Answered: Recognizing that the de drain current…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

(a) The signal voltage applied across the gatesource terminals of an MOS transistor is given by υ_gs = V_M sin 5000πt, and V_GS − V_{T N} = 0.75 V.
Calculate the total harmonic distortion in the drain current of the MOSFET based upon Eq. 13.70 if V_M = 150 mV. (b) repeat for V_M = 300 mV.
(c) Repeat for V_M = 75 mV.

Recognizing that the de drain current is equal to Ip = (K„/2)(VGs – VrN)² and subtracting this
term from both sides of Eq. (13.69) yields an expression for signal current ig:
Km
(2ver (VGs – VrN)+ v²]
ia =
(13.70)
%3|

Expert Solution

Step 1

(a) Given

$v_{g s} = V_{M} \sin 5000 π t V_{G S} - V_{T N} = 0.75 V V_{M} = 150 mV$

The expression for drain current is given by

$\begin{array}{rcl} i_{d} & = & \frac{K_{n}}{2} [2 (V_{G S} - V_{T N}) v_{g s} + {(v_{g s})}^{2}] \\ = & \frac{K_{n}}{2} [2 (0.75) v_{g s} + {(v_{g s})}^{2}] \\ = & \frac{K_{n}}{2} [1.5 (V_{M} \sin 5000 π t) + {(V_{M} \sin 5000 π t)}^{2}] \\ = & \frac{K_{n}}{2} [1.5 V_{M} \sin 5000 π t + V_{M}^{2} (\frac{1 - \cos 2 (5000 π t)}{2})] \{\sin^{2} x = \frac{1 - \cos 2 x}{2} \\ = & \frac{K_{n}}{2} [1.5 V_{M} \sin 5000 π t + 0.5 V_{M}^{2} (1 - \cos 10000 π t)] \end{array}$

Step 2

The expression for total harmonic distortion is given by

$\begin{array}{rcl} T H D & = & \frac{0.5 V_{M}^{2}}{1.5 V_{M}} \\ T H D & = & \frac{V_{M}}{3} \\ % T H D & = & \frac{V_{M}}{3} \times 100 \end{array}$

Put $V_{M} = 150 mV$ in the above equation

$\begin{array}{rcl} % T H D & = & \frac{150 \times 10^{- 3}}{3} \times 100 \\ = & 0.05 \times 100 \\ = & 5 % \end{array}$

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