Figure P 7.12 shows an IC MOS amplifier formed by cascading...

Figure $\mathrm{P} 7.12$ shows an IC MOS amplifier formed by cascading two common-source stages. Assuming that $V_{A n}=\left|V_{A p}\right|$ and that the biasing current sources have output resistances equal to those of $Q_{1}$ and $Q_{2},$ find an expression for the overall voltage gain in terms of $g_{m}$ and $r_{o}$ of $Q_{1}$ and $Q_{2}$

Key Concepts

Voltage Gain Calculation in MOS Amplifiers

The voltage gain in MOS amplifiers, particularly in common?source stages, is typically expressed in terms of the transistor's transconductance (g?) and its output resistance (r?) as approximately –g?r? for a single stage. When amplifiers are cascaded, the overall voltage gain is derived from the multiplication of the individual stage gains, taking into account the interaction between stages, which can include loading effects and biasing considerations.

Cascading Amplifier Stages

Cascading multiple amplifier stages involves connecting the output of one amplifier to the input of another, so that the overall voltage gain is the product of the individual stage gains. This technique is used to achieve higher overall gain and can also affect the bandwidth and stability of the amplifier system if loading effects between stages are significant.

Common?Source Amplifier

A common?source amplifier is a basic MOSFET amplifier configuration where the source terminal is common to both the input and the output. This configuration provides significant voltage gain and inverts the input signal. Its performance is largely dictated by the transistor's transconductance and output resistance, making it a fundamental building block in analog circuit design.

Small?Signal Parameters (g? and r?)

The small?signal transconductance (g?) reflects how effectively a MOS transistor converts a gate voltage change into a change in drain current, while the output resistance (r?) models the effect of channel-length modulation on the drain current, representing the intrinsic impedance looking into the drain. Both parameters are critical in determining the gain and overall performance of MOS amplifiers.

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