Transimpedance amplifier

A transimpedance amplifier (TIA), also called a current-to-voltage converter, is an amplifier whose output voltage is proportional to its input current. The constant of proportionality is a resistance, the transimpedance, in volts per ampere. The common circuit is an inverting operational amplifier with a resistor between its output and its input: the amplifier holds the input at a fixed potential, the current has nowhere to go but through the resistor, and the output is the voltage the current drops across it. A feedback resistor of 1 GΩ turns 1 pA into 1 mV.

The circuit converts photodiode currents into voltages, the use taken as the example in a Texas Instruments application report on compensating it.^[1] It is also the first stage of a patch clamp amplifier, and so of most instruments that record the ionic current through a nanopore, where the currents are picoamperes to nanoamperes and the noise of the first stage sets what the instrument can see. The guide published by Molecular Reality Corporation describes its EDR4, a four-channel patch-clamp amplifier, as "the instrument that applies the voltage and hears the current".^[2]

In the inverting circuit the non-inverting input sits at a reference potential V_ref. Feedback drives the inverting input to the same potential, a virtual ground, so the source of the current sees a load of almost zero impedance and the current I flows through the feedback resistor R_f:

In a patch-clamp amplifier the command potential is applied as V_ref, so the circuit that measures the current also holds the electrode at the commanded voltage, which is why the technique is called voltage clamp. In a nanopore cell one Ag/AgCl electrode connects to the input of the amplifier and the pore current flows into it; the voltage across the pore is the difference between the potentials of the two electrodes.

The resistor sets the first limit. Its thermal noise (Johnson-Nyquist noise) appears as a current of density √(4k_BT/R_f), which at 25 °C is 128 fA/√Hz for 1 MΩ and 4.1 fA/√Hz for 1 GΩ; in a band of width B the root-mean-square current is that density times √B. Raising R_f lowers the noise, and it lowers the largest current the stage can pass without clipping, since the output cannot swing past the supply: with an output limit of ±2.048 V, 1 GΩ clips at ±2.048 nA and 1 MΩ at ±2.048 µA. Gain, range and noise are bought against each other.

A second term rises with frequency. The amplifier's input voltage noise e_n appears across the capacitance C at its input, which is the amplifier's own, that of the wiring, and that of the membrane and its support, and drives a current 2πf C e_n into the summing node. Integrated from zero to B, the root-mean-square value is

so doubling the bandwidth multiplies this noise by 2^3/2, about 2.8. Above 10 kHz it is the dominant term in many nanopore recordings, and the review that makes the point lists the capacitance of the chip as the quantity to attack: glass chips reduced it to under 1 pF from over 300 pF for standard silicon ones.^[3]

With 30 pF at the input, the voltage-noise term of an amplifier like the LMP7721, whose datasheet gives 6.5 nV/√Hz at 1 kHz, equals the thermal noise of a 1 GΩ resistor at 3.3 kHz and exceeds it above that, so a bigger resistor stops helping while the events are still slow. Pore current itself adds shot noise of density √(2qI), 23 fA/√Hz at 1.7 nA, and the amplifier's input bias current, 3 fA typical for the LMP7721, is a current of about 19,000 electrons a second, one for every million or so of the 1.9 × 10¹⁰ charges a second in a pore carrying 3.1 nA.^[4]

Input capacitance forms a pole with the feedback resistor, and with it the amplifier can oscillate. Datasheet guidance for the LMP7721 is that if the pole falls below about 6 to 10 times the intended −3 dB frequency, a feedback capacitor C_f is needed, and the typical input capacitance of the part is about 11 pF.^[4] That capacitor sets its own pole at 1/(2πR_fC_f). Texas Instruments' application report puts the stable choice at

where GBW is the gain-bandwidth product. The bandwidth falls only as the square root of the feedback resistance, and the report's advice for wide bandwidth is a moderate transimpedance stage followed by a broadband voltage-gain stage.^[1] The last two columns of the table are these expressions evaluated for the amplifier described above.^[a]

A 1 GΩ resistor in parallel with 2 pF has a corner at 80 Hz, and holding a corner of 10 kHz at that resistance needs a total feedback capacitance of about 16 fF, less than the 0.1 pF that the bill of materials of the MR1 design gives as the limit for the shunt capacitance of its 1 GΩ resistor.^[5]

A femtoampere input is also a leakage problem. Surface resistance across a circuit board between the input trace and a neighbor at another potential carries current straight into the summing node: 1 V across 10¹⁴ Ω leaks 10 fA. The datasheet's remedy is a guard, "a driven trace or shield that physically surrounds the input trace and feedback circuitry that is held at a potential equal to the average input signal potential", so that stray current goes into the guard and not the input. Unconnected pins sit between the input and the supply pins of the package, so the guard can run beside the input right up to the chip.^[4] The MR1 schematic ties those pins to the net that also feeds the non-inverting input.^[6]

Most nanopore papers use a commercial patch-clamp amplifier, and the company's live stream samples its EDR4 at 200 kHz, one value every 5 µs.^[2] Smeets and colleagues, who measured the noise of solid-state pores, used an Axopatch 200B in resistive feedback mode, an external 8-pole Bessel filter at 49.9 kHz, and a digitizer at 250 or 500 kHz.^[7]

The fast events defeat it. Rosenstein and colleagues note that nucleic acids move through solid-state pores at 10 to 1,000 ns per base, and that "the signals from nanopores represent a flux of several billion ions per second" while measurements had been "constrained to bandwidths below 100 kHz owing to comparatively high background noise". They give the Axopatch a discrete 500 MΩ feedback resistor, with a thermal noise density of 5.7 fA/√Hz. They placed a custom CMOS amplifier next to the pore, replaced the resistor with a servo loop around a low-noise current source, and compared the two at 100 kHz: 3.2 pA RMS against 9 pA RMS for the Axopatch.^[8] A successor amplifier reached an SNR above 10 for single-stranded DNA at 5 MHz, with transient features as short as 200 ns.^[9] In the review of nanopore noise cited above, the on-chip designs have a total input capacitance near 4 pF.^[3]

In the open design of the MR1 Nanopore Reader an LMP7721 transimpedance stage sits on an amplifier board under the cartridge, and the repository describes it in two ways that do not agree. What follows compares the repository as it stood on October 24, 2026. Nothing has been built or measured, and the labels follow the project's own convention: "documented" for what the text and the bill of materials say, "as drawn" for what the schematic contains.^[6][5][10]

The gap is a factor of 100 in gain. A documented noise floor of 1.2 pA is plausible for a 1 GΩ stage, whose resistor alone contributes 0.41 pA in 10 kHz, and impossible for the drawn one: the thermal noise of the 1 MΩ resistor is 12.8 pA in that band, and no stage built around that resistor can be quieter. The documented bandwidth is the harder case to reconcile. A 1 GΩ resistor with the 2 pF listed beside it has a corner at 80 Hz, and the documents give a bandwidth of about 1 to 10 kHz; the drawn pole of 79.6 kHz belongs to the 1 MΩ resistor with the same 2 pF. The host software assumes 1 GΩ and a converter reference of 4.096 V, where the specification says 2.048 V.^[12]

One amplifier cannot match both descriptions. Later documents add a second route, a 100 kΩ stage with an OPA192 for pores 10 to 100 µm wide, and keep the 1 GΩ route for pores under 5 nm. The interposer specification also suggests switching the feedback resistor to 100 MΩ, 10 MΩ or 1 MΩ for larger pores, and the drawn 1 MΩ is among those alternatives.^[5][13] A README line credits the LMP7721 with "sub-femtoampere leakage", which is not a datasheet figure: the datasheet gives 3 fA typical and 20 fA at most at 25 °C.^[14][4] Other links of the chain are described in Analog front end.

• Analog front end
• Johnson-Nyquist noise
• Nanopore noise
• Axopatch 200B
• Bessel filter