Examples
If the GBWP of an operational amplifier is 1 MHz, it means that the gain of the device falls to unity at 1 MHz. Hence, when the device is wired for unity gain, it will work up to 1 MHz (GBWP = gain × bandwidth, therefore if BW = 1 MHz, then gain = 1) without excessively distorting the signal. The same device when wired for a gain of 10 will work only up to 100 kHz, in accordance with the GBW product formula. Further, if the maximum frequency of operation is 1 Hz, then the maximum gain that can be extracted from the device is 1×106.
We can also analytically show that for frequencies [clarification needed] GBWP is constant.
Let be a first-order transfer function given by:
We will show that:
Proof: We will expand using Taylor series and retain the constant and first term, to obtain:
Example for
Note that the error in this case is only about 2%, for the constant term, and using the second term, , the error drops to .06%.