# Gas station without pumps

## 2021 June 21

### Controlling current

Filed under: Circuits course — gasstationwithoutpumps @ 11:06
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In the electrode lab this year, students had even more trouble than usual in understanding that the the goal was to provide a constant current to the silver-wire electrodes for a measured time period, in order to produce a known amount of AgCl on the anode.  I will have to rewrite that section of the book for greater clarity.  I also plan to add a circuit that does the constant-current control for them, so that they don’t have to adjust the voltage to get the desired current (a concept that seems to have eluded many of them).

Here is a possible circuit: This circuit provides a current from Ip to Im of Vri/Rsense, as long as the voltage and current limitations of the op amp are not exceeded.

The negative-feedback loop tries to bring the $I_m$ output to the voltage of the $V_{\rm ri}$ input, which is only possible if the current through the sense resistor is $I=V_{\rm ri}/R_{\rm sense}$.  Let’s say that we want 1mA from Ip to Im—then we would set $V_{\rm ri}= (1\,mA) R_{\rm sense} = (1\,mA)(100\Omega) = 100\,mV$.  If $V_{\rm rail}$ is 5V and the op amp is a rail-to-rail op amp, then we could get the desired 1ma of output as long as the load resistance from Ip to Im is less than 4900Ω (well, 4650Ω really, because of the internal resistance of the op amp).  With a higher load resistance, the voltage at Ip would hit the top rail and still not provide the desired current.  There is no lower limit to the load resistance—even with a short circuit the current would be the desired 1mA.

I chose 100Ω for the sense resistor, so that the control voltages do not get too close to the bottom rail, while leaving enough voltage range for fairly large load resistances.  By using 100Ω, it is possible to specify currents up to 50mA, which is beyond the capability of the op amp to supply.  Since the MCP6004 op amps have a short-circuit current of about 20mA with a 5V supply, about the most we can deliver is 14mA for a short-circuit load, because of the internal resistance of the op amp.

Using a 1kΩ resistor might also be reasonable, since the input voltage in volts would then specify the current in mA, but a 1mA output current would limit the voltage across the output ports to $V_{\rm rail} -1\,V$ (which is probably still fine for the electrode lab). With a 1kΩ resistor and a 5V supply, the maximum specifiable current would be 5mA, and the maximum obtainable is about 4mA.  If you needed 2V across the load, then you could not specify more than 2.4mA (still plenty for the electrode lab).

For the electrode lab, the currents required are low enough that this circuit is adequate, but what if we needed more current?  Here are a couple of circuits that can provide that: By using a pFET, we can have the voltage output of the op amp control the current. No current is needed from the op amp, and we just need that Vrail is large enough that the pFET can be fully turned on. If we use a PNP transistor, then we need to turn the voltage output of the op amp into a current for the base.  That current is about 1/50th or 1/100th of the collector current being controlled (depending on the transistor).

Both these designs have the positive and negative inputs of the op amp reversed from the low-current design, because the pFET or PNP transistor provides a negation—the voltage at Im rises as the voltage at the output of the op amp falls.  I reduced to the sense resistor to 10Ω, to allow specifying higher currents (up to 500mA for a 5V supply).  The main limitations on this design are the thermal limitations of the transistor and the resistor—there may be both a large voltage drop and a large current.  The worst case for the transistor is when the load is a short circuit and the voltage at Im is half the power-supply voltage—then the power dissipated in the transistor (and in the sense resistor) is $(V_{\rm rail}/2)^2/10\Omega$.  For a 400mW limitation on the transistor, we would want to limit $V_{\rm rail}$ to 4V.  For a ¼W resistor, we would want to limit $V_{\rm ri}$ to 1.58V (specifying 158mA), or up the resistor to 100Ω for a 5V limit (but then we could only specify up to 50mA).  We really need a 2.5W resistor if we want to have 10Ω and a 5V supply and use the full range.

For the book, I think I’ll just present the low-current version of the current control—we don’t need the high-current version, and students are likely to request too much current for the electroplating if they have it available (errors in computing the area of the electrodes that are off by a factor of 100 are pretty common—mixing up $({\rm mm})^2$ and $({\rm cm})^2$, for example).

## 1 Comment »

1. […] which talks about providing a constant current for electroplating (see the post Controlling current if you don’t want to waste time watching an 11-minute […]

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