The ac equivalent circuit for an amplifier is shown. Assume the capacitors have infinite value, RI = 100 kΩ, RG = 10 MΩ, RD = 560 kΩ, and R3 = 1.5 MΩ. Calculate the voltage gain for the amplifier if the MOSFETQ-point is (10 μA, 5 V). Assume Kn = 100 μA/V2 and λ = 0.02 V−1. RIRpRGThéveninequivalentFigure P13.101+ I

Answered: RI Rp RG Thévenin equivalent Figure…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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Question

The ac equivalent circuit for an amplifier is shown. Assume the capacitors have infinite value, R_I = 100 kΩ, R_G = 10 MΩ, R_D = 560 kΩ, and R₃ = 1.5 MΩ. Calculate the voltage gain for the amplifier if the MOSFET
Q-point is (10 μA, 5 V). Assume K_n = 100 μA/V² and λ = 0.02 V⁻¹.

RI
Rp
RG
Thévenin
equivalent
Figure P13.101
+ I

Expert Solution

Step 1

Given

$\begin{array}{rcl} R_{I} & = & 100 kΩ \\ R_{G} & = & 10 MΩ \\ R_{D} & = & 560 kΩ \\ R_{3} & = & 1.5 MΩ \\ K_{n} & = & 100 {μA/V}^{2} \\ λ & = & 0.02 V^{- 1} \\ I_{D S} & = & 10 μA \\ V_{D S} & = & 5 V \end{array}$

The expression for the transconductance is,

$\begin{array}{rcl} g_{m} & = & \sqrt{2 K_{n} I_{D S} (1 + λ V_{D S})} \\ = & \sqrt{2 (100 \times 10^{- 6}) (10 \times 10^{- 6}) (1 + 0.02 \times 5)} \\ = & \sqrt{2200} \\ = & 46.90 μs \end{array}$

Step 2

The output resistance is given by

$\begin{array}{rcl} r_{o} & = & \frac{(\frac{1}{λ} + V_{D S})}{I_{D S}} \\ = & \frac{\frac{1}{0.02} + 5}{10 \times 10^{- 6}} \\ = & \frac{55}{10 \times 10^{- 6}} \\ = & 5500 \times 10^{3} \\ = & 5500 kΩ \end{array}$

The output resistance is 5500 k-ohm.

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