# How to calculate maximum gain that can be achieved by an op amp?

I am designing a differential amplifier for a Wheatstone bridge which have small voltage variations like 0uV to 20uV. so need to design an instrumentation amplifier. I do not know how to find the maximum gain that can be get from an opamp (I know how to calculate overall gain from resister values used). data acquisition frequency is not a huge matter in my application. 5Hz or 5 samples per second reading would be enough via an microelectronic.

UA741 how to find maximum gain that can be archive from this opamp(frequency at 5Hz)?

• If you are dealing with voltages in the µV region, you do not want to use an opamp as old as the 741. Its offset voltage and drift would simply swamp out your signal. With voltages this low, you want to use a chopper or auto-zero opamp. Nov 2, 2017 at 14:09

## 2 Answers

Maximum gain is limited to the open loop gain of the op-amp but, for a linear amplifier you should not try and implement a gain value that gets too close to this value because distortion will be an issue and you will also find that the frequency response may be much less than you require. DC accuracy is also made worse with a larger gain so this should also be considered.

Here is the typical open loop gain of an op-amp: -

At a frequency that is somewhat less than 10 Hz the gain is flat down to DC and very high (10$^5$ = 100,000). At about 7 Hz (in the example above) the gain begins to fall at 6 dB per octave and unity gain is seen around 1 MHz.

So if you want a closed-loop gain of (say) 1000, your frequency response will be limited to about 1 kHz and, as your input frequency rises from about 100 Hz, you will notice the output signal gets more distorted because there is less open-loop gain headroom to perform the corrective action that negative feedback brings to the party. Above 1 kHz, the gain will follow the open-loop response.

• @oppo You can however split up the amplification in stages, say you want an amplification of 100. Then you can cascade two op-amps amplifying 10x. You will gain some bandwidth (wanted) at the cost of some delay / phase shift (unwanted). Nov 2, 2017 at 13:24
• @Harry Svensson thank you, and i do not need higher frequency, i will do samlinng on my adc at 10Hz max, so using a single stage i can get more than 10000 gain (according to above figure) right ?
– oppo
Nov 2, 2017 at 13:44
• Theoretically, yes! However, any symmetry error (offset voltage) will cause severe errors resp. can drive the output into saturation. Example: Many opamps have an offset voltage in the order of 1mV - this will cause an output DC error voltage of 10 volts (gain of 1E4)
– LvW
Nov 2, 2017 at 13:47
• @LvW I don't think "two" counts as "many". But good point nonetheless. Nov 2, 2017 at 13:53
• @Andy aka you mentioned keeping the closed-loop gain about 10dB below the open loop gain to achieve good linearity. Does this approach generally work well? Apr 30, 2020 at 21:34

The maximum gain is the open loop gain. It depends on the opamp model, and can go anywhere from 60 dB to 120 dB voltage gain. The open-loop bandwidth is however very small. Another issue is that this gain is very variable between different parts of the same product number due to variations. It is also very sensitive to supply voltage and temperature. In addition, the error you might find using closed-loop gains will become larger as you come closer to this open-loop gain. Idealy, you would want to use multiple stages to get your gain. In addition, larger gain will result in larger impact of the offset voltage. This can be an issue if the DC value is important.

Keep in mind that opamps are desiged to be used closed-loop, and rely on the loop to get good bandwidth and distortion performance. In open loop, their performance will be significantly worse.

• for the UA741 how to find single stage maximum gain ?
– oppo
Nov 2, 2017 at 13:00
• If the manufacturer provides it it will be in the datasheet. Nov 2, 2017 at 13:00
• I saw in data sheet Typical open loop gain is 106 dB while driving a 2000-Ω load. Short circuit tolerance so this is the max 3.9*10^10 gain?
– oppo
Nov 2, 2017 at 13:04
• No, opamps tend to be specified in voltage gain, which is about 2 * 10^5.
– user16324
Nov 2, 2017 at 13:12