How is the gain of an op-amp related to bandwidth as input frequency increases?

The gain of an operational amplifier (op-amp) is typically related to bandwidth according to the principle of gain-bandwidth product. As the frequency of the input signal increases, the gain of the op-amp decreases. This relationship is crucial in determining the performance of the op-amp in various applications.

When the frequency increases, the op-amp’s internal compensation and circuit limitations become more significant, causing the gain to roll off. This roll-off leads to a decrease in gain at higher frequencies. Hence, as gain increases, the bandwidth — the range of frequencies over which the op-amp can operate effectively — decreases, demonstrating an inverse relationship.

The gain-bandwidth product is a constant for a given op-amp, meaning that if you increase gain, the bandwidth decreases proportionately. Thus, the understanding that gain and bandwidth are inversely related is fundamental in designing and analyzing circuits involving op-amps. This is why the correct answer emphasizes that this relationship is always inversely related.