# Gas station without pumps

## 2016 June 25

### Pulse monitor with log-transimpedance amplifier

Filed under: Uncategorized — gasstationwithoutpumps @ 02:04
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I’ve been planning since the Santa Cruz Mini Maker Faire to wire up an optical pulse monitor with a log-transimpedance amplifier as the first stage, so that I could use the pulse monitor in full sun or in a dimly lit room, with a dim green LED or with a bright infrared LED. The idea is to make the output of the first stage proportional to the log of the photocurrent, rather than to the photocurrent, then use a band-pass filter to get rid of the DC component and any 60Hz fluctuation, leaving only the fluctuation due to the pulse.

This pulse signal should be independent of the overall light level but on the absorbance of the finger, because
$\log(I) = c + \log(\mbox{transmitted}) = c+ \log(\mbox{illumination}) + \log(\mbox{transmitted}/\mbox{illumination}$, for some constant $c$. If the illumination is constant or has only high-frequency components, then the bandpass filter will eliminate both $c$ and $\log(\mbox{illumination})$, leaving only the absorbance $\log(\mbox{transmitted}/\mbox{illumination})$.

I deliberately did not start working on it until I had finished my grading for the quarter, so only got it built last week, just before going to Montreal for a family reunion of my wife’s family. So I’m only now getting around to blogging about it.

To make the log-transimpedance amplifier, I need a component where the voltage is proportional to the log of the current.  For this I used a diode-connected PNP transistor:

The base-to-emitter diode has a current that is exponential in the voltage, and the collector-to-emitter current is proportional to the base-to-emitter current, at least until the transistor approaches saturation (which starts around 10mA).

The A1015 PNP transistor has a voltage proportional to the log of current, with about 60mV/decade. I did not use a unity-gain buffer when measuring the voltage and current, connecting the Teensy ADC channels A10 and A11 directly to the emitter and base+collector of the transistor. Measurements at less than 5µA were difficult, because the high impedance of the sense resistor made the ADC measurements inaccurate.

I tried a pulse monitor using the A1015 PNP transistor as the log-impedance element, and it worked ok, but I can do better, I think, using an IR LED as the log-impedance element:

The WP710A10F3C IR LED has a low forward voltage, and can be used from 100nA to 30mA, given that we don’t need high accuracy on the log function. We get about 105mV/decade, so it is more sensitive than the A1015 transistor. Note: I did use a unity-gain butter for these measurements, which allowed me to get down to about 50nA—still much higher than the photocurrents I observed in very low light.

The IR LED has a wide range over which the voltage is the logarithm of the current, or $\frac{dV}{dI} \approx 241mV/I$. For 10nA, the equivalent gain is about 24MΩ, and for 1µA, the gain is about 240kΩ. For 10pA (about the smallest current I’ve observed for operating the pulse monitor in very dim light), the equivalent gain is 24GΩ.

This amplifier uses only 3 op amps: a log-transimpedance stage with an IR LED as the impedance and two bandpass inverting amplifiers.

The 330pF capacitor in parallel with the log-impedance is very important—without it I get very short glitches which the next two stages lengthen into long glitches in the passband of the filters.  Making the capacitor larger reduces the glitches, but makes the corner frequency of the effective low-pass filter too low when light levels are very low, and the signal is attenuated.  Any smaller, and the glitches don’t get adequately removed.

I have tested the pulse monitor over a wide range of light levels, with a DC output of the first stage from 234mV to 1.033V, corresponding to photocurrents of 11pA to 463µA, a range of 42 million (7.6 decades). At very low light levels, the signal tends to be buried in 60Hz interference, but if I ground myself, it is still usable.

In very low light, the capacitive coupling of 60Hz noise buries the signal, but the bandpass filters help recover it.

At high light levels, it is easy to get clean signals, as the 60Hz interference is swamped out by the large photocurrent.

Note that the voltage swing is almost independent of the overall light level, as it depends only on the percentage fluctuation in opacity of the finger, which depends mainly on how much pressure is applied. If you get the pressure on the finger close to the mean arterial pressure (so that the finger throbs), you can get quite a large change in opacity—I’ve computed changes of 17% in opacity.

## 1 Comment »

1. […] on having students do a log-transimpedance amplifier for the optical pulse monitor lab (see Pulse monitor with log-transimpedance amplifier). Previously I’ve looked at V-vs-I curves for base-emitter junctions and for the IR […]

Pingback by More thoughts on log-transimpedance for pulse monitor lab | Gas station without pumps — 2016 August 12 @ 18:32

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