# How to achieve high bandwidth and low noise…

[Guide]In the previous article “How to achieve high bandwidth and low noise while ensuring stability? (1)”, we introduced how to select external components to ensure stability and calculate TIA noise. In this article, we will introduce the noise advantage of a single gain stage.
Noise contributed by programmable gain stage
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 multiplied by 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 caused by the PGA will be 10nV/√Hz or 100nV/√Hz.
To calculate the total noise of the system, you can also sum the square root of the noise contribution of TIA and the noise contribution of PGA, as shown in Figure 1. This example assumes that the PGA includes a 34 kHz filter. It can be seen that when the gain is 10, the noise contribution of the TIA is multiplied by the PGA gain and appears at the output of the PGA.
Figure 1: Total system noise of TIA+PGA architecture
As we expected, the output noise of PGA is slightly greater than 10 times when compared with PGA working with 1 times gain.
The noise advantage of a single gain stage
Another method is to use a transimpedance amplifier with programmable gain to completely eliminate the PGA stage. Figure 9 shows the theoretical Circuit with two programmable transimpedance gains (1MΩ and 10MΩ). Each transimpedance Resistor needs its own capacitance to compensate the input capacitance of the photodiode. To be consistent with the previous example, the signal bandwidth under the two gain settings is still 34kHz. This means that a 0.47pF capacitor should be selected in parallel with a 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, a larger resistance results in higher Johnson noise, higher current noise (the current noise at this time is multiplied by 10MΩ instead of 1MΩ) and a higher noise gain. Similarly, the three main noise sources are:
The total output noise is:
Adding a single-pole RC filter with a bandwidth of 34kHz at the output can reduce noise, and the total system noise is 460μVrms. Due to the higher gain, fp2 is closer to the signal bandwidth, so the noise reduction effect is not as significant as using 1MΩ gain.
Figure 2 is a summary of the noise performance of the two amplifier architectures. For a transimpedance gain of 10MΩ, the total noise is about 12% lower than that of the two-stage circuit.
Figure 2: Comparison of total system noise
Programmable gain transimpedance amplifier
Figure 3 shows a programmable gain transimpedance amplifier. This is a good conceptual design, but the on-resistance and leakage current of the analog switch will introduce errors. On-resistance causes voltage and temperature-related gain errors, and leakage current causes offset errors, especially at high temperatures.
Figure 3: Programmable transimpedance amplifier
The circuit shown in Figure 4 uses two switches in each transimpedance branch, thereby avoiding the above-mentioned problems. Although it requires twice the number of switches, the on-resistance of the left switch is in the feedback loop, so the output voltage depends only on the current through the selected resistor. The switch on the right looks like an output impedance. If the amplifier drives a high impedance load such as an ADC driver, the error it generates is negligible.
Figure 4: Programmable gain transimpedance amplifier with Kelvin switch
The circuit of Figure 4 is suitable for DC and low frequency, but in the off state, the parasitic capacitance on the switch is another big problem. These parasitic capacitances are marked as Cp in Figure 4 and connect the unused feedback path to the output, thus reducing the overall bandwidth. Figure 5 shows how these Capacitors are ultimately connected to the unselected gain branch, thereby turning the transimpedance gain into a parallel combination of the selected gain and the unselected gain-attenuated version.
Figure 5: Total feedback capacitance including switch parasitic capacitance
Depending on the required bandwidth and feedback resistance, parasitic capacitance may cause the expected behavior of the amplifier to differ significantly from the measured behavior. For example, assuming that the amplifier in Figure 5 uses the same 1MΩ and 10MΩ values ​​as the previous circuit, and the corresponding capacitances are 4.7pF and 0.47pF, respectively, we choose a gain of 10MΩ. If each switch has a feedthrough capacitance of about 0.5pF, considering the parasitic path, the difference between the ideal bandwidth and the actual bandwidth is shown in Figure 6.
Figure 6: Transimpedance gain including parasitic switched capacitance
One way to solve this problem is to replace each switch with two switches in series. In this way, the parasitic capacitance will be halved, but more components are required. Figure 7 shows this approach.
Figure 7: Increase the series switch to reduce the total parasitic capacitance
If the application requires higher bandwidth, the third method is to use SPDT switches to connect each unused input to ground. Although the parasitic capacitances of the open switches are still in the circuit, Figure 8b shows how the parasitic capacitances appear to be connected from the output of the op amp to ground, or from the end of the unused feedback branch to ground. The capacitance from the output of the amplifier to the ground often causes the circuit to be unstable and oscillate in response, but in this case, the total parasitic capacitance is only a few pF, which will not have a serious impact on the output. The parasitic capacitance from the inverting input terminal to the ground is added to the shunt capacitance of the photodiode and the op amp’s own input capacitance. Compared with the large shunt capacitance of the photodiode, the increase is minimal. Assuming that each switch has a feedthrough capacitance of 0.5pF, the output of the op amp will add a 2pF load, and most op amps can be driven without difficulty.
Figure 8: Programmable TIA using SPDT switch
However, like anything, the method shown in Figure 8 has disadvantages. It is more complicated and may be difficult to achieve for more than two gains. In addition, the two switches in the feedback loop introduce DC errors and distortion. Depending on the value of the feedback resistor, the additional bandwidth may be important enough to ensure that this small error does not affect circuit operation. For example, for a 1MΩ feedback resistor, the on-resistance of ADG633 produces approximately 50ppm gain error and 5μV offset error at room temperature. However, if the application requires the highest bandwidth, then this can be said to be a disadvantage.
in conclusion
Photodiode amplifiers are an essential part of most chemical analysis and material identification signal chains. With programmable gain, engineers can design instruments to accurately measure very large dynamic ranges. This article explains 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 pros and cons can achieve excellent performance.