In Case Study: Medical Laser System; Part 1: Stabilizing a Laser Feedback Control Loop, the nonlinear flashlamp in the laser control loop had a parabolic transfer function which was gain-compensated with a square-root circuit. This resulted in constant loop gain over the output power range. In this sequel, more of the feedback loop design is addressed, notably the photodiode amplifier in the feedback path.
In Part 1, attention was on the forward path of the loop and the linearization of the square-law laser-flashlamp subsystem. The laser output reflected off a mirror, and a photodiode behind the mirror sensed it. A small but fixed fraction of laser light would transmit through the mirror. The fraction was different for different polarizations of light, and that caused an apparent “drift” in output power as polarization changed. Before this fact was discovered, it was thought that power drift was caused by drift in the photodiode amplifier (PDA).
The original PDA design is shown below. The redesign goal was to make it less noisy, simpler, less costly, and extended at the low end of the linear dynamic range to zero volts.
The full-scale photodiode current is 15 μA and the zero-scale value is 0.15 μA. The 100 to 1 range corresponds to a laser output power from 50 mW to 5 W. The original PDA has a split-supply (+V /2) biasing of the detector input and uses the photodiode in the fast but noisy voltage mode. Although +V /2 is common-mode-rejected from the input of U1, CMRR is not infinite and allows some supply noise to be amplified by the PDA. The OP-07 has good input characteristics, including low noise, and would not contribute appreciable drift. It is also costlier than “commodity” op-amps. The wide range of variability of the gain was necessary to cover the variations in mirror transmittance and photodiode sensitivity. The PDA output is scaled to 500 mV/W of output power.
The photodiode was a critical design choice. As the laser output sensor, its scale-factor stability would directly impact accuracy. The photodiode chosen for the application was an EG&G Judson J16 series germanium (Ge) diode with standard p-n structure, suitable for use in the 100 Hz to 100 MHz range. The active detector is circular, with a 1 mm diameter. The responsivity of the diode is typically 0.65 A/W at a 1.3 μm wavelength of input light, and peaks at 1.55 μm at 25o C, slightly above the 1.32 μm NdYAG laser output. The temperature coefficient (TC) of the responsivity (which no amount of feedback could correct) crosses 0 %/o C at 1.55 μm of wavelength and is flat below that, at a TC of –0.1 %/o C. Above 1.50 μm, the curve increases quickly to almost +3 %/o C at 1.8 μm.
The diode also has an equivalent shunt resistance at 25o C of at least 100 kΩ at a reverse voltage of 10 mV, a maximum reverse voltage, VR , of 5 V, and a dark current at this voltage of typically 2 μA and no more than 5 μA. Its capacitance at VR = 0 V is 1 nF.
A plot of J16 output current versus incident power density increases linearity as observed in the specifications. The product specification required that output power not vary more than +/-5 % over a four-hour interval. The conclusion drawn from these specs is that this diode easily meets these requirements.
Given the adequacy of the photodiode, the next question is how best to use it in a circuit. Photodiodes can be used in either of two modes: voltage or current. In voltage mode, a relatively large reverse voltage is applied to the diode. Incident photons generate minority-carrier pairs in the depletion zone of the p-n junction. They are swept toward the opposite-polarity terminal of the diode, creating an output current. Voltage mode has the advantage of reducing the junction capacitance in two ways: by widening the junction, thereby thickening its capacitive dielectric and reducing capacitance; and by reverse bias, which sweeps out of the junction the diffusion charge contribution to diffusion capacitance. The result is a fast diode. The disadvantage is that with the reverse-biased electric field across the junction, minority carriers are accelerated by it, causing avalanche multiplication of carriers. Thermal generation of hole-electron pairs provides the carriers. The result is additional “dark current” – current without incident illumination from the intended light source. In the J16 photodiode, dark current is specified as typically 2 μA at 5 V reverse bias. With a 15 μA fs input from laser light, dark current adds appreciable noise.
For this application, the bandwidth from previous calculations is not demanding, and the voltage mode is not required to meet speed requirements. Consequently, the current mode is more optimal. In current mode, the photodiode is operated with zero volts across it. This has the inconsequential disadvantage of substantially increasing the junction capacitance, thereby slowing the device response. The significant advantage is that the dark current is vastly reduced, to 0.1 μA for 10 mV of reverse bias, as the specs show. This is clearly the optimal mode for this application, and was used in the redesign.
The original design has an even larger limitation; the diode is not resistively loaded, but is left to float, connected to the op-amp non-inverting input. The generated current thus develops a voltage across the internal diode shunt resistance. For a diode reverse voltage of 10 mV, this is specified as typically 100 kΩ. The 2 μA of dark current would develop a voltage of 200 mV across it, leaving the noninverting input at V /2 – 0.2 V. This amount of reverse bias places the diode in more of the current than voltage mode, but the diode output amplified by the op-amp is voltage – voltage dependent upon diode resistance, which has a large TC of a decade per 20o C, or 50 %/o C. This scheme is highly temperature-dependent!
Amplifier Circuit Simplification
The two op-amp ICs of the original design were combined into a dual chopper-stabilized op-amp that has very acceptable input characteristics: the Linear Technology Inc. LTC1051. The input has 0.5 μV of input offset voltage with 10 nV/o C of drift from 0 Hz to 10 Hz, and input noise voltage of 1.5 μV pk-pk from 0.1 Hz to 10 Hz. The gain-bandwidth product is 2.5 MHz. This is an application that could make good use of a chopper-stabilized op-amp, with its excellent input characteristics at a low price. The tradeoff, of course, is that the chopping contributes some digital noise to the front end. The laser loop, however, needs only 70 Hz bandwidth, which is not much noise-bandwidth. The redesigned circuit is shown below.
The gain of the first op-amp stage is a transresistance of R1 or 10.0 kΩ . A zero at 106 kHz is added by the 150 pF capacitor shunting R1 . It frequency-compensates the feedback divider of the op-amp, with its shunt diode capacitance and resistance across the op-amp inputs. The transresistance stage is followed by a low-pass filter with a pole at 100 Hz. This reduces the loop bandwidth and also PDA noise. The second op-amp stage is a voltage amplifier with gain adjustable from about 2.8 to 21. By placing gain calibration in the second stage, the additional sensitivity of the first-stage amplification is avoided. Any drift in the trim-pot will not have the additional gain of the first stage.
For 500 mV/W out and a 15 μA fs input, the overall transresistance needs to be 33.33 kΩ, making the nominal value of second-stage gain 3.33. The gain range could perhaps be better centered around this value. The fraction of laser output power transmitted through the mirror is (15 μA)/(0.65 A/W)x(5W) = 4.6 μ (ppm). This small fraction might be a clue as to why rear pick-off from a first-surface mirror might not be the best way to feed back output power.
The laser system had a –5 V supply, which was also used to extend the low-voltage end of the PDA dynamic range. Adding a supply is not really a simplification, though it was already there to be used, and eliminated the +V/2 divider.
The additional pole-zero compensation of the second stage figures in to the overall loop compensation scheme, a design problem which will be left for the next part of this series.