# The Transimpedance Amplifier Circuit

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## Introduction: The Transimpedance Amplifier Circuit

The Transimpedance Amplifier (TIA) is a useful circuit that allows the circuit-designer to turn light hitting a photodiode into an output voltage. With this circuit in your toolbox, you will be significantly closer to being able to design more advanced circuits such as servomechanisms. This exciting branch of circuits are those that adjust their quiescent voltages and currents through feedback loops to control a desired output. A Transimpedance Amplifier can help in the sense that it proportionally adjusts its output voltage to match the photocurrent generated in a photodiode through illumination. Through a short section on the components of the TIA and a discussion of their particular arrangement, we will arrive at the circuit law Iphoto = Vphoto*R. This article assumes that the reader has been exposed to Ohm's Law and some basic electronics.

## Step 1: 1. the Components

This circuit uses a photodiode, an operational amplifier (Op-Amp), and a resistor. The next section will be devoted to reviewing the properties of these components.

Photodiode

This is a special type of diode made of a semiconductor material that effectively turns incident photons into a current. between its leads.The generated current is named the photocurrent, and can be described as a positive charge that flows from its positive end towards its negative (or its longer lead to its shorter lead). Note that this direction is opposite to the direction of current flow in a regular diode; it is for this reason that the current induced in a photodiode is sometimes called a "leakage current."

Operational Amplifier

Without going into too much detail (as the details get complicated), the operational amplifier is basically a high-gain voltage amplifier that takes two inputs, compares them, and uses the difference to set an output voltage. These two inputs are named the inverting/(-) and noninverting/(+) inputs. The output voltage is capped by two inputs that power the Op-Amp. While different configurations of the Op-Amp result in different behaviors and rules and a full discussion of these behaviors would be unnecessary and lengthy, we can still hone in on two "Golden Rules" of Op-Amps that will make this circuit seem more intuitive. These are...

1. The inputs draw no current.

2. If you connect a wire from the output to the (-) input, then the (-) will set itself to be equal in voltage to the (+) input.

Keeping these rules in mind is key to understanding the properties the TIA.

Capacitor

This is any device that contains two conductive plates separated by a dielectric material and stores electrical potential in an electric field around it. Its complex impedance being 1/jwC, where j is sqrt(-1), w is the angular frequency of the current, and C is the capacitance, the capacitor is used primarily in this circuit to stabilize the output of voltage of the circuit.

Resistor

This is any electronic element that follows Ohm's Law, namely V=IR. In words, the voltage drop across the resistor is equal to the current through it multiplied by the resistance. The complex impedance of this circuit element is simply its resistance, R.

## Step 2: The Basic Transimpedance Amplifier

Layout

Next we will analyze what causes the circuit law Iphoto = Vphoto*R. In the above picture, we see the photodiode on the left connected on its negative end to ground and on its positive end to the inverting/(-) input of the Op-Amp. We also see a wire connecting the output of the Op-Amp to its (-) input, with a resistor of value Rf in series. Thus, no matter what components are attached to the Op-Amp, it is going to set its output voltage such that the (-) input is at the same voltage as the (+) input. As the (+) input is connected to ground, the voltage at the (-) must also be equal to 0V. Such a spot in our circuit that has an electric potential of 0V is called a "virtual ground."

Circuit Law

To find a circuit law, we will need to track where the current is going. As discussed, the induced photocurrent is oriented such that it moves from the negative end of the terminal to the positive end. Moving along to the junction of the inverting input, it becomes clear that as, according to Golden Rule #1, the Op-Amp draws and provides no current, all of the current has to move through the wire containing the resistor. But this resistor follows Ohm's Law, V=IR, and thus there would exist a voltage drop across the resistor equal to Vdrop=Iphoto*Rf. This voltage drop requires there to be this difference across the points to the right and left of the resistor. Since the (-) has to remain a virtual ground (at 0V), the Op-Amp would set the voltage at its output to be able to achieve this voltage drop. Depending on the direction of the current, the output voltage would have the opposite sign in order to enable this voltage drop to occur. Thus, our circuit law arises: Vout=(-Iphoto)*Rf. In particular, this law shows how the "gain" of our circuit is given by the chosen value of our resistor Rf. Note that changing the orientation of the photodiode will reverse the sign of the output voltage.

## Step 3: Stabilization

With our circuit as it is, with only a resistor in the wire connecting the output to the (-) input, the circuit law only truly applies for DC currents induced in the photodiode. In other words, the law only works if the light hitting the photodiode is constant. If the light is being generated by an AC source, the photocurrent will have that same AC frequency. With this AC setting, the response of the circuit becomes increasingly unstable in that there is a lot of high-frequency noise originating from the properties of the Op-Amp. In order to stabilize the voltage output of the TIA, it is customary to add in a capacitor in parallel. This will significantly decrease the noise.

## Step 4: Final Words

With the capacitor added in parallel, the schematic shows the complete layout of a basic transimpedance amplifier. The possibilities that knowledge of this circuit provides are countless, with applications including building light meters and feedback in various circuits that can be found on instructables.

Have fun playing around with this circuit and incorporating it into designs!