This post builds on a couple of earlier posts of mine, LIGO modulation and RLC filters. In this post we will look into the Advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO)’s photodiode circuit and analyze its noise performance. (Also see a follow up post: An SNR analysis of aLIGO circuit)
The actual circuit in use at the moment is shown in Fig. 1, and we will refer to it as v5 in the following pages as it is the version number.
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Figure 1: The actual amplifier circuit used in the current set up.
Let us take a closer look at the photodiode bias circuit as shown in Fig. 2. The diode is under reverse bias, and it will behave as a current source when exposed to light.
Figure 2: This voltage regulator circuit applies reverse bias to the photo diode. Hover over the orange-colored elements to see what their functions are. … [+]
The output voltage is set to \(5\)V via every electronics hobbyist’s favorite LM317T voltage regulator with some reverse bias protection. Note the two parallel capacitors in the output, \(10\mu\)F and \(10\)nF. The \(10\)nF is a ceramic capacitor which is used to reduce to equivalent serial resistance at higher frequencies to dampen possible oscillations in the output voltage.
The anode of the phododiode is fed into a farm of fine-tuned notches as in Fig. 3.
Figure 3: Notch farm to remove various harmonics. Hover over the coils to see their properties. Hover over the info icons to see bode plots … [+]
Each block is tuned such that the natural frequency \(1/\sqrt{LC}\) is around the target frequency to be carved out. Hover over the info icon, , to see the corresponding Bode plot, and the coils to see their frequency response. In the Bode plot. we just use the series resistance along with the inductance. Skin depth effects and shunt capacitance are not included in the Bode plots. We will certainly include them later.
The selectors are shown in Fig. 4.
Figure 4: Selector filters. Hover over the coils to see their properties. Hover over the info icons to see bode plots. … [+]
The Trans-impedance amplifiers (TIA) are shown in Fig. 5.
Figure 5: Basic inverting amplifiers with a gain of \(10\) for the RF outputs. … [+]
| L7 | C30 | L9 | C35+C38 | L3 | C12+C15 | L1 | C2+C4 | L2 | C7+C10 | L4 | C16+C17 | L5 | C25+C26 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 220nH | 100nH | 1.8 \(\mu\)F | 173.7pF | 390nH | 32.2pF | 390nH | 208pF | 180nH | 109pF | 100nH | 87pF | 100nH | 31pF |
We build this circuit in LTspice as shown Fig. 6 and simulate. The LTspice file can be found here.
Figure 6: LTSpice circuit for simulation.
We can collect the LTspice simulation data via Python. It is convenient to measure the noise at the OPAMP output in terms its input current equivalent: \[\begin{equation} \text{Equivalent Current Noise}= \frac{(V/\text{gain})^2}{2 e }, \tag{1} \end{equation}\] where the gain is the transimpedance. We plot the noise spectrum in Fig. 7.
Figure 7: Baseline noise for the readout ports DC, 9.1MHz, and 45.5MHz. The critical values are marked on the plot.
The values annotated in Fig. 7 are the values we will want to reduce and they provide us with a benchmark. Can we beat these values and design a circuit with lower noise? That is exactly what we are going to do in following posts. Find a warm up SNR analysis here An SNR analysis of aLIGO circuit