# Transimpedance amplifier calculating feedback capacitor

What is the correct way to calculate $$\C_F\$$ of the transimpedance amplifier? Since I have seen two different documents, and each has a different way to calculate it.

These two documents are:

1. Akshay Bhat, "Stabilize Your Transimpedance Amplifier", Application Note 5129, February 3, 2012.
2. John Caldwell, "Transimpedance Amplifiers: What Op Amp Bandwidth do I Need? Parts I, II and III" Texas Instruments Precision Hub Blog, May 8, 2014.

According to Bhat (Maxim), $$\C_F\$$ should be calculated by the following equation (here for the original picture) $$C_F=\frac{1}{4\pi R_F f_\text{GBWP}}\left(1+\sqrt{1+8\pi R_F C_i f_\text{GBWP}}\right)$$ where

• $$\f_\text{GBWP}\$$ is the 60% of unity gain bandwidth of the OpAmp, while
• $$\C_i\$$ is its input capacitance (including the junction capacitance of the input photodiode).

According to Caldwell (TI), $$C_F \ll 1/(2\pi R_ff_P)$$ where $$\f_p\$$ is the pole frequency associated to the feedback loop.

• CF may work out to pico-farads (or less), and doesn't include printed circuit board parasitic capacitance. CF may need a different value once a printed circuit board layout is finalized. Commented Jun 10, 2019 at 14:59
• Without correct CF you can choose correct opamp since you do not know the require gain bandwidth of opamp. Without correct CF the Vout will not be stable. Commented Jun 10, 2019 at 15:03
• Can you draw the OpAmp open loop gain curve, and insert the Cdiode (or the source capacitance) with a feedback resistor, to show the extra phaseshift that causes peaking or oscillation? Commented Jun 10, 2019 at 15:16

The first thing to do is choose the bandwidth of the system, how fast of risetime/bandwidth do you need to be able to detect. Then select an opamp and capacitor.

The capacitor pole formed by the RC times constant cannot be higher frequency than the bandwidth of the op amp. That is what TI is telling you.

Maxim is telling you to pick an RC time constant that is lower than the GBWP.

Realize that parasitic inductance and capacitance of the board or wires or whatever you are building this circuit with will change this pole. So try and keep the traces short as possible, or calculate what the parasitics will do to the circuit.

• In a circuit that I am designing, I am connecting a sensor which generates a constant current base on the oxygen level, what should assume for frequency . but unfortunately, the manufacturer does not provide the Junction capacitance of the sensor. Commented Jun 10, 2019 at 15:53
• What is the bandwidth requirement of the system? How fast do you need to read the oxygen sensor? Commented Jun 10, 2019 at 15:55
• Not very fast maybe 1-10Khz. I tried to calculate the Cf base on 1.5Khz (RF= 10M) which is around 15pF, but this makes the Vout very noisy (ringing) until I change the capacitor to 0.680uF Commented Jun 10, 2019 at 16:01
• How do you have this circuit implemented? is it on a breadboard, PCB? Commented Jun 10, 2019 at 16:13
• Is on PCB I will attach a drawing to the question U7 is opamp, C17 is Feedback Capacitor, U4 is multiplexer which chooses gain Resistor and U12 is virtual Ground Commented Jun 10, 2019 at 16:30

Both are correct.

The 1st is an example with equality (=) that includes Ci, (the junction capacitance of the photodiode in parallel with the input capacitance of the op-amp).

This is wise, with conservative 60% GBW for choosing $$\f_p\$$

The 2nd shows Cf "<< an upper limit" for reference (<< bigger limit than above.)

You need to update your question with datasheets, schematic and measurements.

This is how Honeywell does it.