Calculate the output impedance of the two-transistor...

Calculate the output impedance of the two-transistor diode-connected circuit shown in Fig. P6.18 using smallsignal analysis. Assume both transistors are in the active region, ignore the body effect, and assume $g_{m 1}=g_{m 2}$, $r_{d s 1}=r_{d s 2}$, and $g_{m} r_{d s}>>1$.

Key Concepts

Small-Signal Analysis

Small-signal analysis is a technique used to linearize nonlinear components around their bias point, enabling the study of circuit behavior for small perturbations. This method replaces the nonlinear devices (such as transistors) with linearized models, allowing the calculation of parameters like gain, impedance, and frequency response, which is essential for understanding and designing analog circuits.

Diode-Connected Transistor

A diode-connected transistor is a configuration where the transistor’s gate and drain are shorted together, effectively forcing it to operate in a diode-like manner. This configuration is commonly used to create biasing networks or load elements, and its small-signal model shows reduced output impedance characteristics that are beneficial in feedback and current mirror circuits.

Transistor Output Impedance

The output impedance of a transistor circuit is the effective resistance seen looking into the drain (or collector) terminal when the input is fixed. In small-signal analysis, this impedance is influenced by parameters like the drain-source resistance (r_ds) and the transconductance (gm). Understanding this impedance is vital for predicting how the circuit drives loads and interacts with subsequent stages.

Transconductance and Channel-Length Modulation

Transconductance (gm) is a measure of the control the gate voltage has over the drain current in a transistor, while channel-length modulation (represented by r_ds) accounts for the finite output resistance in the active region due to changes in the effective channel length. In circuits where the product gm·r_ds is much greater than one, these parameters simplify the analysis, as they indicate high intrinsic gain and dominant small-signal behavior.

Please give Ace some feedback