4.2.2 The Bandwidth of Analog Systems

To calculate the delay of an inverter accurately one must view it as an analog circuit. Delays can be used also as a figure of merit for analog systems. However, in several types of analog circuits the phase error introduced by delays is not critical and the bandwidth or the gain-bandwidth product (GBW) are the mostly used performance parameters.

The bandwidth of an analog system is the range of frequencies where the system operates within a specified fraction of the nominal gain (typically $\pm$3dB). For operational amplifiers it is common practice to characterize their AC performance specifying the frequency where the open-loop voltage gain is unitary.

Figure 4.4: Basic single-stage amplifier model.

Using the operational amplifier as an example, the bandwidth and and gain-bandwidth product depend on the gain of the amplifying devices and the complex impedance of the higher-impedance nodes. This, in turn, is a function of technology parameters, biasing conditions and the total node capacitance. For a single stage amplifier, whose model is presented in Figure 4.4, the gain-bandwidth product is (for both weak and strong inversion) equal to

$$GBW = f_{strong}() \cdot \frac{\sqrt{I_{bias}}}{C_{eq}}~~~~~(strong~inversion)$$

$$GBW = ~~~f_{weak}() \cdot \frac{I_{bias}}{C_{eq}}~~~~~(weak~inversion)$$ (4.10)

where $C_{eq}$ is the total capacitance at output node (including parasitics), $I_{bias}$ is the biasing current and $f_{strong}()$ and $k_{weak}()$ are functions of technology parameters.