Transimpedance amplifier

In electronics, a transimpedance amplifier (TIA) is a current to voltage converter, almost exclusively implemented with one or more operational amplifiers (opamps). The TIA can be used to amplify the current output of Geiger–Müller tubes, photo multiplier tubes, accelerometers, photodetectors and other sensors (that are modeled well as a current source) into a usable voltage. Current to voltage converters are used with sensors that have a current response to their measured physical quantity that is more linear than their voltage response. This is the case with photodiodes where it is not uncommon for the current response to have better than 1% nonlinearity over a wide range of light input. The transimpedance amplifier presents a low impedance to the sensor and isolates it from the output voltage of the operational amplifier. In its simplest form (Fig. 1), a transimpedance amplifier is just an opamp with a large-valued feedback resistor, Rf. This resistor sets the amplifier's transimpedance (i.e. its change in output voltage divided by its change in input current, sometimes simply referred to as "gain") to -Rf. This is negative since the amplifier is in an inverting configuration. There are several different configurations of transimpedance amplifiers, each suited to a particular application. The one factor they all have in common is the requirement to convert the low-level current of a sensor to a voltage. The gain, bandwidth, as well as current and voltage offsets change with different types of sensors, requiring different configurations of transimpedance amplifiers.

DC operation In the circuit shown in Figure 1, a sensor (represented as a current source) such as a photodiode is connected between ground and the inverting input of the opamp. The other input of the opamp is also connected to ground, so the non-inverting input becomes a virtual ground. This provides a low-impedance load for the photodiode, which keeps the photodiode voltage low. The photodiode operates in photovoltaic mode with no external bias. The high gain of the opamp keeps the photodiode current equal to the feedback current through Rf. The input offset voltage due to the photodiode is very low in this self-biased photovoltaic mode. This permits a large gain without any large output offset voltage. This configuration is used with photodiodes that are illuminated with low light levels and require a lot of gain. The DC and low-frequency gain of a transimpedance amplifier is determined by the equation

− I in = V out R f , {\displaystyle -I_{\text{in}}={\frac {V_{\text{out}}}{R_{\text{f}}}},}

so

V out I in = − R f . {\displaystyle {\frac {V_{\text{out}}}{I_{\text{in}}}}=-R_{\text{f}}.}

This ratio is in units of resistance, which in SI units are ohms (Ω), and is more technically called transimpedance instead of gain (which is a dimensionless quantity). If the gain is large, any input offset voltage at the non-inverting input of the opamp will result in an output DC offset. An input bias current on the inverting terminal of the opamp will similarly result in an output offset. To minimize these effects, transimpedance amplifiers are usually designed with field-effect transistor (FET) input opamps that have very low input offset voltages.An inverting TIA can also be used with the photodiode operating in the photoconductive mode, as shown in Figure 2. A positive voltage at the cathode of the photodiode applies a reverse bias. This reverse bias increases the width of the depletion region and lowers the junction capacitance, improving the high-frequency performance. The photoconductive configuration of a transimpedance photodiode amplifier is used where higher bandwidth is required. The feedback capacitor Cf is usually necessary to improve stability.

Bandwidth and stability

The frequency response of a transimpedance amplifier is inversely proportional to the gain set by the feedback resistor. The sensors which transimpedance amplifiers are used with usually have more capacitance than an opamp can handle. The sensor can be modeled as a current source in parallel with a capacitance C i {\displaystyle C_{\text{i}}} , as shown in Figure 3. This capacitance across the input terminals of the opamp, which includes the internal capacitance of the opamp, introduces a low-pass filter in the feedback path. The low-pass frequency response of this filter can be characterized as the feedback factor:

β = 1 1 + R f C i s , {\displaystyle \beta ={\frac {1}{1+R_{\text{f}}C_{\text{i}}s}},}

When the effect of this low-pass filter response is considered, the circuit's response equation becomes:

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