Transimpedance amplifier (TIA)

A photodiode produces a current proportional to optical power, and nearly everything downstream wants a voltage. A transimpedance amplifier makes the conversion by driving the photocurrent $I_p$ through a feedback resistor $R_f$ around an inverting amplifier, so that the output is $V_{out} = -I_p R_f$ and the gain is quoted in ohms (or dBΩ in optical receivers). The inverting input is held at virtual ground, which keeps the voltage across the diode constant whatever the light level; the diode's capacitance is therefore never charged and discharged by the signal, and that is the property that makes the circuit worth its complexity.

The comparison with the simplest alternative, a load resistor, shows why. A photodiode of capacitance $C_{in}$ (diode plus amplifier input) loaded by $R$ has a bandwidth of $1/(2\pi R C_{in})$: 15.9 MHz for 10 kΩ and 1 pF. The same 10 kΩ used as $R_f$ in a TIA whose amplifier has gain-bandwidth product $GBW$ gives, to first order,

which is 126 MHz for $GBW$ = 1 GHz: the same transimpedance at eight times the bandwidth. A small feedback capacitor $C_f$ across $R_f$ is needed to keep the loop stable, and choosing it is most of the practical design; too small and the response peaks or oscillates, too large and it limits the bandwidth to $1/(2\pi R_f C_f)$.

Noise

The feedback resistor contributes thermal noise current $\sqrt{4k_BT/R_f}$ at the input, which is why sensitive receivers use the largest $R_f$ the bandwidth allows. Setting it equal to the shot noise of the photocurrent, $\sqrt{2eI_p}$, gives the photocurrent above which the receiver is shot-noise limited, $I_p = 2k_BT/(eR_f)$.

The table is computed from the two expressions above. It omits the amplifier's own noise, which enters in two parts: its input current noise adds directly, and its input voltage noise $e_n$ appears across $C_{in}$ and produces a current noise $e_n \cdot 2\pi f C_{in}$ that rises with frequency. In wideband receivers this $e_nC$ term, not the resistor, usually dominates the integrated noise, which is why low-capacitance diodes and short connections to the amplifier matter as much as the amplifier's datasheet noise figure. The combined input-referred noise current divided by responsivity is the receiver's noise-equivalent power, and it sets receiver sensitivity when the signal is weak.

In optical links and in the lab

In a data receiver the TIA sits millimeters from the diode, often in the same package, and is followed either by a limiting amplifier (NRZ, and the classic TIA, limiting amplifier and clock recovery chain of a burst-mode receiver) or kept linear for PAM4 and coherent signals, where the DSP needs the waveform intact. Linear pluggable optics depend on exactly this linearity, because the host equalizer sees whatever the TIA passes. On a measurement bench the same circuit appears as a switchable-gain current amplifier, and the gain setting chosen for a photodetector characterization or a RIN measurement fixes both the bandwidth and the noise floor of the result; balanced detection subtracts two photocurrents before a single TIA so that common-mode intensity noise never reaches it.

References: E. Säckinger, Analysis and Design of Transimpedance Amplifiers for Optical Receivers (Wiley, 2017); J. G. Graeme, Photodiode Amplifiers: Op Amp Solutions (McGraw-Hill, 1996).