Transimpedance Amplifier

Why a photodiode is a current source

A photodiode is fundamentally a current-output device. Each absorbed photon with energy above the bandgap creates one electron-hole pair, and the pair gets swept out of the depletion region by the built-in electric field. At 850 nm in silicon, with a typical 50 percent quantum efficiency, one milliwatt of incident optical power produces about 340 microamps of photocurrent. The current is linear with light over six to seven decades, from picoamps in starlight to tens of milliamps in direct sunlight, as long as the diode is held at zero or fixed reverse bias.

The natural temptation is to "convert" that current to voltage by simply putting a resistor across the diode. It works — but badly. As current flows through the resistor, voltage develops across both the resistor and the photodiode. The diode is now forward-biased by that voltage, which changes its junction capacitance, its dark current, and its response linearity. A 1 microamp signal across a 1 megohm load gives 1 volt across the diode, deep into the I-V curve's nonlinear elbow. The response is no longer proportional to light; the bandwidth collapses; the noise is set by the resistor's thermal floor with no way to improve it. For any application that wants linearity over more than 30 dB of dynamic range, the passive resistor solution is dead in the water.

A transimpedance amplifier solves all three problems at once. The op-amp's inverting input is a virtual ground — the op-amp drives its output until the inverting and non-inverting inputs match in voltage, and since the non-inverting input is grounded, the inverting input sits at zero. The photodiode's anode is tied to that virtual ground; its cathode is grounded (photovoltaic mode) or reverse-biased (photoconductive mode). The diode's voltage is fixed regardless of current. All the photocurrent has nowhere to go but through R_f, where it produces V_out = -I_in·R_f. The output voltage is exactly proportional to the photocurrent, the diode sees zero or fixed bias, and the gain can be made huge by simply picking a big R_f.

Worked example: a pulse oximetry front-end

Concrete numbers make the design choices stick. A pulse oximeter uses two LEDs (red 660 nm and infrared 940 nm) shining alternately through a fingertip onto a single silicon photodiode. The signal of interest is the small modulation of transmitted light by the arterial pulse — roughly 1 percent of the DC light level, at 0.5 to 5 Hz heart-rate frequencies.

Photodiode (BPW34-class):
  Active area      7 mm²
  Junction cap C_d 70 pF at 0 V bias
  Responsivity     0.55 A/W at 850 nm
  Dark current     2 nA

Light through fingertip:
  Incident optical power on diode    50 μW (typical)
  Steady photocurrent     50e-6 W × 0.55 A/W = 27.5 μA
  Pulse modulation         ≈ 1% → 275 nA peak-peak

TIA design:
  R_f = 100 kΩ → DC output = 27.5 μA × 100 kΩ = 2.75 V (in op-amp range)
  Pulse signal at output  = 275 nA × 100 kΩ = 27.5 mV peak-peak
  Op-amp: low-bias-current FET input (input bias < 10 pA so doesn't add to signal)
  C_f for stability with C_d = 70 pF, GBW = 10 MHz:
     f_zero = 1 / (2π·R_f·C_d) = 1 / (2π·100k·70p) = 22.7 kHz
     f_opt  = √(f_zero · GBW) = √(22.7k · 10M) ≈ 477 kHz
     C_f = 1 / (2π·R_f·f_opt) = 1 / (2π·100k·477k) ≈ 3.3 pF
  Signal bandwidth: 1 / (2π·R_f·C_f) = 1 / (2π·100k·3.3p) ≈ 482 kHz

The 482 kHz signal bandwidth is hugely overkill for the 5 Hz heart rate, so we cascade the TIA into a 10 Hz active low-pass filter that throws away noise outside the pulse band. The TIA's job is just to do the current-to-voltage conversion with no instability, no nonlinearity, and dark-current contribution below the signal — and the rest of the chain does the filtering and amplification. That cascade — TIA → DC blocking and gain → bandpass filter → ADC → SpO2 algorithm — is essentially the entire signal path of a pulse oximeter.

The stability problem and the compensation capacitor

The textbook ideal of "V_out = -I_in·R_f" works fine in DC. At high frequencies the photodiode's junction capacitance C_d (the inverse-bias depletion-region capacitance, anywhere from 1 pF on a small high-speed diode to several nanofarads on a large area-cooled APD) sits from inverting input to ground. From the op-amp's point of view, R_f and C_d form a feedback network whose noise gain (1 / β, where β is the feedback factor) rises with frequency. There's a corner frequency f_z = 1 / (2π·R_f·C_d) above which the noise gain transitions from 1 to a rising +20 dB/decade.

If the op-amp's open-loop gain has rolled off to unity (the gain-bandwidth product, GBW) inside that noise-gain rise, the closed-loop circuit has too little phase margin and oscillates. Big photodiode + big R_f + fast op-amp is the classic recipe for an ugly multi-megahertz ringing on every output edge. The cure is the compensation capacitor C_f, a small picofarad cap in parallel with R_f. C_f puts a pole in the noise gain at f_p = 1 / (2π·R_f·C_f). If C_f is sized so f_p sits at the geometric mean of f_z and GBW, the noise gain levels off before crossing the open-loop curve, and the loop has roughly 45 to 65 degrees of phase margin — well damped, no ringing.

Photoreceiver front-end comparison

Front-end	Topology	Linearity	Bandwidth	Dynamic range	Typical use
Passive resistor	R across diode	Poor (1 decade)	R·C limited	20 dB	Crude on-off detect
Standard TIA	Op-amp + R_f + C_f	Linear 6 decades	kHz to 100 MHz	120 dB	Fiber, LIDAR, oximeter
Switched-gain TIA	TIA + relay-switched R_f	Linear in each range	kHz	Effective 200 dB	Light meters, photometry
Logarithmic TIA	Op-amp + diode feedback	Logarithmic by design	Hz-kHz	140 dB single range	Densitometers, lux meters
Bootstrapped TIA	TIA with cathode driven	Linear 6 decades	10× faster	120 dB	High-speed APD readout
Integrating TIA	Reset-and-integrate	Linear by integration	Pixel-rate	140 dB with cooling	CMOS imagers, X-ray

The standard TIA is the workhorse. The variants exist because real applications run into one of the standard topology's three weak spots — limited dynamic range without changing R_f, bandwidth limit set by R_f·C_d, or noise. Switched-gain TIAs ladder R_f values under microcontroller control to cover seven decades of light from photographic daylight to a single photon per millisecond. Logarithmic TIAs put a diode (or a transistor wired as a diode) in the feedback path so V_out is proportional to log(I_in), giving 140 dB of compressed range in one stage — exactly what an analog densitometer or a starlight imager wants. Bootstrapped TIAs drive the photodiode's cathode with a buffered copy of the inverting-node voltage, cancelling the C_d displacement current and gaining roughly an order of magnitude in bandwidth. Each variant trades complexity for a particular performance corner.

Why TIAs matter

• Optical communications. Every fiber receiver, from gigabit Ethernet to 400G coherent links, starts with a TIA bonded to the photodiode.
• LIDAR. Avalanche-photodiode TIAs detect the picojoule reflected pulse from a 200-meter object in under 10 ns.
• Medical instrumentation. Pulse oximetry, blood-gas analysis, spectrophotometers, scintillation gamma counters.
• Industrial sensing. Particle counters, smoke detectors, gas analyzers, encoder reading heads.
• Consumer optics. Optical computer mice, barcode scanners, autofocus IR sensors.
• Scientific imaging. Photomultiplier tube anodes, single-photon avalanche diodes, CCD/CMOS pixel readout.
• Quantum experiments. Trapped-ion fluorescence detection, single-photon homodyne detectors.

Common misconceptions

• Bigger R_f is always better. Gain grows linearly with R_f but bandwidth falls linearly and stability gets harder; pick R_f for the smallest signal, not the headroom.
• C_f is optional. Without C_f a TIA with non-negligible C_d will ring or oscillate; it's a stability requirement, not a tuning luxury.
• FET op-amps always win. Low input current matters at huge R_f, but FET op-amps have higher voltage noise — for low R_f, a bipolar op-amp is better.
• Photovoltaic mode is always best. It's lower noise but slower; LIDAR and fiber need photoconductive mode to hit gigahertz bandwidths.
• Layout doesn't matter at low frequency. The high-impedance node is the most sensitive in analog electronics; guard rings and short traces matter even at DC.
• Dark current is negligible. At room temperature, dark current adds shot noise that can dominate at low light; cooling or chopping is needed for sub-femtoamp signals.