand. However, using the values in the example above, we can make a rough approximation. At frequencies close to DC, the resistors dominate and the gain is close to 0dB because the shunt resistance of the diode is two orders of magnitude larger than the feedback resistor. As the frequency increases, the impedance of the capacitor decreases and begins 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, Cf , the gain begins to increase with frequency. Fortunately, the gain does not increase indefinitely because the pole formed by the feedback capacitor and resistor prevents the gain from increasing, and eventually the bandwidth of the op amp takes over and the gain begins to roll off.
Figure 8 shows the amplifier's noise gain vs. frequency, along with the location of the poles and zeros in the transfer function.
Figure 8. Amplifier noise gain transfer function.
As with the resistor noise density, the most accurate way to convert the output noise density of Figure 8 to voltage noise, V rms , is to square the noise density, integrate over the entire frequency spectrum, and then calculate the square root. However, inspection of the response reveals that a much simpler method produces only a small error. For most systems, the first zero and pole occur at a relatively low frequency than the second pole. For example, using the specifications shown in Table 1 and Table 2, the circuit has the following poles and zeros:
The peak noise is:
Note that fz1 and fp1 occur at relatively low frequencies compared to fp2 . Simply assuming that the output noise is equal to the plateau noise from DC to fp2 (N2 from Equation 11) will greatly simplify the math required to calculate the output noise.
Under this assumption, the output noise is equal to the input noise density times the plateau gain times the ENBW, or fp2 × π/2:
Once the equivalent output noise of all three noise sources is known, they can be combined to find the total output noise of the system. These three noise sources are independent of each other and are Gaussian, so the root sum square (RSS) can be taken instead of adding them. When combining multiple terms using RSS, if one term is about three orders of magnitude larger than the other terms, the result will be dominated by that term.
The response in Figure 8 clearly shows that the op amp’s noise bandwidth is much greater than the signal bandwidth. The extra bandwidth does nothing but contribute noise, so a low-pass filter can be added to the output to attenuate noise at frequencies outside the signal bandwidth. Adding a single-pole RC filter with a 34kHz bandwidth reduces the voltage noise from 254μV rms to 45μV rms and the total noise from 256μV rms to only 52μV rms .
If a PGA is added after the transimpedance amplifier, the noise at the output will be the sum of the PGA noise plus the TIA noise times the additional gain. For example, if the application requires gains of 1 and 10, and a PGA with a total input noise density of 10nV/√Hz is used, the output noise contributed by the PGA will be 10nV/√Hz or 100nV/√Hz.
To calculate the total noise of the system, the noise contribution of the TIA and the noise contribution of the PGA can again be squared, as shown in Table 3. This example assumes that the PGA includes a 34 kHz filter. It can be seen that at a gain of 10, the noise contribution of the TIA multiplied by the PGA gain appears at the output of the PGA.
Table 3. Total System Noise of TIA + PGA Architecture
As we would expect, the output noise of a PGA operating at a gain of 10 is slightly greater than that of a PGA operating at a gain of 1.
Another approach is to use a transimpedance amplifier with programmable gain and eliminate the PGA stage entirely. Figure 9 shows a theoretical circuit with two programmable transimpedance gains (1MΩ and 10MΩ). Each transimpedance resistor requires its own capacitance to compensate for the input capacitance of the photodiode. To keep with the previous example, the signal bandwidth is still 34kHz for both gain settings. This means that a 0.47pF capacitor should be chosen in parallel with the 10MΩ resistor. In this case, the output voltage noise when using a 1MΩ resistor is the same as Equation 12. When using a 10MΩ transimpedance gain, the larger resistor results in higher Johnson noise, higher current noise (this time multiplied by 10MΩ instead of 1MΩ), and higher noise gain. Similarly, the three main noise sources are:
The total output noise is:
在输出端添加一个带宽为34kHz的单极点RC滤波器可降低噪声，系统总噪声为460μVrms。由于增益较高，fp2更接近信号带宽，因此降噪效果不如使用1MΩ增益那样显著。
A summary of the noise performance of the two amplifier architectures is shown in Table 4. For a transimpedance gain of 10 MΩ, the total noise is approximately 12% lower than the two-stage circuit.
Table 4. System Total Noise Comparison
Figure 9 shows a programmable gain transimpedance amplifier. This is a good conceptual design, but the on-resistance and leakage current of the analog switches introduce errors. The on-resistance causes voltage- and temperature-dependent gain errors, and the leakage current causes offset errors, especially at high temperatures.
Figure 9. Programmable transimpedance amplifier.
The circuit shown in Figure 10 avoids this problem by using two switches in each transimpedance branch. Although it requires twice the number of switches, the on-resistance of the left switch is within the feedback loop, so the output voltage depends only on the current through the selected resistor. The right switch appears as an output impedance, which produces negligible error if the amplifier is driving a high impedance load such as an ADC driver.
Figure 10. Programmable gain transimpedance amplifier with Kelvin switch.
The circuit of Figure 10 is suitable for DC and low frequencies, but in the off state, parasitic capacitances on the switches are another problem. These parasitic capacitances, marked as Cp in Figure 10, connect the unused feedback path to the output, thereby reducing the overall bandwidth. Figure 11 shows how these capacitances are ultimately connected to the unselected gain branches, thus changing the transimpedance gain to a parallel combination of the selected gain and an attenuated version of the unselected gain.
Figure 11. Total feedback capacitance including switch parasitic capacitance.
Depending on the desired bandwidth and feedback resistors, parasitic capacitance can cause the expected behavior of an amplifier to differ significantly from the measured behavior. For example, assume the amplifier in Figure 11 uses the same 1MΩ and 10MΩ values as the previous circuit, with corresponding capacitances of 4.7pF and 0.47pF, respectively, and we choose a gain of 10MΩ. If each switch has a feedthrough capacitance of approximately 0.5pF, the difference between the ideal bandwidth and the actual bandwidth, taking into account parasitic paths, is shown in Figure 12.
Figure 12. Transimpedance gain including parasitic switch capacitance.
One way to solve this problem is to replace each switch with two switches in series. This will halve the parasitic capacitance, but will require more components. Figure 13 shows this approach.
Figure 13. Adding series switches to reduce total parasitic capacitance.
If the application requires higher bandwidth, a third approach is to connect each unused input to ground using an SPDT switch. Although the parasitic capacitance of each open switch is still in the circuit, Figure 14b shows how each parasitic capacitance appears to be connected from the output of the op amp to ground, or from the end of the unused feedback branch to ground. Capacitance from the amplifier output to ground often causes circuit instability and ringing, but in this case the total parasitic capacitance is only a few pF and will not have a serious impact on the output. The parasitic capacitance from the inverting input to ground will add the shunt capacitance of the photodiode and the op amp's own input capacitance, and the increase is negligible compared to the large shunt capacitance of the photodiode. Assuming a 0.5pF feedthrough capacitance for each switch, this will add a 2pF load to the op amp output, which most op amps can drive without difficulty.
Figure 14. Programmable TIA using SPDT switches.
However, like anything, the approach shown in Figure 14 has disadvantages. It is more complex and can be difficult to implement for gains above two. In addition, the two switches in the feedback loop introduce dc errors and distortion. Depending on the value of the feedback resistor, the extra bandwidth may be significant enough to ensure that such small errors do not affect the circuit operation. For example, with a 1-MΩ feedback resistor, the on resistance of the ADG633 produces approximately 50 ppm of gain error and 5 μV of offset error at room temperature. However, if the application requires the highest bandwidth, then this can be considered a disadvantage.
in conclusion
Photodiode amplifiers are an essential component of most chemical analysis and material identification signal chains. Using programmable gain, engineers can design instruments to accurately measure very large dynamic ranges. This article shows how to achieve high bandwidth and low noise while ensuring stability. Designing a programmable gain TIA involves challenges such as switch configuration, parasitic capacitance, leakage current, and distortion, but choosing the right configuration and carefully weighing the trade-offs can achieve excellent performance.
Give you a careful heart, please click "Watching"
京公网安备 11010802033920号