Electrical – Negative Voltage Reference For Instrumentation Amplifer

The offset voltage of each of the op-amps you're using can be as much as +/-3mV at room temperature. So, the difference between two outputs could be as much as 6mV different from the inputs with unity gain. You're seeing 5.4mV which is large, but within specifications and therefore plausible.

Since you don't have much gain in the first stage (only 3) you also have to consider the offset voltage in the second stage. In any case, 638 times your measured differential input offset voltage of 5.4mV + 2.5mV signal is almost 5V.

You can either use better op-amps (such as autozero or 'zero drift' types) or null out the offset voltage by some means (trimpot or reduce the gain and do it digitally). You should also consider the drift of the op-amps you're using which is not guaranteed, but is fairly reasonable typically (+/-1.7uV/K).

You have 3V applied to the inverting input and 2.5V applied to the non-inverting input. Thus, your output should be -1V with a gain of 2 (assuming reference grounded). It should work properly if the amplifier has a reasonable negative supply (say -5V). However, you show no negative supply, so the amplifier cannot work- the best it can do is get within some tens of mV of the negative supply, as shown in the datasheet.

If you connect the reference to a stiff voltage of 2.5V then it should output 2.5V minus 1.0V or 1.5V with the bridge connected. However you'll need something like a voltage divider plus an op-amp buffer to get the stiff 2.5V supply, a simple voltage divider will not cut it.

It's really not clear what you are trying to achieve with this. In the particular case here you can simply ground the reference input, swap the inverting and non-inverting inputs and get 1V output, however if you need to handle the bridge being unbalanced in either direction you'll need to bias the output by setting Vref to something other than 0V.