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Circuits, electronics and noise
Transimpedance amplifier output voltage
Output of an ideal transimpedance amplifier whose non-inverting input is held at Vref and whose feedback resistor Rf sets the conversion.
- Ref
- ELN-30
- Rev
- v1
- Field
- Circuits, electronics and noise
- Result
- Vo [V]
A transimpedance amplifier turns an input current into a voltage. With the non-inverting input at Vref, the inverting node also sits at Vref and the current Ii flows through Rf, so Vo = Vref − Ii Rf. A positive current into the inverting node lowers the output. The gain is Rf in volts per amp, so it is set by one resistor; a small capacitor across Rf is needed to keep a photodiode input stable.
Output of an ideal transimpedance amplifier whose non-inverting input is held at Vref and whose feedback resistor Rf sets the conversion. A positive input current into the inverting node lowers the output.
Calculator
- Transimpedance gain, −Rf−1,000,000 V/A
- Voltage drop across Rf, Ii Rf2 V
- Largest current before the output reaches 0 V2.5×10−6 A
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- A 2 µA photocurrent through 1,000,000 Ω moves the output 2 V below the 2.5 V reference, to 0.5 V.
- A larger Rf gives a larger signal and, since its noise rises only with the square root of Rf, a better signal-to-noise ratio.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (V) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Rf Feedback resistor | 1,000 to 1e8 Ω | −197.5 | 2.498 | 200 | +10% | −40 % |
| Ii Input current into the inverting node | 1e-9 to 1e-4 A | −97.5 | 2.499 | 100 | +10% | −40 % |
| Vref Reference voltage at the non-inverting input | 0 to 5 V | −2 | 3 | 5 | +10% | +50 % |
Sweep of Feedback resistor
| Feedback resistor (Ω) | Output voltage (V) |
|---|---|
| 1,000 | 2.498 |
| 4,217 | 2.492 |
| 17,780 | 2.464 |
| 74,990 | 2.35 |
| 316,200 | 1.868 |
| 1,334,000 | −0.167 |
| 5,623,000 | −8.747 |
| 2.371e7 | −44.93 |
| 1e8 | −197.5 |
Sweep one variable
Variables and how each one contributes
Output voltage
What the equation gives you. Everything else feeds it.
Reference voltage at the non-inverting input
The reference voltage at the non-inverting input, in V. Shifts the output up one for one. Raising it by 10 % (to 2.75) moves the result by +50 %, from 0.5 to 0.75 V.
Input current into the inverting node
The input current into the inverting node, in A. A larger current lowers the output in direct proportion. Raising it by 10 % (to 2.2×10−6) moves the result by −40 %, from 0.5 to 0.3 V.
Feedback resistor
The feedback resistor, in Ω. A larger Rf gives more volts per amp, so the output drops further. Raising it by 10 % (to 1,100,000) moves the result by −40 %, from 0.5 to 0.3 V.
Worked example with the values above
- Drop across Rf: Ii Rf = 2×10−6 × 1,000,000 = 2 V.
- Subtract from the reference: 2.5 − 2.
- Vo = 0.5 V.
Assumptions and limits
- An ideal op amp with infinite gain and no input current, in its linear range with negative feedback.
- Output limited only by the supply, and signals within the useful bandwidth.
Common mistakes
- Forgetting that a current into the inverting node lowers the output.
- Leaving out a small capacitor across Rf, so the circuit oscillates with a photodiode.
- Ignoring the bias current and the leakage of the diode.
Statistics and uncertainty
Resistor tolerances set the gain accuracy, so use 1 % parts or better for precision, and a matched network for the difference amplifier, where mismatch converts common-mode voltage into error. Real op amps add offset, bias current and finite gain.
Where it is used
- Signal mixing, scaling, integration and current-to-voltage conversion in instrumentation.
- Photodiode, sensor and ramp-generator circuits.
Maths you need
- Virtual ground: the inverting input sits at the non-inverting voltage
- Negative feedback: the output acts to cancel the input difference
- Kirchhoff’s current law: currents at a node add to zero