Small-Signal Modeling and Amplification

calendar_today October 16, 2025 article 314 words access_time 2 min replay Modified November 2, 2025

Table of Contents

Amplifier Introduction

Amplifiers use electronic devices that are in the active region
- BJTs can be amplifiers when biased in forward-active
- FET can be amplifiers if in the pinch-off/saturation region
- We refer to these regions as active regions, as the transistors can be used as linear amplification devices
In these regions, transistors provide high voltage/current/power gains
- We will be asked to determine the voltage gain and input/output resistance, which will help calculate the lower/upper cutoff frequencies of amplifiers
Bias is needed to stabilize the Q-point in the desired operation region
The Q-Point tells us some important characteristics about the amplifier:
- Small-signal parameters
- Voltage gain, input/output resistance
- Max input/output signal amplifiers
- Power consumption

If a solid-state device or transistor is operating at the Q-Point, then it acts as a linear circuit element for “small AC signals” near that Q-Point
- Small-signal condition for Diode/BJT: $v_d \le 5$ mV
- Small-signal condition for MOSFET: $v_{gs} \le 0.2 V_{OD}$
In this case, a diode can be modeled as a resistor with $R_D =\frac{1}{g_{d}}$, where $g_d$ is the diode conductance
- Near the origin, $g_d =\frac{I_{S}}{V_{T}},$ so $R_D =\frac{V_{T}}{I_{S}}$

Extrapolated intercept of the near-linear part of the output characteristic extended back to the voltage axis
- Magnitude is $V_A$
Physical interpretation: the variation of effective channel/base width with drain or collector voltage causes output current to rise with output voltage even at fixed inputs
Provides finite output resistance in small-signal analysis

The small-signal parameters, which are determined by the Q-Point are:
- Transconductance: $g_m = 40i_C$
- Input resistance: $r_{\pi} = \frac{\beta_{o}}{g_m}$
- Output resistance: $r_{o} = \frac{V_{A} + V_{CE}}{i_C}$

Small-signal parameters:
- Transconductance: $g_{m} = \frac{2 I_{D}}{V_{OD}}$
- Output resistance: $r_{o} = \frac{1 + \lambda V_{DS}}{\lambda I_{D}}$

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