Current to Voltage Converter, Pt 1 - Background

Electronics

Since this is a new website, I am going to start documenting some of the electronics projects that are currently in the works. The first up is my new photo-current amplifier circuit, lovingly named I2V_v3 (current to voltage converter version 3) by the very clever marketing department in my head. Since the project is nearing completion I will be documenting the development process with the benefit of hindsight, which of course means to anyone reading these notes that it will be written completely in hindsight. Which may or may not be useful depending on what you are trying to get out of this.

Background

To set the scope lets discuss what the heck a current to voltage converter is, why I need one, and (the most important question) why the heck couldn't I just buy one.

As you may have guessed a current to voltage converter is a device for making a voltage output that has a well-defined relationship to an input current.

Super simple top-level diagram

As you might imagine, in a lab that relies heavily on lasers a device that can produce an electrical signal proportional to the laser power is a pretty important device for many applications. In particular I need a low noise power detector with a large frequency bandwidth (~1 MHz) which will be used for power monitoring and to correct small changes in laser power, since laser power fluctuations can be the limiting factor in the dephasing of the fragile atomic qubits we create. So this will act as the detection stage in the laser power stabilization system we are creating, and could potentially limit the effectiveness of the whole system if incorrectly designed.

Usually they are used with devices that produce very small currents, that would be too small to transmit to another detector without significant noise pickup. Most inputs will expect a voltage and therefore be high impedance, causing large voltage inputs (1 MOhm * 1 mA = 1 kV) assuming the the detector could even supply the necessary voltage to maintain linearity on an oscilloscope. Even if you are driving a device with a 50 Ohm input you can potentially have a huge(!) current loop with a 50 Ohm impedance causing you to pick up lots of unwanted noise, since if the EMI is constant the current pickup will be lower for lower impedance loops.

Mutual inductance! My only weakness!

In addition, driving a transmission line is a tricky business and high speed signals have to be properly impedance matched so that reflections don't cause weird behavior and there is maximal power transfer at all interfaces. Finally, the capacitance of 1 meter of RG-58 cable is about 100 pF, driving a 1 MOhm terminated input directly would have a time constant of about 600 us. For a 50 Ohm terminated input that drops to 30 ns. I'm not going to do a full transmission line analysis here (at least yet), but lets all just promise we won't use a photo-diode to directly drive an oscilloscope input and expecting to see any AC characteristics worth mentioning.

What did I just say?!?

Ok, so we can't drive a device that is expecting a voltage input with a current input or we'll have bad times. The answer is therefore obvious(!), we need to convert it to a voltage signal first. How can we do it? Well that is exactly what a resistor does V=IR. How is that different from the all those things I was just yammering on about? Because of where we are going to put the resistor in the implementation, of course! By putting the resistor right next to the device creating the current signal, we minimize the physical dimensions of any low impedance loops, where the area of the loop is the important factor. This minimizes noise current pickup since the big loop has the input impedance of the measurement device.

A better passive schematic

This scheme will work but it has limited transimpedance (that's what its called when a current is turned into a voltage) since it will be limited by the input impedance of the measurement device, because they are effectively in parallel. In order to remedy this situation one might consider inserting a voltage follower that decouples the voltage generation (I*R) from the transmission line and input impedance of the measurement device, so now we can safely have a large transimpedance and still drive a standard input impedance of 50 Ohms.

Let's get active

This isn't a great design though since the current producing device still has to drive the current through the resistor and with a large transimpedance the capacitance of, for example, a photo-diode limits the bandwidth significantly. A much better design will instead send the current through a feedback resistor on the op amp. This has the advantage that the current source sees a virtual ground on the op amp input, stated another way it see sees an (ideally) 0 input impedance.

A better active transimpedance amplifier

Of course here in the real world, with a finite open-loop gain op amp, the input impedance is not 0, but instead Z = Rf*f/GBW, where f is the signal frequency and GBW is the op-amp's gain bandwidth product. Interestingly enough, this means that the transimpedance amplifier looks like an inductor with value L = Rf/(2*pi*GBW). So what does that mean for the circuit? Well, any parasitic capacitances will create a resonant LC circuit which can cause significant amounts of high frequency noise to be detected, and you will see a corresponding gain bump in the Bode plot near the edge of the bandwidth.

Thats one sub-optimal bump!

To fix this all we need to do is add a capacitor Cf in parallel with Rf to limit the closed-loop op-amp gain so that where the bump would occur the gain is already dropping off.

And here we are a circuit we can now continue to optimize

We'll look at some of the application specific features we are going to want to have in the next entry.